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BEGIN:VEVENT
SUMMARY:Konrad Aguilar (University of Southern Denmark)
DTSTART:20200422T190000Z
DTEND:20200422T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/1
DESCRIPTION:Title:
Quantum metrics on the tensor product of a commutative C*-algebra and an A
F C*-algebra.\nby Konrad Aguilar (University of Southern Denmark) as p
art of Noncommutative geometry in NYC\n\n\nAbstract\nGiven a compact metri
c space X and a unital AF algebra A equipped with a faithful tracial state
\, we place quantum\nmetrics on the tensor product of C(X) and A given est
ablished quantum metrics on C(X) and A from work with Bice\nand Latremolie
re. We prove the inductive limit of C(X) tensor A given by A is a metric l
imit in the Gromov-Hausdorff\npropinquity. We show that our quantum metric
is compatible with the tensor product by producing a Leibniz rule on\nele
mentary tensors and showing the diameter of our quantum metric on the tens
or product is bounded above the diameter\nof the Cartesian product of the
quantum metric spaces. We provide continuous families of C(X) tensor A whi
ch extends\nour previous results with Latremoliere on UHF algebras.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Ciccoli (Università di Perugia)
DTSTART:20200506T190000Z
DTEND:20200506T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/2
DESCRIPTION:Title:
Orbit correspondence and groupoid C*-algebras\nby Nicola Ciccoli (Univ
ersità di Perugia) as part of Noncommutative geometry in NYC\n\n\nAbstrac
t\nIn those NC C*-algebras arising as quantization of a Poisson manifold o
ne can try to establish a relation between the symplectic foliation of the
manifold and the unitary dual of its quantization. This relation is what
goes under the name of orbit correspondence. In the best behaved cases thi
s correspondence is an homeomorphism. We will review some results on speci
fic examples\, stressing the use of "groupoid quantization" as a tool to
better understand features of this correspondence.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Tao 🇳🇴 (Norwegian University of Science and Technology)
DTSTART:20200429T190000Z
DTEND:20200429T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/3
DESCRIPTION:Title:
A twisted local index formula for curved noncommutative two tori\nby J
im Tao 🇳🇴 (Norwegian University of Science and Technology) as part o
f Noncommutative geometry in NYC\n\n\nAbstract\nWe consider the Dirac oper
ator of a general metric in the \ncanonical conformal class on the noncomm
utative two torus\, \ntwisted by an idempotent (representing the $K$-theor
y class \nof a general noncommutative vector bundle)\, and derive a local
\nformula for the Fredholm index of the twisted Dirac operator. Our \nappr
oach is based on the McKean-Singer index formula\, and \nexplicit heat exp
ansion calculations by making use of Connes' \npseudodifferential calculus
. As a technical tool\, a new rearrangement \nlemma is proved to handle ch
allenges posed by the noncommutativity of \nthe algebra and the presence o
f an idempotent in the calculations in addition \nto a conformal factor. T
his is joint work with Farzad Fathizadeh and Franz Luef.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Branimir Cacic (University of New Brunswick)
DTSTART:20200513T190000Z
DTEND:20200513T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/4
DESCRIPTION:Title:
Gauge theory on quantum principal bundles\nby Branimir Cacic (Universi
ty of New Brunswick) as part of Noncommutative geometry in NYC\n\n\nAbstra
ct\nIn this talk\, I’ll give a brief (and somewhat idiosyncratic) introd
uction to gauge theory on quantum principal bundles. I’ll give a quick o
verview of the classical setting and sketch its noncommutative generalisat
ion à la Brzeziński–Majid\, Hajac\, et al. Then I’ll revisit the not
ions of principal connection and gauge transformation from the perspective
of recent work by Ć.–Mesland. I'll illustrate these concepts using the
irrational rotation algebra as a quantum principal U(1)-bundle over the c
ircle.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200603T190000Z
DTEND:20200603T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/5
DESCRIPTION:Title:
Index theorems in KK-theory\nby Emil V Prodan (Yeshiva University) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nConsider an extended
(Delone) point pattern in the d-dimensional Euclidean space such that eac
h point hosts N degrees of freedom. In many practical applications\, rangi
ng from quantum materials to meta-materials\, one is interested in the col
lective dynamics of the degrees of freedom hosted by the pattern. As we sh
all see\, the generators of any pattern-equivariant dynamics belong to a s
pecific C*-algebra\, which in general takes the form of a groupoid algebra
and\, in more manageable cases\, of crossed products with discrete groups
. The non-commutative geometry program for the aperiodic patterns consists
in computing the C*-algebra\, its K-theory and cyclic co-homology\, as we
ll as establishing index theorems for the K-theory and cyclic co-homology
pairings. In these seminars I will describe several interesting cases wher
e this program has been carried almost entirely. I have a large number of
numerical simulations\, which I will try to use throughout to exemplify th
e power of these methods.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200520T190000Z
DTEND:20200520T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/6
DESCRIPTION:Title:
The C*-algebra of equivariant Hamiltonians over point patterns\nby Emi
l V Prodan (Yeshiva University) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nConsider an extended (Delone) point pattern in the d-dimens
ional Euclidean space such that each point hosts N degrees of freedom. In
many practical applications\, ranging from quantum materials to meta-mater
ials\, one is interested in the collective dynamics of the degrees of free
dom hosted by the pattern. As we shall see\, the generators of any pattern
-equivariant dynamics belong to a specific C*-algebra\, which in general t
akes the form of a groupoid algebra and\, in more manageable cases\, of cr
ossed products with discrete groups. The non-commutative geometry program
for the aperiodic patterns consists in computing the C*-algebra\, its K-th
eory and cyclic co-homology\, as well as establishing index theorems for t
he K-theory and cyclic co-homology pairings. In these seminars I will desc
ribe several interesting cases where this program has been carried almost
entirely. I have a large number of numerical simulations\, which I will tr
y to use throughout to exemplify the power of these methods.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200527T190000Z
DTEND:20200527T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/7
DESCRIPTION:Title:
Cyclic co-homology\, Fredholm modules\, Kasparov’s generalizations\n
by Emil V Prodan (Yeshiva University) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nConsider an extended (Delone) point pattern in the d-
dimensional Euclidean space such that each point hosts N degrees of freedo
m. In many practical applications\, ranging from quantum materials to meta
-materials\, one is interested in the collective dynamics of the degrees o
f freedom hosted by the pattern. As we shall see\, the generators of any p
attern-equivariant dynamics belong to a specific C*-algebra\, which in gen
eral takes the form of a groupoid algebra and\, in more manageable cases\,
of crossed products with discrete groups. The non-commutative geometry pr
ogram for the aperiodic patterns consists in computing the C*-algebra\, it
s K-theory and cyclic co-homology\, as well as establishing index theorems
for the K-theory and cyclic co-homology pairings. In these seminars I wil
l describe several interesting cases where this program has been carried a
lmost entirely. I have a large number of numerical simulations\, which I w
ill try to use throughout to exemplify the power of these methods.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Menevse Eryuzlu (Arizona State University)
DTSTART:20200610T190000Z
DTEND:20200610T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/8
DESCRIPTION:Title:
Enchilada Categories\nby Menevse Eryuzlu (Arizona State University) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nMuhly and Solel dev
eloped a notion of Morita equivalence for C*-correspondences\, and they \n
proved a very important result: If two injective C*-correspondences are M
orita equivalent then the corresponding Cuntz-Pimsner algebras are Morita
equivalent in the sense of Rieffel. \nInstead of proving it directly\, we
build a functor that will give us the result of Muhly and Solel\, \nin fac
t a more generalized version of their result\, as a special case.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Azzali (Universität Hamburg)
DTSTART:20200617T190000Z
DTEND:20200617T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/9
DESCRIPTION:Title:
KK-theory with real coefficients\, traces\, and discrete group actions
\nby Sara Azzali (Universität Hamburg) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nThe groups of KK-theory were introduced by Kasparov
in the 1980’s and have important applications to many geometric and top
ological problems which are tackled by C*-algebraic techniques. \n\nIn thi
s talk\, we investigate KK-theory groups with coefficients in $\\mathbb R$
. By construction\, the adding of real coefficients provides natural recep
tacles for classes coming from traces on $C^*$-algebras. \nWe focus on app
lications to the study of discrete groups actions on $C^*$-algebras. \nWe
show that in equivariant KK-theory with coefficients one can "localize at
the unit element“ of the discrete group\, and this procedure has interes
ting consequences on the Baum–Connes isomorphism conjecture.\nBased on j
oint works with Paolo Antonini and Georges Skandalis.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianchao Wu (Texas A & M)
DTSTART:20200624T190000Z
DTEND:20200624T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/10
DESCRIPTION:Title: The Novikov conjecture\, groups of diffeomorphisms\, and infinite dimensi
onal nonpositively curved spaces\nby Jianchao Wu (Texas A & M) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nThe rational strong Novi
kov conjecture is a prominent problem in noncommutative geometry. It impli
es deep conjectures in topology and differential geometry such as the (cla
ssical) Novikov conjecture on higher signatures and the Gromov-Lawson conj
ecture on positive scalar curvature. Using C*-algebraic and K-theoretic to
ols\, we prove that the rational strong Novikov conjecture holds for geome
trically discrete subgroups of the group of volume preserving diffeomorphi
sms of any closed smooth manifold. The crucial geometric property of these
groups that we exploit is the fact that they admit isometric and proper a
ctions on a type of infinite-dimensional symmetric space of nonpositive cu
rvature called the space of $L^2$-Riemannian metrics. In fact\, our result
holds for any discrete group admitting an isometric and proper action on
a (possibly infinite-dimensional) nonpositively curved space that we call
an admissible Hilbert-Hadamard space\; thus our result partially extends e
arlier ones of Kasparov and Higson-Kasparov. This is joint work with Sherr
y Gong and Guoliang Yu.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bruce (Queen Mary University of London)
DTSTART:20200708T190000Z
DTEND:20200708T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/11
DESCRIPTION:Title: C*-algebras from actions of congruence monoids\nby Chris Bruce (Queen
Mary University of London) as part of Noncommutative geometry in NYC\n\n\
nAbstract\nI will give an overview of recent results for semigroup C*-alge
bras associated with number fields. These results are already interesting
in the case where the field is the rational numbers\, and I will focus mos
tly on this case to make everything more explicit and accessible.\nC*-alge
bras of full ax+b-semigroups over rings of algebraic integers were first s
tudied by Cuntz\, Deninger\, and Laca\; their construction has since been
generalized by considering actions of congruence monoids. Semigroup C*-alg
ebras obtained this way provide an example class of unital\, separable\, n
uclear\, strongly purely infinite C*-algebras which\, in many cases\, comp
letely characterize the initial number-theoretic data. They also carry can
onical time evolutions\, and the associated C*-dynamical systems exhibit i
ntriguing phenomena. For instance\, the striking similarity between the K-
theory formula and the parameterization space for the low temperature KMS
states\, observed by Cuntz in the case of the full ax+b-semigroup\, persis
ts in the more general setting.\nPart of this work is joint with Xin Li\,
and part is joint with Marcelo Laca and Takuya Takeishi.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Ponge (Sichuan University)
DTSTART:20200715T190000Z
DTEND:20200715T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/12
DESCRIPTION:Title: Analysis on curved noncommutative tori\nby Raphael Ponge (Sichuan Uni
versity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nNoncommu
tative tori are important examples of noncommutative spaces. Following sem
inal work by Connes-Tretkoff\, Connes-Moscovici\, Fathizadeh-Khalkhali\, a
nd others a differential geometric apparatus on NC tori is currently being
built. So far the main focus has been mostly on conformal deformation of
the (flat) Euclidean metric or product of such metrics. \n\nThis talk will
report on ongoing work to deal with general Riemannian metrics on NC tori
(in the sense of Jonathan Rosenberg). Results include local and microloca
l Weyl laws\, Gauss-Bonnet theorems metrics\, and local index formulas.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tushar Das (University of Wisconsin - La Crosse)
DTSTART:20200805T190000Z
DTEND:20200805T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/13
DESCRIPTION:Title: The Varieties of Discrete Experience\, and Other Tales of Isometric Actio
ns on Gromov Hyperbolic Metric Spaces\nby Tushar Das (University of Wi
sconsin - La Crosse) as part of Noncommutative geometry in NYC\n\n\nAbstra
ct\nWe survey joint work with David Simmons and Mariusz Urbanski that expl
ores extensions of the classical theory of Kleinian groups acting on a fin
ite-dimensional hyperbolic space to analogous actions on hyperbolic metric
spaces in the sense of Gromov\, a broad class of spaces which includes in
finite-dimensional rank one symmetric spaces of noncompact type and much m
ore!\n\nSeveral phenomena induced by greater degrees of freedom than in fi
nite dimensions (e.g. the different shades of discreteness alluded to in t
he title) introduce new delicacies and thereby uncover fresh seams that aw
ait investigation. The talk is aimed at students and beginners who are une
ncumbered by the wisdom of experts and others tragically burdened by knowi
ng too much. Being a novice\, any help from the audience in generating new
questions will be graciously accepted.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Duwenig (University of Wollongong)
DTSTART:20200701T190000Z
DTEND:20200701T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/14
DESCRIPTION:Title: Non-commutative Poincaré Duality of the irrational rotation algebra\
nby Anna Duwenig (University of Wollongong) as part of Noncommutative geom
etry in NYC\n\n\nAbstract\nThe irrational rotation algebra is known to be
self-dual in a KK-theoretic sense. The required K-homology fundamental cla
ss was constructed by Connes out of the Dolbeault operator on the 2-torus\
, but there has not been an explicit description of the dual element. In t
his talk\, I will geometrically construct that K-theory class by using a p
air of transverse Kronecker flows on the 2-torus. This is based on joint w
ork with my PhD advisor\, Heath Emerson.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haluk Sengun (University of Sheffield)
DTSTART:20200722T190000Z
DTEND:20200722T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/15
DESCRIPTION:Title: Selberg's Trace Formula in operator K-theory\nby Haluk Sengun (Univer
sity of Sheffield) as part of Noncommutative geometry in NYC\n\n\nAbstract
\nSelberg introduced his celebrated trace formula in 1956. Since\nthen\, t
he trace formula has become an indispensable tool in number\ntheory\, with
spectacular applications to the Langlands program. After an\nexposition o
f the trace formula\, I will present an identity in the\nsetting of K-theo
ry of group C*-algebras that is an analogue of the\ntrace formula. Time re
maining\, I will exhibit how one can derive the\nindex theoretic version o
f the trace formula (due to Barbasch and\nMoscovici) from our identity via
the theory of higher indices.\n\nThis is joint work with Bram Mesland (Le
iden) and Hang Wang (Shanghai).\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerry Kaminker (UC Davis)
DTSTART:20200729T190000Z
DTEND:20200729T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/16
DESCRIPTION:Title: Odd analytic differential K-homology\nby Jerry Kaminker (UC Davis) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nDifferential K-theo
ry can be viewed as K-theory for vector bundles with connection. We are\nd
eveloping a dual version in the the Brown-Douglas-Fillmore setting of K-ho
mology. The\nrole of a connection is played by a projection. Our goal is t
o obtain secondary invariants for\npairs of projections that yield equival
ent Toeplitz extensions. The talk will include a general discussion of dif
ferential K-theory. This is joint work with Xiang Tang.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Quigg (Arizona State University)
DTSTART:20200819T190000Z
DTEND:20200819T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/17
DESCRIPTION:Title: Baum-Connes\, coactions\, and the Tilde Problem\nby John Quigg (Arizo
na State University) as part of Noncommutative geometry in NYC\n\n\nAbstra
ct\nTrouble with the Baum-Connes Conjecture (with coefficients) can in som
e way be blamed upon the existence of groups for which the reduced-crossed
-product functor is not exact. The full crossed product is exact but doesn
't fix the conjecture. Efforts to fix the conjecture have focused upon the
``minimal exact crossed product''\, whose existence is known through abst
ract nonsense\, but a construction remains elusive. Baum\, Guentner\, and
Willett propose a candidate formed in part by tensoring with a fixed actio
n. Our contribution to the [BGW] ``exotic crossed product'' program involv
es composing the full crossed product with coaction functors\, hoping that
the shift to coactions will add new insights. In particular\, we replace
the [BGW] candidate by tensoring with a fixed coaction. For a long time we
had a hard time proving that our functor is exact. The ``natural'' approa
ch involves embedding into ``tilde multiplier algebras'' (which I'll defin
e in the talk). But we can't see how to prove that this gives an exact fun
ctor\, and we call this the Tilde Problem. To get around this\, we initial
ly proved exactness of our coaction functor another --- extremely unsatisf
ying --- way: a long odyssey through equivariant C*-correspondences\, ``na
tural'' Morita equivalence\, crossed-product duality\, and --- the final h
umiliation --- appealing to exactness of the [BGW] crossed-product functor
itself\, completely thwarting our goal of doing everything within the rea
lm of coactions. Fortunately\, we recently saw how to use our incomplete k
nowledge of the tilde functor to prove exactness of our coaction functor.\
nThis is joint work with Steve Kaliszewski and Magnus Landstad.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Deeley (University of Colorado\, Boulder)
DTSTART:20200812T190000Z
DTEND:20200812T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/18
DESCRIPTION:Title: Minimal dynamical systems with prescribed K-theory\nby Robin Deeley (
University of Colorado\, Boulder) as part of Noncommutative geometry in NY
C\n\n\nAbstract\nI will speak about joint work in progress with Ian Putnam
and Karen Strung. The goal of the project is to study the existence of mi
nimal homeomorphisms on compact metric spaces. In particular\, I will disc
uss partial results related to the following question: What is the range o
f the K-theory (or more generally the Elliott invariant) for minimal cross
ed products? Our approach to this question is based on the systematic cons
truction of minimal homeomorphisms with prescribed K-theoretic properties.
\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Yu. Savin (Peoples' Friendship University\, Moscow)
DTSTART:20200826T190000Z
DTEND:20200826T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/19
DESCRIPTION:Title: A local index formula for metaplectic operators\nby Anton Yu. Savin (
Peoples' Friendship University\, Moscow) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nLet A be the algebra of unitary operators acting i
n $H=L_2(R^n)$ and generated by translations\, orthogonal transformations\
, products with exponentials $e^{ikx}$\nand fractional Fourier transforms.
Equivalently\, A is the algebra generated by quantizations of isometric a
ffine canonical transformations in $T^*R^n$. We show that the well-known i
ndex one operator in $R^n$ (which is obtained from the creation and annihi
lation operators\, see Higson-Kasparov-Trout 1998) denoted by D defines a
spectral triple (A\,H\,D) in the sense of Connes. Our main result is an ex
plicit formula for the Connes--Moscovici residue cocycle for this spectral
triple. For the subalgebra in A generated by translations and exponentia
ls\, this gives a local index formula for noncommutative tori. \nThis is j
oint work with Elmar Schrohe (Hannover)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Clare (William & Mary)
DTSTART:20201007T190000Z
DTEND:20201007T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/20
DESCRIPTION:Title: Essential representations of real reductive groups\nby Pierre Clare (
William & Mary) as part of Noncommutative geometry in NYC\n\n\nAbstract\nT
he tempered dual of a real reductive group G equipped with the Fell\ntopol
ogy identifies with the space of irreducible representations of the\nreduc
ed C*-algebra of G. The Connes-Kasparov isomorphism allows to\ncompute the
K-theory of this C*-algebra by using the index theory of\nDirac-type oper
ators on the symmetric space G/K. The goal of the work\npresented here (jo
int with N. Higson\, Y. Song and X. Tang) is to provide\na representation-
theoretic approach to this isomorphism. We will\ndescribe the structure of
the reduced C*-algebra up to Morita\nequivalence and characterize represe
ntations that contribute to the\nK-theory in terms of Dirac cohomology.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahya Ghandehari (University of Delaware)
DTSTART:20200916T190000Z
DTEND:20200916T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/21
DESCRIPTION:Title: Fourier algebras of the group of $\\mathbb{R}$-affine transformations and
a dual convolution\nby Mahya Ghandehari (University of Delaware) as p
art of Noncommutative geometry in NYC\n\n\nAbstract\nA major trend in Non-
commutative Harmonic Analysis is to investigate function spaces related to
Fourier analysis (and representation theory) of non-abelian groups.\n\nTh
e Fourier algebra\, which is associated with the left regular representati
on of the ambient group\, is an important example of such function spaces.
This function algebra encodes the properties of the group in various ways
\; for instance the existence of derivations on this algebra translates in
to information about the commutativity of the group itself. \n\n\n\nIn thi
s talk\, we investigate the Fourier algebra of the group of $\\mathbb{R}$-
affine transformations. In particular\, we discuss the non-commutative Fo
urier transform for this group\, and provide an explicit formula for the
convolution product on the ``dual side'' of this transform. As an applicat
ion of this new dual convolution product\, we show an easy dual formulatio
n for (the only known) symmetric derivative on the Fourier algebra of the
group. \n\n\n\nThis talk is mainly based on joint articles with Y. Choi.\
n
LOCATION:https://researchseminars.org/talk/NYC-NCG/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toke Meier Carlsen (University of the Faroe Islands)
DTSTART:20200902T190000Z
DTEND:20200902T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/22
DESCRIPTION:Title: Cuntz-Krieger algebras\, topological Markov shifts and groupoids\nby
Toke Meier Carlsen (University of the Faroe Islands) as part of Noncommuta
tive geometry in NYC\n\n\nAbstract\nIt is well-known that there is a stron
g connection between Cuntz-Krieger algebras and a certain type of shifts o
f finite type called topological Markov shifts. Recently\, it has been dis
covered that topological Markov shifts can be recovered up to different ki
nds of equivalence from the corresponding Cuntz-Krieger algebras.\n\nI wil
l give an overview of these results and explain how groupoids can be used
to prove and generalise them.\n\nThe talk will primarily be based on the f
ollowing papers.\n\nK. Matsumoto: "Orbit equivalence of topological Markov
shifts and Cuntz-Krieger algebras".\n\nK. Matsumoto: "Continuous orbit eq
uivalence\, flow equivalence of Markov shifts and circle actions on Cuntz
–Krieger algebras".\n\nK. Matsumoto and H. Matui: "Continuous orbit equi
valence of topological Markov shifts and Cuntz–Krieger algebras".\n\nT.
M. Carlsen\, S. Eilers\, E. Ortega\, and G. Restorff: "Flow equivalence an
d orbit equivalence for shifts of finite type and isomorphism of their gro
upoids".\n\nT. M. Carlsen and J. Rout: "Diagonal-preserving gauge-invarian
t isomorphisms of\ngraph C*-algebras".\n\nT. M. Carlsen\, E. Ruiz\, A. Sim
s\, and M. Tomforde: "Reconstruction of groupoids and C*-rigidity of dynam
ical systems".\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Glubokov (Ave Maria University\, Florida)
DTSTART:20200909T190000Z
DTEND:20200909T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/23
DESCRIPTION:Title: Cluster Algebras and their applications to Index Theorem\nby Andrey G
lubokov (Ave Maria University\, Florida) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nCluster Algebras were introduced in 2000 by Fomin
and Zelevinsky and since then their applications were developed in many ar
eas of mathematics and theoretical physics. We would like to introduce som
e of the Cluster Algebras and to explore the connections between them and
Jones Index Theorem.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayan Chakraborty (Indian Statistical Institute\, Kolkata)
DTSTART:20200923T190000Z
DTEND:20200923T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/24
DESCRIPTION:Title: Morita equivalence of noncommutative orbifolds\nby Sayan Chakraborty
(Indian Statistical Institute\, Kolkata) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nWe consider group actions on noncommutative tori a
nd study the corresponding 'noncommutative quotients' as crossed product C
*-algebras. We will show how such actions appear naturally and also give M
orita equivalence classes of such crossed products. The results are an ext
ension of similar results obtained by Elliott and Rieffiel for the case of
noncommutative tori.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Ivanescu (MacEwan University\, Alberta)
DTSTART:20200930T190000Z
DTEND:20200930T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/25
DESCRIPTION:Title: The Cuntz semigroup and the classification of separable amenable C*-algeb
ras\nby Cristian Ivanescu (MacEwan University\, Alberta) as part of No
ncommutative geometry in NYC\n\n\nAbstract\nNuclear C*-algebras (or equiva
lently amenable C*-algebras) are a large class of C*-algebras amenable to
study due to their finite-dimensional approximation property. Z-stable C*-
algebras are C*-algebras that satisfy a regularity property which proves f
undamental for the known classification results that we know so far. In th
is talk\, I will describe the Cuntz semigroup and its properties. Evidence
that the Cuntz semigroup can be used as an invariant to classify amenable
C*-algebras will be discussed.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Braverman (Northeastern University)
DTSTART:20201014T190000Z
DTEND:20201014T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/26
DESCRIPTION:Title: Spectral Flow of Toeplitz operators and bulk-edge correspondence\nby
Maxim Braverman (Northeastern University) as part of Noncommutative geomet
ry in NYC\n\n\nAbstract\nWe show that the (graded) spectral flow of a fami
ly of Toeplitz operators on a complete Riemannian manifold is equal to the
index of a certain Callias-type operator. When the dimension of the manif
old is even this leads to a cohomological formula for the spectral flow. A
s an application\, we compute the spectral flow of a family of Toeplitz op
erators on a strongly pseudoconvex domain in $\\mathbb{C}^n$. This result
is similar to the Boutet de Monvel's computation of the index of a single
Toeplitz operator on a strongly pseudoconvex domain. Finally\, we show tha
t the bulk-boundary correspondence in a tight-binding model of topological
insulators is a special case of our results. At the end I will explain KK
-theoretical extension of the main theaorem to families of Toeplitz operat
ors parametrized by an arbitrary compact manifold\, obtained by Koen van d
en Dungen.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andre Kornell (Tulane University)
DTSTART:20201118T200000Z
DTEND:20201118T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/27
DESCRIPTION:Title: Finite quantum structures\nby Andre Kornell (Tulane University) as pa
rt of Noncommutative geometry in NYC\n\n\nAbstract\nWeaver's quantum relat
ions provide a basis for a unified understanding of several classes of qua
ntum structures. In full generality\, quantum relations are defined for ar
bitrary von Neumann algebras\, but to simplify the discussion\, this talk
will focus on finite-dimensional von Neumann algebras. I will talk about q
uantum graphs\, quantum posets\, quantum groups\, quantum metric spaces an
d quantum families of permutations and of graph isomorphisms. I will empha
size that each of these quantum generalizations can be motivated from Birk
hoff and von Neumann's original conception of quantum logic as the logic o
f closed subspaces of a Hilbert space. (arXiv:2004.04377)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Etesi (Budapest University of Technology and Economics)
DTSTART:20201021T190000Z
DTEND:20201021T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/28
DESCRIPTION:Title: The universal von Neumann algebra of smooth 4-manifolds with an applicati
on to gravity\nby Gabor Etesi (Budapest University of Technology and E
conomics) as part of Noncommutative geometry in NYC\n\n\nAbstract\nMaking
use of its smooth structure only\, out of a connected\noriented smooth $4$
-manifold a von Neumann algebra is constructed. As a\nspecial four dimensi
onal phenomenon this von Neumann algebra is\napproximated by algebraic (i.
e.\, formal) curvature tensors of the\nunderlying $4$-manifold and the von
Neumann algebra itself is a\nhyperfinite factor of ${\\rm II}_1$ type hen
ce is unique up to abstract\nisomorphisms of von Neumann algebras. Neverth
eless over a fixed\n$4$-manifold this von Neumann algebra admits a represe
ntation on a Hilbert\nspace such that its unitary equivalence class is pre
served by\norientation-preserving diffeomorphisms. Consequently the Murray
--von\nNeumann coupling constant of this representation is well-defined an
d gives\nrise to a new and computable real-valued smooth $4$-manifold inva
riant: In\nan appropriate sense this invariant along all simply connected
closed\n$4$-manifolds is generated by its surely non-trivial value on\n${\
\mathbb C}P^2$ (with its standard smooth structure) alone.\n\nIn the secon
d half of the seminar (i.e. if time remains) some consequences\nof this co
nstruction for quantum gravity are also discussed. Namely\nreversing the c
onstruction by starting not with a particular smooth\n$4$-manifold but wit
h the unique hyperfinite ${\\rm II}_1$ factor\, a\nconceptually simple but
manifestly four dimensional\, covariant\,\nnon-perturbative and genuinely
quantum theory is introduced whose\nclassical limit is general relativity
in an appropriate sense. Therefore\nit is reasonable to consider it as a
sort of quantum theory of gravity. In\nthis model\, among other interestin
g things\, the observed positive but\nsmall value of the cosmological cons
tant acquires a natural explanation.\n\nReference\n\n1. G. Etesi: The univ
ersal von Neumann algebra of smooth four-manifolds\,\nto appear in Adv. Th
eor. Math. Phys.\, arXiv: 1712.01828 [math-ph]\;\n\n2. G. Etesi: Gravity a
s a four dimensional algebraic quantum field theory\,\nAdv. Theor. Math. P
hys. 20\, 1049-1082 (2016)\, arXiv: 1402.5658 [hep-th].\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Deaconu (University of Nevada\, Reno)
DTSTART:20201028T190000Z
DTEND:20201028T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/29
DESCRIPTION:Title: Symmetries of the $C^∗$-algebra of a vector bundle\nby Valentin Dea
conu (University of Nevada\, Reno) as part of Noncommutative geometry in N
YC\n\n\nAbstract\nWe consider $C^*$-algebras constructed from compact grou
p actions on complex vector bundles $E\\to X$ endowed with a Hermitian me
tric. An action of $G$ by isometries on $E\\to X$ induces an action on
the $C^*$-correspondence $\\Gamma(E)$ over $C(X)$ consisting of continuo
us sections\, and on the associated Cuntz-Pimsner algebra $\\mathcal{O}_E$
\, so we can study the crossed product $\\mathcal{O}_E\\rtimes G$.\n\nIf t
he action is free and rank $E=n$\, then we prove that $\\mathcal{O}_E\\rt
imes G$ is \nMorita-Rieffel equivalent to a field of Cuntz algebras $\\mat
hcal O_n$ over the orbit space $X/G$.\n\nIf the action is fiberwise\, th
en $\\mathcal{O}_E\\rtimes G$ becomes a continuous field of crossed produc
ts $\\mathcal{O}_n\\rtimes G$. For transitive actions\, we show that \n$\
\mathcal{O}_E\\rtimes G$ is Morita-Rieffel equivalent to a graph $C^*$-alg
ebra.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik van Erp (Dartmouth College)
DTSTART:20201104T200000Z
DTEND:20201104T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/30
DESCRIPTION:Title: The Heisenberg calculus\, index theory\, and cyclic cohomology\nby Er
ik van Erp (Dartmouth College) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nOn a compact contact manifold\, a pseudodifferential operato
r with an invertible symbol in the Heisenberg calculus is a hypoelliptic F
redholm operator. Its symbol determines an element in the K-theory of the
noncommutative algebra of Heisenberg symbols. In joint work with Alexander
Gorokhovksy\, we construct a cyclic cocycle which\, when paired with the
Connes-Chern character of the principal Heisenberg symbol\, calculates the
index.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nik Weaver (Washington University)
DTSTART:20201111T200000Z
DTEND:20201111T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/31
DESCRIPTION:Title: Quantum graph theory\nby Nik Weaver (Washington University) as part o
f Noncommutative geometry in NYC\n\n\nAbstract\nIn recent years operator s
ystems --- unital self-adjoint spaces of operators --- have come to be see
n as "quantum" graphs. The original motivation for this analogy came from
quantum error correction\, but the subject has developed a life of its ow
n. I will discuss quantum Ramsey theory\, the quantum Turan problem\, and
quantum chromatic number.\n\nI will mostly stick to the finite dimensiona
l setting\, so there will be few prerequisites beyond linear algebra over
the complex numbers.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bram Mesland (Leiden University)
DTSTART:20201125T200000Z
DTEND:20201125T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/32
DESCRIPTION:Title: Gabor frames and Wannier bases from groupoid Morita equivalences\nby
Bram Mesland (Leiden University) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nA key question in Gabor analysis is the reconstruction of
elements in a Hilbert space \nvia a Gabor frame. Gabor frames arise from a
finite set of vectors acted upon by a canonically defined \nset of operat
ors (typically translation and modulation). \nThis data is often convenien
tly encoded in the algebraic structure of a groupoid. In this talk we will
discuss how the natural notion of Morita equivalence of groupoids gives r
ise to Gabor frames for the Hilbert space localisation of \nthe Morita equ
ivalence bimodule of the reduced groupoid $C^*$-algebras. For finitely gen
erated and projective submodules\, we show these Gabor frames are orthonor
mal \nbases if and only if the module is free. \nIf time allows\, we will
discuss an application of this result to spectral subspaces of Schroedinge
r operators with atomic potentials supported on (aperiodic) Delone sets.\
n\nThis is joint work with Chris Bourne (Tohoku University)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jekel (UC San Diego)
DTSTART:20201202T200000Z
DTEND:20201202T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/33
DESCRIPTION:Title: Non-commutative transport of measure\nby David Jekel (UC San Diego) a
s part of Noncommutative geometry in NYC\n\n\nAbstract\nGiven self-adjoint
operators $X_1\, \\dots\, X_d$ and $Y_1\, \\dots\, Y_d$\, it is difficult
to tell when the von Neumann algebra generated by the $X_j$'s and $Y_j$'s
are isomorphic. Viewing the operators as non-commutative random variable
s\, the isomorphism of von Neumann algebras is equivalent to the existence
of a non-commutative function that will push forward the non-commutative
probability distribution of $X = (X_1\,\\dots\,X_d)$ to that of $Y =(Y_1\,
\\dots\,Y_d)$. It was proved by Guionnet\, Shlyakhtenko\, and Dabrowski t
hat certain nice non-commutative probability distributions known as free G
ibbs laws can be transported to the non-commutative Gaussian distribution\
, and thus the associated von Neumann algebras are all isomorphic. More r
ecently\, we have shown that this transport can be done in a lower triangu
lar manner\, so that the von Neumann algebra generated by $X_1\, \\dots\,
X_k$ is mapped to the von Neumann algebra generated by $Y_1\, \\dots\, Y_k
$ for $k = 1\, \\dots\, d$. Furthermore\, this transport arises in a natu
ral way as the large-$n$ limit of classical transport of measure for rando
m variables in the space of $d$-tuples $n \\times n$ matrices that approxi
mate $(X_1\,\\dots\,X_d)$ as $n \\to \\infty$.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Goncalo Tabuada (University of Warwick)
DTSTART:20210120T160000Z
DTEND:20210120T170000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/34
DESCRIPTION:Title: Noncommutative Weil conjecture\nby Goncalo Tabuada (University of War
wick) as part of Noncommutative geometry in NYC\n\n\nAbstract\nThe Weil co
njectures (proved by Deligne in the 70's) played a key role in the develop
ment of modern algebraic geometry. In this talk I will extend the Weil con
jectures from the realm of algebraic geometry to the broad noncommutative
setting of differential graded categories and describe some of its numerou
s applications.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kennedy (University of Waterloo)
DTSTART:20210127T200000Z
DTEND:20210127T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/35
DESCRIPTION:Title: Amenability\, proximality and higher order syndeticity\nby Matthew Ke
nnedy (University of Waterloo) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nI will present new descriptions of some universal flows asso
ciated to a discrete group\, obtained using what we view as a kind of "top
ological Furstenberg correspondence." The descriptions are algebraic and
relatively concrete\, involving subsets of the group satisfying a higher o
rder notion of syndeticity. We utilize them to establish new necessary and
sufficient conditions for strong amenability and amenability. Furthermore
\, utilizing similar techniques\, we obtain a characterization of "dense o
rbit sets\," answering a question of Glasner\, Tsankov\, Weiss and Zucker.
Throughout the talk\, I will discuss connections to operator algebras.\n\
nThis is joint work with Sven Raum and Guy Salomon.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vrej Zarikian (U.S. Naval Academy)
DTSTART:20210203T200000Z
DTEND:20210203T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/36
DESCRIPTION:Title: Unique Extension Properties for C*-Inclusions\nby Vrej Zarikian (U.S.
Naval Academy) as part of Noncommutative geometry in NYC\n\n\nAbstract\nL
et $\\mathcal{A} \\subseteq \\mathcal{B}$ be a $C^*$-inclusion\, i.e.\, an
inclusion of unital $C^*$-algebras with the same unit. Structural propert
ies of the inclusion are often reflected by the fact that certain families
of UCP (unital completely positive) maps on $\\mathcal{A}$ extend uniquel
y to UCP maps on $\\mathcal{B}$. In particular\, depending on the structur
e of $\\mathcal{A} \\subseteq \\mathcal{B}$\, it could be the case that\n\
ni. every pure state on $\\mathcal{A}$ extends uniquely to a pure state on
$\\mathcal{B}$ (i.e.\, $\\mathcal{A} \\subseteq \\mathcal{B}$ has the pur
e extension property)\;\n\nii. a weak* dense set of pure states on $\\math
cal{A}$ extend uniquely to pure states on $\\mathcal{B}$ (i.e.\, $\\mathca
l{A} \\subseteq \\mathcal{B}$ has the almost extension property)\;\n\niii.
the identity map $\\operatorname{id}:\\mathcal{A} \\to \\mathcal{A}$ exte
nds uniquely to a UCP map $E:\\mathcal{B} \\to \\mathcal{A}$ (i.e.\, $\\ma
thcal{A} \\subseteq \\mathcal{B}$ has a unique conditional expectation)\;\
n\niv. the identity map $\\operatorname{id}:\\mathcal{A} \\to \\mathcal{A}
$ extends uniquely to a UCP map $\\theta:\\mathcal{B} \\to I(\\mathcal{A})
$\, where $I(\\mathcal{A})$ is the injective envelope of $\\mathcal{A}$ (i
.e.\, $\\mathcal{A} \\subseteq \\mathcal{B}$ has a unique pseudo-expectati
on).\n\nIn this talk\, we explore properties (i)-(iv) above\, with a speci
al emphasis on abelian inclusions $C(X) \\subseteq C(Y)$ and inclusions $\
\mathcal{A} \\subseteq \\mathcal{A} \\rtimes_r G$ arising from actions of
discrete groups. Applications to determining the simplicity of reduced cro
ssed products are provided.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Arici (Leiden University)
DTSTART:20201209T200000Z
DTEND:20201209T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/37
DESCRIPTION:Title: SU(2)-symmetries\, exact sequences of C*-algebras and subproduct systems<
/a>\nby Francesca Arici (Leiden University) as part of Noncommutative geom
etry in NYC\n\n\nAbstract\nMotivated by the study of symmetries of C*-alge
bras as well as by multivariate operator theory\, in this talk we will int
roduce the notion of an SU(2)-equivariant subproduct system of Hilberts sp
aces. Through an explicit construction in operator theory\, we will obtain
Toeplitz and Cuntz-Pimsner algebras\, and provide results about their to
pological invariants. \n\nIn particular\, we will show that the Toeplitz a
lgebra of the subproduct system of an irreducible SU(2) representation is
equivariantly KK-equivalent to the algebra of complex numbers\, so that th
e (K)K-theory groups of the Cuntz-Pimsner algebra can be effectively compu
ted using an exact sequence involving an analogue of the Euler class.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marat Markin (California State University\, Fresno)
DTSTART:20201216T200000Z
DTEND:20201216T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/38
DESCRIPTION:Title: On the Smoothness of Weak Solutions of an Abstract Evolution Equation wit
h a Scalar Type Spectral Operator\nby Marat Markin (California State U
niversity\, Fresno) as part of Noncommutative geometry in NYC\n\n\nAbstrac
t\nGiven the abstract evolution equation\n\n$$y\\prime (t) = Ay(t)\, \\qua
d t ≥ 0\, \\hskip2cm (AEE)$$\n\nwith a scalar type spectral operator $A$
in a complex Banach space\, we find conditions on $A$\, formulated exclus
ively in terms of the location of its spectrum in the complex plane\, nece
ssary and sufficient for all weak solutions of the equation\, which a prio
ri need not be strongly differentiable\, to be strongly infinite different
iable or strongly Gevrey ultradifferentiable of order $\\beta\\ge 1$\, \ni
n particular analytic or entire\, on $[0\,\\infty)$ or \n$(0\, \\infty)$.
We also reveal certain inherent smoothness improvement effects and show th
at\, if all weak solutions of the equation are Gevrey ultradifferentiable
of orders less than one\, then the operator is necessarily bounded.\n\nIn
addition\, we find characterizations of the generation of strongly infinit
e differentiable and Gevrey ultradifferentiable $C_0$-semigroups by scalar
type spectral operators.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvie Paycha (Universität Potsdam)
DTSTART:20210210T200000Z
DTEND:20210210T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/39
DESCRIPTION:Title: Regularised traces and Getzler’s rescaling revisited\nby Sylvie Pay
cha (Universität Potsdam) as part of Noncommutative geometry in NYC\n\n\n
Abstract\nInspired by Gilkey's invariance theory\, Connes' deformation to
the\nnormal cone and Getzler's rescaling method\, we single out a class o
f\ngeometric operators among pseudodifferential operators acting on\nsecti
ons of a class of natural vector bundles\, to which we attach a \nrescalin
g degree.\nThis degree is then used to express regularised traces of ge
ometric\noperators in terms of a rescaled limit of Wodzicki residues. When
\napplied to complex powers of the square of a Dirac operator\, this \namo
unts to expressing the index of a Dirac operator in terms of a local\nresi
due involving the Getzler rescaled limit of its square.\n\nThis is join
t work with Georges Habib.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clément Dell'Aiera (ENS Lyon)
DTSTART:20210217T200000Z
DTEND:20210217T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/40
DESCRIPTION:Title: Dynamic asymptotic dimension and homology\nby Clément Dell'Aiera (EN
S Lyon) as part of Noncommutative geometry in NYC\n\n\nAbstract\nGroupoid
homology has attracted increasing attention from from the topological dyna
mics and operator algebras communities following the work of Matui. Matui'
s HK conjecture predicts that the K-theory groups of the reduced C*-algebr
a of a minimal essentially principal ample groupoid coincides with its hom
ology groups. We prove that homology of principal ample groupoids vanish i
n degree above its dynamical asymptotic dimension\, a notion of dimension
from topological dynamics. We deduce several consequences: Matui's HK conj
ecture holds for low dimensional principal ample groupoids\, and classific
ation of their reduced C*-algebra. (Joint work with Christian Bonicke\, Ja
mie Gabe and Rufus Willett)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aristides Katavolos (University of Athens)
DTSTART:20210224T200000Z
DTEND:20210224T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/41
DESCRIPTION:Title: Harmonic functions\, crossed products and approximation properties\nb
y Aristides Katavolos (University of Athens) as part of Noncommutative geo
metry in NYC\n\n\nAbstract\nThe space of harmonic functions on a locally c
ompact group $G$ is the fixed point space of a\ncertain Markov operator. I
ts `quantization'\, the corresponding fixed point space of operators on $L
^2(G)$\, coincides with the weak-* closed bimodule over the group von Neum
ann algebra generated by this space. We examine the analogous spaces of jo
intly harmonic functions\nand their quantized operator bimodules. This lea
ds to two different notions of crossed product of operator spaces by actio
ns of $G$\, which coincide when $G$ satisfies a certain approximation prop
erty. The corresponding (dual) notions of crossed products of (co-) action
s by the von Neumann algebra of $G$ always coincide. This gives a new appr
oach to the correspondence between spectral synthesis and operator synthes
is.\n\n\nThe talk is a survey of joint work with M. Anoussis and I.G. Todo
rov\, and of recent work by D. Andreou.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Gonçalves (Universidade Federal de Santa Catarina)
DTSTART:20210303T200000Z
DTEND:20210303T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/42
DESCRIPTION:Title: A generalization of shifts of finite type motivated by C*-algebra theory<
/a>\nby Daniel Gonçalves (Universidade Federal de Santa Catarina) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nUltragraphs algebras gen
eralized Exel-Laca and graph algebras. In this talk we describe ultragraph
s\, their associated edge shift spaces (which generalize SFT for infinite
alphabets)\, and their associated C*-algebras and groupoids. At the end\,
we present results regarding continuous orbit equivalence and full groups
associated to ultragraphs\, and describe how to apply these results to gra
ph and Exel-Laca algebras.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joakim Arnlind (Linköping University)
DTSTART:20210310T200000Z
DTEND:20210310T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/43
DESCRIPTION:Title: Curvature for a class of noncommutative minimal surfaces\nby Joakim A
rnlind (Linköping University) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nThe theory of minimal surfaces is an old and still quite act
ive field\nof research\, and it is natural to ask if there exists a corres
ponding\ntheory in noncommutative geometry? In particular\, analogues of m
inimal\nsubmanifolds appear in physical theories related to quantum gravit
y\n(string/membrane theory). I will present an approach to noncommutative\
nminimal surfaces taking an equational point of view (rather than a\nvaria
tional one). After providing some background material leading to\nour defi
nition of noncommutative minimal surfaces\, I will discuss a\nframework fo
r constructing Levi-Civita connections and curvature of\nsuch surfaces. Th
ese considerations naturally lead to a general\ndiscussion of metric conne
ctions on hermitian modules.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Arhancet (Lycée Lapérouse)
DTSTART:20210317T190000Z
DTEND:20210317T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/44
DESCRIPTION:Title: Entangling quantum information theory and Fourier multipliers on operator
algebras\nby Cédric Arhancet (Lycée Lapérouse) as part of Noncommu
tative geometry in NYC\n\n\nAbstract\nOne of the most fundamental question
s in quantum information concerns with the amount of information that can
be transmitted reliably through a quantum channel. For that\, many capacit
ies and entropies was introduced for describing the capability of the chan
nel for delivering information from the sender to the receiver. In this ta
lk\, we will explain how to obtain the exact values of some of these quant
ities for large classes of channels by using the theory of Fourier multipl
iers on quantum groups.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia Kuznetsova (Université de Franche-Comté)
DTSTART:20210324T190000Z
DTEND:20210324T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/45
DESCRIPTION:Title: Quantum semigroups\, what is known or not\nby Yulia Kuznetsova (Unive
rsité de Franche-Comté) as part of Noncommutative geometry in NYC\n\n\nA
bstract\nWhereas it is straightforward to define a topological group\, one
\nneeds more caution when dealing with semigroups: their multiplication mi
ght\nbe only separately and not jointly continuous. This happens in the ca
se as\nnatural as the weakly almost periodic of a locally compact group. T
he\ndistinction exists also in the quantum case\, first addressed by Mattt
hew\nDaws. After discussing it\, I will speak on duality and known links w
ith\nquantum compactifications. Finally\, I will pass to some results on t
he\nstructure of quantum semigroups. The last part is work in progress wit
h\nBiswarup Das.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Fulman (Arizona State University)
DTSTART:20210428T190000Z
DTEND:20210428T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/47
DESCRIPTION:Title: Introduction to von Neumann Algebras\, I\nby Igor Fulman (Arizona Sta
te University) as part of Noncommutative geometry in NYC\n\n\nAbstract\nBa
sic examples. Strong\, weak and operator norm topology. Bicommutant theore
m.\nProjections.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Fulman (Arizona State University)
DTSTART:20210505T190000Z
DTEND:20210505T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/48
DESCRIPTION:Title: Introduction to von Neumann Algebras\, II\nby Igor Fulman (Arizona St
ate University) as part of Noncommutative geometry in NYC\n\n\nAbstract\nF
actors. Direct sum of factors. Finite and infinite projections. Purely inf
inite projections. Factors of type I\, II and III. Examples.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Fulman (Arizona State University)
DTSTART:20210512T190000Z
DTEND:20210512T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/49
DESCRIPTION:Title: Introduction to von Neumann Algebras\, III\nby Igor Fulman (Arizona S
tate University) as part of Noncommutative geometry in NYC\n\n\nAbstract\n
Examples of factors of type I\, II and III . Group von Neumann algebras. C
rossed products.\nIntroduction to Tomita-Takesaki theory.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasilisa Shramchenko (Université de Sherbrooke)
DTSTART:20210421T190000Z
DTEND:20210421T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/50
DESCRIPTION:Title: Poncelet theorem and Painlevé VI\nby Vasilisa Shramchenko (Universit
é de Sherbrooke) as part of Noncommutative geometry in NYC\n\n\nAbstract\
nIn 1995 Hitchin constructed explicit algebraic solutions to the Painlevé
VI (1/8\,-1/8\,1/8\,3/8) equation starting with any Poncelet trajectory\
, that is a closed billiard trajectory inscribed in a conic and circumscri
bed about another conic. In this talk I will show that Hitchin's construct
ion is nothing but the Okamoto transformation between Picard's solution an
d the general solution of the Painlevé VI (1/8\,-1/8\,1/8\,3/8) equation.
Moreover\, this Okamoto transformation can be written in terms of an Abel
ian differential of the third kind on the associated elliptic curve.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikolaev (St. John's University)
DTSTART:20210331T190000Z
DTEND:20210331T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/51
DESCRIPTION:Title: Quantum dynamics of elliptic curves\nby Igor Nikolaev (St. John's Uni
versity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe calcu
late the $K$-theory of a crossed product $C^*$-algebra \n $\\mathscr{A}
_{RM}\\rtimes\\mathscr{E}(K)$\, where $\\mathscr{A}_{RM}$ is the \n nonc
ommutative torus with real multiplication and $\\mathscr{E}(K)$ is an el
liptic curve \n over the number field $K$. We use this result to evalua
te the rank and \n the Shafarevich-Tate group of $\\mathscr{E}(K)$.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angel Roman (William & Mary)
DTSTART:20210407T190000Z
DTEND:20210407T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/52
DESCRIPTION:Title: The Mackey bijection for reductive groups and continuous fields of reduce
d group C*-algebras\nby Angel Roman (William & Mary) as part of Noncom
mutative geometry in NYC\n\n\nAbstract\nIn the 1970's\, George Mackey prop
osed that there should be some kind of analogy between unitary representat
ions of semisimple groups $G$ and unitary representations of its Cartan m
otion group $G_0=K\\ltimes \\mathfrak{g}/\\mathfrak{k}$\, where $K$ is a m
aximal compact subgroup of $G$. Eventually a precise bijection was constru
cted between the irreducible tempered unitary representations of $G$ and t
he irreducible unitary representations of $G_0$. In a joint work with Nige
l Higson we characterized the Mackey bijection using continuous fields of
reduced group $C^*$-algebra of complex reductive group. We constructed an
embedding between the reduced $C^*$-algebras of $G_0$ and $G$. Time permit
ting\, I will discuss ongoing work (with Nigel Higson and Pierre Clare) to
ward a generalization to a wider class of groups.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Frei (University of Copenhagen)
DTSTART:20210414T190000Z
DTEND:20210414T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/53
DESCRIPTION:Title: Relative Cuntz-Pimsner algebras: Gauge-invariant uniqueness theorem and t
he lattice of gauge-invariant ideals\nby Alexander Frei (University of
Copenhagen) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe s
tart with an abstract definition of C*-correspondences comparing them to F
ell bundles.\nAfter a first few basic results\, we then swiftly move on to
their representations.\nWe introduce here the concept of covariances and
relative Cuntz-Pimsner algebras.\n\nFrom here we go into a detailed analys
is of covariances within the category of C*-correpondences.\nWe obtain her
e a systematic reduction leading us to a parametrisation of relative Cuntz
-Pimsner algebras.\n\nWith this at hand we arrive at the gauge-invariant u
niqueness theorem\, for all (arbitrary) gauge-equivariant representations
at once.\n\nFrom here we move on to the analysis part of the program.\nWe
study the covariances in the case of the Fock representation and its quoti
ents.\nAs a result we derive that the parametrisation of relative Cuntz-Pi
msner algebras is classifying.\nIn other words\, we obtain a complete and
intrinsic picture of the lattice of quotients\, and equivalently of gauge-
invariant ideals.\n\nIf time permits\, we finish off with the next chapter
on their induced Fell bundles\, as already investigated by Schweizer.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Katz (St. John's University)
DTSTART:20210602T190000Z
DTEND:20210602T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/54
DESCRIPTION:Title: On real Sigma*-algebras\nby Alexander Katz (St. John's University) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nReal analogues of (
complex) Sigma*-algebras are introduced and their basic properties and con
nections with real von Neumann algebras are discussed.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Afgoustidis (CNRS\, l’Institut Élie Cartan de Lorrain
e)
DTSTART:20210519T150000Z
DTEND:20210519T160000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/55
DESCRIPTION:Title: The tempered dual of real or p-adic reductive groups\, and its noncommuta
tive geometry (joint work with Anne-Marie Aubert)\nby Alexandre Afgous
tidis (CNRS\, l’Institut Élie Cartan de Lorraine) as part of Noncommuta
tive geometry in NYC\n\n\nAbstract\nSuppose G is a real or p-adic reductiv
e group. The space of irreducible tempered representations of G comes equi
pped with the Fell topology\, which encodes important phenomena in represe
ntation theory. The topology is usefully studied by noncommutative-geomet
ric methods: the tempered dual naturally identifies with the spectrum of t
he C*-algebra of G\, and its connected components identify with the spectr
a of certain `blocks’ in the C*-algebra. \n\nFor real reductive groups\,
A. Wassermann proved in 1987 that each `block’ has\, up to Morita equiv
alence\, a beautiful and simple structure. This was a crucial step in his
proof of the Baum-Connes-Kasparov conjecture for G. For p-adic groups\, it
is not obvious at all that such a structure can exist\, but important exa
mples were given by R. Plymen and his students. \n\nIn my talk\, I will re
port on joint work with Anne-Marie Aubert which (1) for arbitrary G\, give
s a geometric condition for the existence of a Wassermann-type structure o
n a given block\, and (2) when G is a quasi-split symplectic\, orthogonal
or unitary group\, explicitly determines the connected components of the t
empered dual for which the geometric assumption is satisfied.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Bonicke (University of Glasgow)
DTSTART:20210526T190000Z
DTEND:20210526T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/56
DESCRIPTION:Title: Regularity properties for ample groupoids and the type semigroup\nby
Christian Bonicke (University of Glasgow) as part of Noncommutative geomet
ry in NYC\n\n\nAbstract\nI will introduce the type semigroup of an ample g
roupoid and explain how it encodes dynamical properties of the groupoid in
an algebraic framework. In particular I will explain how the fine structu
re of the type semigroup relates to certain regularity properties of the g
roupoid\, which play a prominent role in recent attempts to develop a dyna
mical analogue of the Toms-Winter conjecture for simple separable nuclear
C*-algebras.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Perera (Universitat Autònoma de Barcelona)
DTSTART:20210609T190000Z
DTEND:20210609T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/57
DESCRIPTION:Title: Traces on ultrapower C*-algebras\nby Francesc Perera (Universitat Aut
ònoma de Barcelona) as part of Noncommutative geometry in NYC\n\n\nAbstra
ct\nEvery sequence of traces on a C*-algebra induces a limit trace on a fr
ee ultrapower. I will discuss the natural question of characterizing when
this set of limit traces is dense\, and mention the use of techniques comi
ng from the theory of Cuntz semigroups to obtain such a characterization.
This talk is based on joint work with Ramon Antoine\, Leonel Robert\, and
Hannes Thiel.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shanna Dobson (California State University\, Los Angeles)
DTSTART:20210623T190000Z
DTEND:20210623T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/58
DESCRIPTION:Title: Pro-Diamond and the Geometrization of Local Langlands\nby Shanna Dobs
on (California State University\, Los Angeles) as part of Noncommutative g
eometry in NYC\n\n\nAbstract\nWe recently conjectured a pro-diamond in our
Efimov K-theory of Diamonds\, for diamonds in the sense of Scholze. In th
is talk\, we discuss our pro-diamond formalism and survey the many incarna
tions of diamonds in the geometrization of the local Langlands Corresponde
nce.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20210630T190000Z
DTEND:20210630T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/59
DESCRIPTION:Title: Stratified equivalences and Bernstein Center\nby Anne-Marie Aubert (C
NRS\, Sorbonne Université - Université de Paris) as part of Noncommutati
ve geometry in NYC\n\n\nAbstract\nIn the first part of the talk\, we will
introduce the notion of stratified equivalence for finite type k-algebras\
, which is a weakening of Morita equivalence\, and illustrate it with exam
ples.\n\nNext\, we will recall the Bernstein decomposition of the category
of smooth representations of a p-adic reductive group and show how strati
fied equivalence occurs in this context\, notably in the case of inner for
ms of the special linear group.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Cipriani (Politecnico di Milano)
DTSTART:20210714T190000Z
DTEND:20210714T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/60
DESCRIPTION:Title: On a noncommutative Sierpiński gasket\nby Fabio Cipriani (Politecnic
o di Milano) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe i
llustrate the construction of a C*-algebra A that can be genuinely interpr
eted as a quantization of the classical Sierpiński gasket\, the most stud
ied instance of a self-similar fractal space. We further describe the disc
rete and continuous spectrum of A\, the structure of the traces on A as we
ll as the construction of a Dirichlet form E and of a spectral triple (A\,
D\,H).\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Spaas (UCLA)
DTSTART:20210707T190000Z
DTEND:20210707T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/61
DESCRIPTION:Title: Cohomological obstructions to lifting properties for full C*-algebras of
property (T) groups\nby Pieter Spaas (UCLA) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nWe will introduce and discuss the lifting p
roperty (LP) and local lifting property (LLP) for full group C*-algebras.
We will then introduce a new method to refute these properties\, based on
non-vanishing of second cohomology groups. This will allow us to derive th
at many natural examples of (relative) property (T) groups fail the LLP\,
and further large classes fail the LP. This is based on joint work with Ad
rian Ioana and Matthew Wiersma.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitch Haslehurst (University of Victoria)
DTSTART:20210616T190000Z
DTEND:20210616T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/62
DESCRIPTION:Title: Relative K-theory with applications to factor groupoids\nby Mitch Has
lehurst (University of Victoria) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nIn this talk I will speak about a portrait of relative K-t
heory for C*-algebras inspired by a setup due to Max Karoubi using Banach
categories. After presenting some useful exact sequences\, I will show how
the portrait gives the same data\, although through a different lens\, as
the K-groups that arise from the mapping cone construction. After this\,
I will \npresent some examples of C*-algebras from factor groupoids whose
K-theory data are computable (in fact\, controllable\, to a certain degree
) using these relative K-theory tools.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Kaad (University of Southern Denmark)
DTSTART:20210818T190000Z
DTEND:20210818T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/63
DESCRIPTION:Title: Exterior products of compact quantum metric spaces\nby Jens Kaad (Uni
versity of Southern Denmark) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nThe theory of compact quantum metric spaces was initiated by R
ieffel in the late nineties. Important inspiration came from the fundament
al observation of Connes saying that the metric on a compact spin manifold
can be recovered from the Dirac operator. A compact quantum metric space
is an operator system (e.g. a unital C*-algebra) equipped with a seminorm
which metrizes the weak-*-topology on the state space via the associated M
onge-Kantorovich metric. In this talk we study tensor products of compact
quantum metric spaces with specific focus on seminorms arising from the ex
terior product of spectral triples. On our way we obtain a novel character
ization of compact quantum metric spaces using finite dimensional approxim
ations and we apply this characterization to propose a completely bounded
version of the theory.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Schmieding (University of Denver)
DTSTART:20210721T190000Z
DTEND:20210721T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/64
DESCRIPTION:Title: Flow equivalence and mapping class groups for symbolic dynamical systems<
/a>\nby Scott Schmieding (University of Denver) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nThere have been many fruitful connections b
etween symbolic dynamical systems and operator algebras. We'll first give
a very brief survey of some examples of this\, before focusing on the noti
on of flow equivalence and mapping class groups in the context of symbolic
dynamics. The talk will be designed so that little to no knowledge of dyn
amical systems is necessary.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Burgstaller (Universidade Federal de Santa Catarina)
DTSTART:20210728T190000Z
DTEND:20210728T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/65
DESCRIPTION:Title: A kind of KK-theory of rings\nby Bernhard Burgstaller (Universidade F
ederal de Santa Catarina) as part of Noncommutative geometry in NYC\n\n\nA
bstract\nA group equivariant $KK$-theory\nfor rings will be defined and st
udied\nin analogy to Kasparov's $KK$-theory for\n$C^*$-algebras.\nIt is a
kind of linearization of the category\nof rings by allowing addition of ho
momorphisms\, imposing also homotopy invariance\, invertibility of matrix
corner embeddings\,\nand allowing morphisms which are the opposite split o
f split exact sequences.\nWe demonstrate the potential of this theory\nby
proving for example equivalence induced by Morita equivalence\nand a Green
-Julg isomorphism in this framework.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Cantier (Universitat Autònoma de Barcelona)
DTSTART:20210908T190000Z
DTEND:20210908T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/66
DESCRIPTION:Title: Classification of unitary elements of a C*-algebra\nby Laurent Cantie
r (Universitat Autònoma de Barcelona) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nThe Cuntz semigroup has emerged as an essential tool
for the classification of (non-simple) C*-algebras. For instance\, it has
been shown that the functor Cu classifies positive elements of any C*-alg
ebra of stable rank 1 (up to approximately unitarily equivalence). An imme
diate corollary is that the Cuntz semigroup is a complete invariant for AI
algebras. In this talk\, I will raise the question of classification of u
nitary elements of a C*-algebra (of stable rank 1). It is unlikely that th
e Cuntz semigroup alone is sufficient to classify these elements and one c
an speculate that an ingredient with $K_1$ flavor has to be added. Neverth
eless\, I will prove that this remains true when restricting to AF algebra
s and I will discuss how one could to extend this classification result to
a larger class of C*-algebra.\n\nEven though I will recall definitions of
the Cuntz semigroup and classifying functor\, it might good to point out
that knowledge about C*-algebras are needed.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lyudmila Turowska (Chalmers University of Technology)
DTSTART:20210901T190000Z
DTEND:20210901T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/67
DESCRIPTION:Title: Multipliers and Approximation Properties\nby Lyudmila Turowska (Chalm
ers University of Technology) as part of Noncommutative geometry in NYC\n\
n\nAbstract\nOne can encode various properties of locally compact groups f
rom properties of Banach algebras associated to the groups and vice versa.
In this talk I will explain how Herz-Schur multipliers have been used to
study some of those properties. Then I will talk about generalization of s
uch multipliers to the setting of dynamical systems and explain how the te
chnique of Herz-Schur multipliers can be extended to study approximation p
roperties of crossed product C*-algebras. I shall also discuss compact and
completely compact multipliers.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Wagner (Blekinge Institute of Technology)
DTSTART:20210825T190000Z
DTEND:20210825T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/68
DESCRIPTION:Title: Factor systems as a computational framework for noncommutative principal
bundles - with an application to Atiyah’s famous Lie algebra sequence\nby Stefan Wagner (Blekinge Institute of Technology) as part of Noncommu
tative geometry in NYC\n\n\nAbstract\nFree C*-dynamical systems\, in the s
ense of Ellwood\, provide a natural framework for noncommutative principal
bundles\, which are becoming increasingly prevalent in various applicatio
ns to noncommutative geometry and mathematical physics. \nOne of the key f
eatures of free C*-dynamical systems are their associated factor systems\,
which make them accessible to classification\, K-theoretic considerations
\, and computations in general. \nIn this talk we present the recent theor
y of factor systems for free C*-dynamical systems and apply it to give a d
erivation-based Atiyah sequence for noncommutative principal bundles.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Brix (University of Glasgow)
DTSTART:20210915T190000Z
DTEND:20210915T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/69
DESCRIPTION:Title: Flow equivalence and C*-algebras\nby Kevin Brix (University of Glasgo
w) as part of Noncommutative geometry in NYC\n\n\nAbstract\nTopological dy
namical systems are an abundant source of examples of interesting C*-algeb
ras\, e.g. Cuntz-Krieger algebras\, graph C*-algebras and their higher ran
k and twisted variations. Dynamical relations such as conjugacy or flow eq
uivalence are an invitation to study the fine structure of these C*-algebr
as and isomorphisms between them. I intend to discuss some central results
as well as important open questions in this field.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Schenkel (Ohio University)
DTSTART:20210811T190000Z
DTEND:20210811T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/70
DESCRIPTION:Title: Regular Ideals of Locally-Convex Kumjian-Pask Algebras\nby Timothy Sc
henkel (Ohio University) as part of Noncommutative geometry in NYC\n\n\nAb
stract\nWe give a vertex set description for basic\, graded\, regular idea
ls of locally-convex Kumjian-Pask Algebras. We also show that Condition (B
) is preserved when taking the quotient by a basic\, graded\, regular idea
l. We further show that when a locally-convex\, row-finite k-graph satisfi
es Condition (B)\, all regular ideals are graded.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Martínez (University of Madrid)
DTSTART:20211006T190000Z
DTEND:20211006T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/71
DESCRIPTION:Title: C* and geometric properties of inverse semigroups\nby Diego Martínez
(University of Madrid) as part of Noncommutative geometry in NYC\n\n\nAbs
tract\nInverse semigroups are a generalization of groups\, where elements
in an inverse semigroup can be thought of as partial symmetries of a space
(instead of global symmetries\, as in the group case). Out of these one c
an construct a uniform Roe algebra algebra just as in the group case\, and
study its properties. In this talk\, we shall characterize when such C*-a
lgebra is nuclear by means of an intrinsic metric in the semigroup\, and p
rove that its nuclearity is equivalent to the semigroup having property A
. Moreover\, one can also study amenability notions in this case\, and rel
ate the trace space of the uniform Roe algebra with certain invariant meas
ures in the semigroup. This talk is based on joint work with Pere Ara and
Fernando Lledó.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Plazas (Pontificia Universidad Javeriana)
DTSTART:20210922T190000Z
DTEND:20210922T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/72
DESCRIPTION:Title: Noncommutative geometry of arithmetic groups\nby Jorge Plazas (Pontif
icia Universidad Javeriana) as part of Noncommutative geometry in NYC\n\n\
nAbstract\nIn this talk we look at constructions from noncommutative geome
try which encode various number theoretic properties of arithmetic groups.
\n\nIn the first part of the talk we will discuss the relation between Con
way's big picture and the Connes-Marcolli Gl(2) system. This relation lead
s to noncommutative spaces encoding properties of groups commensurable wi
th the modular group. In the second part of the talk we discuss Hecke oper
ators for Bianchi groups and the action of these in K-homology via Bredon
homology and the Baum-Connes conjecture.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tyrone Crisp (University of Maine)
DTSTART:20210929T190000Z
DTEND:20210929T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/73
DESCRIPTION:Title: Frobenius C*-algebras and local adjunctions of C*-correspondences\nby
Tyrone Crisp (University of Maine) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nMany interesting and important C*-algebras do not have
multiplicative identities\, and C*-algebraists have long known how to deal
with this fact by using approximate identities\, multiplier algebras\, et
c. A similar situation arises when one attempts to use methods of category
theory to study modules over C*-algebras: objects like "the category of c
ompact operators on Hilbert spaces" don't fit neatly into the standard the
ory of categories\, because they lack identity morphisms\; but they do fit
nicely into a theory of non-unital C*-categories and their multiplier cat
egories\, as developed by Kandelaki\, Mitchener\, Vasselli\, Antoun-Voigt\
, and others. This talk concerns an adaptation of the important categorica
l notion of adjoint functors to this non-unital-category point of view. I
will present a definition (taken from joint work with Pierre Clare and Nig
el Higson) of adjoint functors between categories of compact operators on
Hilbert C*-modules\, and I will explain how this definition corresponds to
a natural notion of Frobenius C*-algebra\, mirroring a correspondence bet
ween two-sided adjunctions and Frobenius algebras in classical category th
eory.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Castro (Universidade Federal de Santa Catarina)
DTSTART:20211103T190000Z
DTEND:20211103T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/74
DESCRIPTION:Title: KMS states for generalized gauge actions on C*-algebras associated with s
elf-similar sets\nby Gilles Castro (Universidade Federal de Santa Cata
rina) as part of Noncommutative geometry in NYC\n\n\nAbstract\nOn the one
hand\, equilibrium states in quantum statistical mechanics can be describe
d using the KMS condition. On the other hand\, in classical statistical me
chanics\, one way of finding equilibrium states is via an operator called
the Ruelle operator. It turns out that for some noncommutative C*-algebras
built from classical objects\, there are some relationships between KMS s
tates on the C*-algebras and properties of the Ruelle operator. In this ta
lk\, after recalling the needed definitions\, I will present some results
in this direction for C*-algebras associated with self-similar sets.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Becky Armstrong (Universität Münster)
DTSTART:20211013T190000Z
DTEND:20211013T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/75
DESCRIPTION:Title: A uniqueness theorem for twisted groupoid C*-algebras\nby Becky Armst
rong (Universität Münster) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nTwisted groupoid C*-algebras were introduced by Renault in 198
0 and are a generalisation of twisted group C*-algebras\, which are the C*
-algebraic analogue of twisted group rings. Through the work of Renault an
d more recently of Li\, it has emerged that every simple classifiable C*-a
lgebra can be realised as a twisted groupoid C*-algebra\, a result that ha
s led to increased interest in the structure of these C*-algebras. In this
talk I will describe the construction of reduced twisted C*-algebras of H
ausdorff étale groupoids. I will then discuss my recent preprint in which
I prove a uniqueness theorem for these algebras and use this to character
ise simplicity in the case where the groupoid is effective.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vadim Alekseev (Technische Universität Dresden)
DTSTART:20211110T200000Z
DTEND:20211110T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/76
DESCRIPTION:Title: Geometry of sofic approximations\nby Vadim Alekseev (Technische Unive
rsität Dresden) as part of Noncommutative geometry in NYC\n\n\nAbstract\n
In the recent years\, there has been substantial activity\nconnecting grap
h theory and group theory via the concept of a metric\napproximation of an
infinite group by finite objects (groups or\ngraphs)\, particularly aroun
d sofic groups. This lead to numerous\nresults which describe approximatio
n properties of the group (for\ninstance\, amenability or Haagerup propert
y) in terms of geometric\nproperties of its approximations (e.g. hyperfini
teness or coarse\nembeddability in a Hilbert space of a graph sequence). I
n this talk\, I\nwill describe these connections between the two worlds (g
roups and\ngraphs) and some recent results around them.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Monod (École Polytechnique Fédérale de Lausanne)
DTSTART:20211020T190000Z
DTEND:20211020T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/77
DESCRIPTION:Title: Type I\, Gelfand pairs and Iwasawa decompositions\nby Nicolas Monod (
École Polytechnique Fédérale de Lausanne) as part of Noncommutative geo
metry in NYC\n\n\nAbstract\nIn this talk\, we will prove that every Gelfan
d pair admits an Iwasawa\ndecomposition.\n\nBefore that\, we will explain
what Gelfand pairs are and why Iwasawa\ndecompositions are useful.\n\nAt t
he end\, we will discuss a conjecture studied in collaboration with\nM. Ka
lantar and P.-E. Caprace\, speculating about similar results for\ntype I g
roups.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Glubokov (Purdue University)
DTSTART:20211027T190000Z
DTEND:20211027T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/78
DESCRIPTION:Title: Cluster algebra and Jones polynomials\nby Andrey Glubokov (Purdue Uni
versity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nCluster
$C^*$-algebra of the sphere with two cusps and its K-theory is being inves
tigated to demonstrate a connection to the Jones polynomials.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Tikuisis (University of Ottawa)
DTSTART:20211117T200000Z
DTEND:20211117T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/79
DESCRIPTION:Title: Nuclear dimension and Z-stability of simple C*-algebras\nby Aaron Tik
uisis (University of Ottawa) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nMuch recent work in C*-algebra theory has focused on regularit
y properties. This is a response to examples of "irregular" simple nuclear
C*-algebras by Villadsen (algebras with perforation in their ordered K-th
eory)\, Rordam (algebras with both finite and infinite projections)\, and
Toms (algebras that cannot be distinguished by ordered K-theory and traces
). I will describe two regularity properties: finite nuclear dimension and
Z-stability (aka Jiang-Su-stability). In joint work with Castillejos\, Ev
ington\, White\, and Winter\, we showed that these properties coincide for
simple separable nuclear unital C*-algebras\, verifying a conjecture of T
oms and Winter. I will discuss this result and its implications.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Ma (University of Memphis)
DTSTART:20211124T200000Z
DTEND:20211124T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/80
DESCRIPTION:Title: Fiberwise amenability and almost elementariness for étale groupoids\
nby Xin Ma (University of Memphis) as part of Noncommutative geometry in N
YC\n\n\nAbstract\nIn this talk\, I will discuss two new properties for loc
ally compact Hausdorff étale groupoids. One is from a coarse geometric vi
ew called fiberwise amenability. Another one is called almost elementarine
ss\, which is a new finite-dimensional approximation property. I will expl
ain how these notions related to almost finiteness defined by Matui and re
fined by Kerr and show our almost elementariness implying tracial Z-stabil
ity of reduced groupoid C*-algebras. As an application. This implies that
Matui's almost finiteness in the groupoid setting also implies Z-stability
when the groupoid is minimal 2nd countable and topological amenable. This
was open in general before. I will also present more applications if time
permits. This is based on joint work with Jianchao Wu.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Huang (University of Michigan)
DTSTART:20211201T200000Z
DTEND:20211201T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/81
DESCRIPTION:Title: Point count of the variety of modules over the quantum plane over a finit
e field\nby Yifeng Huang (University of Michigan) as part of Noncommut
ative geometry in NYC\n\n\nAbstract\nIn 1960\, Feit and Fine gave a formul
a for the number of pairs of commuting n by n matrices over a finite field
. We consider a quantum deformation of the problem\, namely\, counting pai
rs (A\,B) of n by n matrices over a finite field that satisfy AB=qBA for a
fixed nonzero scalar q. We give a formula for this count in terms of the
order of q as a root of unity\, generalizing Feit and Fine's result. In th
is talk\, after explaining the title and the results\, we will discuss a c
urious phenomenon that one sees when comparing the commutative case (q=1)
and the general case from a geometric viewpoint.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Réamonn Ó Buachalla (Charles University\, Prague)
DTSTART:20211208T200000Z
DTEND:20211208T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/82
DESCRIPTION:Title: Quantum Root Vectors and a Dolbeault Double Complex for the A-Series Quan
tum Flag Manifolds\nby Réamonn Ó Buachalla (Charles University\, Pra
gue) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIn the 2000s
a series of seminal papers by Heckenberger and Kolb introduced an essenti
ally unique covariant $q$-deformed de Rham complex for the irreducible qua
ntum flag manifolds. In the years since\, it has become increasingly clear
that these differential graded algebras have a central role to play in th
e noncommutative geometry of Drinfeld–Jimbo quantum groups. Until now\,
however\, the question of how to extend Heckenberger and Kolb’s construc
tion beyond the irreducible case has not been examined. Here we address th
is question for the A-series Drinfeld–Jimbo quantum groups $U_q(\\mathfr
ak{sl}_{n+1})$\, and show that for precisely two reduced decompositions of
the longest element of the Weyl group\, Lusztig’s associated space of q
uantum root vectors gives a quantum tangent space for the full quantum fla
g manifold $\\mathcal{O}_q(F_{n+1})$ with associated differential graded a
lgebra of classical dimension. Moreover\, its restriction to the quantum G
rassmannians recovers the $q$-deformed complex of Heckenberger and Kolb\,
giving a conceptual explanation for their origin. Time permitting\, we wil
l discuss the noncommutative Kähler geometry of these spaces and the prop
osed extension of the root space construction to the other series. (Joint
work with P. Somberg.)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Priyanga Ganesan (Texas A&M)
DTSTART:20211215T200000Z
DTEND:20211215T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/83
DESCRIPTION:Title: Spectral bounds for chromatic number of quantum graphs\nby Priyanga G
anesan (Texas A&M) as part of Noncommutative geometry in NYC\n\n\nAbstract
\nQuantum graphs are a non-commutative generalization of classical graphs
that have appeared in different branches of mathematics including operator
algebras\, non-commutative topology and quantum information theory. In th
is talk\, I will review the different perspectives to quantum graphs and i
ntroduce a chromatic number for quantum graphs using a non-local game with
quantum inputs and classical outputs. I will then show that many spectral
lower bounds for chromatic numbers in the classical case (such as Hoffman
’s bound) also hold in the setting of quantum graphs. This is achieved u
sing an algebraic formulation of quantum graph coloring and tools from lin
ear algebra.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yavar Abdolmaleki (University of New Brunswick)
DTSTART:20220202T200000Z
DTEND:20220202T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/84
DESCRIPTION:Title: Equivariant KK-theory and its application in Index theory\nby Yavar A
bdolmaleki (University of New Brunswick) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nIn this talk\, we show how using the calculation o
f a couple of Kasparov products of asymptotically equivariant cycles we ca
n find the index of an asymptotically equivariant Dirac-Schrodinger operat
or on a Hyperbolic manifold. In fact\,\nusing the calculation of the Kaspa
rov products of a couple of asymptotically equivariant cycles\, we reduce
the problem of finding the index to the\ncase in which the manifold is com
pact and so the problem reduces to the Atiyah-Singer index theorem.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Vigolo (University of Münster)
DTSTART:20220209T200000Z
DTEND:20220209T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/85
DESCRIPTION:Title: Strong ergodicity\, projections and Markov operators\nby Federico Vig
olo (University of Münster) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nThe aim of this talk is to illustrate how some insights from t
he theory of Markov processes can be adapted to prove that certain project
ions belong to "Roe-like" C*-algebras of dynamical origin. Given an action
of a countable discrete group on a measure space\, one may define a C*-al
gebra by taking the closure of an algebra of operators with finite propaga
tion. I will explain that this C*-algebra contains a certain natural famil
y of rank-one projections if and only if the action is strongly ergodic. T
his result can be used to construct more counterexamples to the coarse Bau
m-Connes conjecture.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Pennig (Cardiff University)
DTSTART:20220216T200000Z
DTEND:20220216T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/86
DESCRIPTION:Title: Bundles of C*-algebras - An Introduction to Dixmier-Douady theory\nby
Ulrich Pennig (Cardiff University) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nA bundle of C*-algebras is a collection of algebras con
tinuously parametrised by a topological space. There are (at least) two di
fferent definitions in operator algebras that make this intuition precise:
Continuous C(X)-algebras provide a flexible analytic point of view\, whil
e locally trivial C*-algebra bundles allow a classification via homotopy t
heory. The section algebra of a bundle in the topological sense is a C(X)-
algebra\, but the converse is not true. In this talk I will compare these
two notions using the classical work of Dixmier and Douady on bundles with
fibres isomorphic to the compacts as a guideline. I will then explain joi
nt work with Marius Dadarlat\, in which we showed that the theorems of Dix
mier and Douady can be generalized to bundles with fibers isomorphic to st
abilized strongly self-absorbing C*-algebras. An important feature of the
theory is the appearance of higher analogues of the Dixmier-Douady class.\
n
LOCATION:https://researchseminars.org/talk/NYC-NCG/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Rivet (Université Clermont Auvergne)
DTSTART:20220223T200000Z
DTEND:20220223T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/87
DESCRIPTION:Title: Geometric view of semisimple quantum groups representations\nby Damie
n Rivet (Université Clermont Auvergne) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nThe representations of the principal series of a s
emisimple quantum group can be\, as in the classical case\, constructed as
induced representations from the characters of a quantum Borel subgroup.
Rieffel's framework for induction can be adapted to quantum groups and all
ows to give a simple expression for the principal series representations.
In particular this leads\, as Clare did in the classical case\, to gather
all these representations into a single Hilbert module built from a certai
n quantum homogeneous space.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Makoto Yamashita (University of Oslo)
DTSTART:20220302T150000Z
DTEND:20220302T160000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/88
DESCRIPTION:Title: Homology and K-theory of dynamical systems\nby Makoto Yamashita (Univ
ersity of Oslo) as part of Noncommutative geometry in NYC\n\n\nAbstract\nA
theory of homology for étale groupoids was developed by Crainic and Moer
dijk based on simplicial structure of nerves of groupoids\, as a companion
to Haeflier's theory of cohomology for groupoids. We relate this to anoth
er (co)homology of groupoids\, namely the operator K-groups of the associa
ted convolution algebra\, when the base is totally disconnected. Such a co
nnection was conjectured by Matui through his study of Cantor dynamical sy
stems. Our proof is based on the triangulated categorical structure of gro
upoid equivariant KK-theory\, following the categorical approach to the Ba
um-Connes conjecture by Meyer and Nest. Along the way we uncover the close
connection to Putnam's homology theory for hyperbolic dynamical systems (
Smale spaces). Based on joint works with Valerio Proietti.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fidaleo (Università di Roma "Tor Vergata")
DTSTART:20220314T150000Z
DTEND:20220314T160000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/89
DESCRIPTION:Title: Modular Spectral Triples and deformed Fredholm modules (Part I)\nby F
rancesco Fidaleo (Università di Roma "Tor Vergata") as part of Noncommuta
tive geometry in NYC\n\n\nAbstract\nDue to possible applications to the at
tempt to provide a set of equations which unify the four elementary intera
ctions in nature (the grand-unification) and in another\, perhaps connecte
d\, direction in proving the long-standing\, still unsolved\, Riemann conj
ecture about the zeroes of the $\\zeta$-function\, Connes’ non- commutat
ive geometry grew up rapidly in the last decades.\n\nAmong the main object
s introduced (by A. Connes) for handling noncommutative geometry there are
the so called spectral triples\, encoding most of the properties enjoyed
by the (quantum) ”manifold” into consideration\, and the associated Fr
edholm modules.\n\nOn the other hand\, the so-called Tomita modular theory
is nowadays assuming an increasingly relevant role for several applicatio
ns in mathematics and in physics. Such a scenario suggests the necessary n
eed to take the modular data into account in the investigation of quantum
manifolds. In such a situation\, the involved Dirac operators should be su
itably deformed (by the use of the modular operator)\, and should come fro
m non-type $II_1$ representations.\n\nTaking into account such comments\,
we discuss the preliminary necessary step consisting in the explicit const
ruction of examples of non type $II_1$ representations and relative spectr
al triples\, called modular. This is done for the noncommutative 2-torus $
A_{\\alpha}$\, provided α is a (special kind of) Liouville number\, where
the nontrivial modular structure plays a crucial role.\n\nFor such repres
entations\, we briefly discuss the appropriate Fourier analysis\, by provi
ng the analogous of many of the classical known theorems in harmonic analy
sis such as the Riemann-Lebesgue lemma\, the Hausdorff-Young theorem\, and
the $L_p$-convergence results associated to the Cesaro means (i.e. the Fe
jer theorem) and the Abel means reproducing the Poisson kernel. We show ho
w those Fourier transforms ”diagonalise” appropriately some examples o
f the Dirac operators associated to the previous mentioned spectral triple
s.\n\nFinally\, we provide a definition of a deformed generalisation of
”Fredholm module”\, i.e. a suitably deformed commutator of the ”phas
e” of the involved Dirac operator with elements of a subset (the so-call
ed Lipschitz $\\star$-algebra or Lipschitz operator system) which\, depend
ing on the cases under consideration\, is either a dense $\\star$-algebra
or an essential operator system. We also show that all models of modular
spectral triples for the noncommutative 2-torus mentioned above enjoy the
property to being also a deformed Fredholm module. This definition of defo
rmed Fredholm module is new even in the usual cases associated to a trace\
, and could provide other\, hopefully interesting\, applications.\n\nThe p
resent talk is based on the following papers:\n\n[1] F. Fidaleo and L. Sur
iano: Type $III$ representations and modular spectral triples for the nonc
ommutative torus\, J. Funct. Anal. 275 (2018)\, 1484-1531.\n\n[2] F. Fidal
eo: Fourier analysis for type III representations of the noncommutative to
rus\, J. Fourier Anal. Appl. 25 (201)\, 2801-2835.\n\n[3] F. Ciolli and F.
Fidaleo: Type $III$ modular spectral triples and deformed Fredholm module
s\, preprint.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fidaleo (Università di Roma "Tor Vergata")
DTSTART:20220413T190000Z
DTEND:20220413T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/90
DESCRIPTION:Title: Spectral actions for q-particles and their asymptotic (Part II)\nby F
rancesco Fidaleo (Università di Roma "Tor Vergata") as part of Noncommuta
tive geometry in NYC\n\n\nAbstract\nFor spectral actions made of the avera
ge number of particles and arising from open systems made of general free
$q$-particles (including Bose\, Fermi and classical ones corresponding to
$q=\\pm1$ and $0$\, respectively) in thermal equilibrium\, we compute the
asymptotic expansion with respect to the natural cut-off. We treat both re
levant situations relative to massless and massive particles\, where the n
atural cut-off is $1/\\beta=k_{\\rm B}T$ and $1/\\sqrt{\\beta}$\, respecti
vely. \nWe show that the massless situation enjoys less regularity proper
ties than the massive one. We also consider the passage to the continuum d
escribing infinitely extended open systems in thermal equilibrium. We brie
fly discuss the appearance of condensation phenomena occurring for Bose-li
ke $q$-particles\, for which $q\\in(0\,1]$\, after passing to the continuu
m. We also compare the arising results for the finite volume situation (di
screte spectrum) with the corresponding infinite volume one (continuous sp
ectrum).\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward McDonald (PennState)
DTSTART:20220323T190000Z
DTEND:20220323T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/91
DESCRIPTION:Title: Littlewood-Paley inequalities and other analytic issues in noncommutative
Euclidean spaces\nby Edward McDonald (PennState) as part of Noncommut
ative geometry in NYC\n\n\nAbstract\nI will discuss some analytic issues t
hat arose in the course of investigations of the problem of characterising
quantum differentiability in noncommutative spaces. These issues highligh
t some of the peculiar features of certain noncommutative spaces where cla
ssical results become meaningless or trivially false. In particular I disc
uss the apparent lack of a Poincaré inequality on noncommutative Euclidea
n planes (Moyal planes) and how this necessitates the use of new technique
s.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Ponge (Sichuan University)
DTSTART:20220330T190000Z
DTEND:20220330T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/92
DESCRIPTION:Title: Dixmier trace formulas and negative eigenvalues of Schroedinger operators
on noncommutative tori\nby Raphael Ponge (Sichuan University) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nIn this talk\, we shall
first address a question raised by Alain Connes during a conference at Fud
an University in Shanghai in 2017. We will also explain a link that has co
me to light only recently between noncommutative geometry and the work of
Birman-Solomyak on semiclassical analysis of Schroedinger operators in the
70s. We will then present results obtained jointly with Ed McDonald (UNSW
-Sydney) on Cwikel-type estimates on NC tori. As an application we obtain
a version of Connes' integration formulas under very weak assumptions. Fu
rther applications include versions of the Cwikel-Lieb-Rozenblum and Lieb-
Thirring inequalities for negative eigenvalues of Schroedinger operators o
n noncommutative tori. Ultimately\, we get a seminclassical Weyl law for c
urved noncommutative tori\, i.e.\, NC tori endowed with arbitrary Riemanni
an metrics.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Yu. Aristov (Moscow State University)
DTSTART:20220406T140000Z
DTEND:20220406T150000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/93
DESCRIPTION:Title: Complex analytic quantum groups\nby Oleg Yu. Aristov (Moscow State Un
iversity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe disc
uss a missing link in quantum group theory - quantum analogues of complex
Lie groups. As such analogues\, I propose to take topological Hopf algebra
s with a finiteness condition (holomorphically finitely generated or HFG
for short). This approach is not directly related to C*-algebraic quantum
groups (at least for now) but is an alternative view. Nevertheless\, the
topic seems to offer a wide range of research opportunities.\n\nOur focus
is on examples\, such as analytic forms of some classical quantum groups (
a deformation of a solvable Lie group and Drinfeld-Jimbo algebras). I al
so present some general results: 1) the category of Stein groups is anti-e
quivalent to the category of commutative Hopf HFG algebras\; 2) If $G$ is
a compactly generated Lie group\, the cocommutative topological Hopf alg
ebra $\\widehat{A(G)}$ (naturally associated with $G$) is HFG. When in
addition\, $G$ is connected linear\, the structure of $\\widehat{A(G)}$ c
an be described explicitly.\n\nI also plan to discuss briefly holomorphic
duality in the sense of Akbarov (which is parallel to Pontryagin duality).
\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Strung (Czech Academy of Sciences)
DTSTART:20220504T190000Z
DTEND:20220504T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/94
DESCRIPTION:Title: An introduction to C*-algebras\, I\nby Karen Strung (Czech Academy of
Sciences) as part of Noncommutative geometry in NYC\n\n\nAbstract\nBanach
algebras\, definition of C*-algebra\, spectrum\, Gelfand transform\, char
acters.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Strung (Czech Academy of Sciences)
DTSTART:20220511T190000Z
DTEND:20220511T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/95
DESCRIPTION:Title: An introduction to C*-algebras\, II\nby Karen Strung (Czech Academy o
f Sciences) as part of Noncommutative geometry in NYC\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benton Duncan (North Dakota State University)
DTSTART:20220907T190000Z
DTEND:20220907T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/96
DESCRIPTION:Title: Abstract operator algebras and enveloping C*-algebras\nby Benton Dunc
an (North Dakota State University) as part of Noncommutative geometry in N
YC\n\n\nAbstract\nWe will consider nonselfadjoint operator algebras and th
e $C^*$-algebras they generate. We will look at motivating examples of cla
sses of nonselfadjoint operator algebras. We will outline several construc
tions of enveloping $C^*$-algebras for operator algebras and develop examp
les of the various enveloping $C^*$-algebras.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariusz Tobolski (University of Wrocław)
DTSTART:20220420T190000Z
DTEND:20220420T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/97
DESCRIPTION:Title: Noncommutative numerable principal bundles from group actions on C*-algeb
ras\nby Mariusz Tobolski (University of Wrocław) as part of Noncommut
ative geometry in NYC\n\n\nAbstract\nThe notion of a compact noncommutativ
e (or quantum) principal bundle\, which generalizes the Cartan compact pri
ncipal bundle from topology (local triviality not assumed)\, emerged in th
e literature almost 30 years ago. Recently\, the difficulty of introducing
the local-triviality condition to the noncommutative realm was overcome u
sing the notion of the local-triviality dimension of an action of a compac
t quantum group on a unital C*-algebra. In this talk\, I will propose a de
finition of a locally trivial noncommutative principal bundle in the setti
ng of actions of locally compact Hausdorff groups on (possibly non-unital)
C*-algebras. I will discuss various motivations and technical difficultie
s that appear in the non-compact case. I will also provide some basic resu
lts and examples. The key difference is that\, although the problem itself
can be described in the language of C*-algebra\, one is quickly led beyon
d the Gelfand-Naimark duality and to the theory of multipliers of the Pede
rsen ideal.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Strung (Czech Academy of Sciences)
DTSTART:20220525T190000Z
DTEND:20220525T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/99
DESCRIPTION:Title: An introduction to C*-algebras\, III\nby Karen Strung (Czech Academy
of Sciences) as part of Noncommutative geometry in NYC\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slawomir Klimek (Indiana University–Purdue University Indianapol
is)
DTSTART:20220427T190000Z
DTEND:20220427T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/100
DESCRIPTION:Title: Smooth subalgebras in noncommutative geometry\nby Slawomir Klimek (I
ndiana University–Purdue University Indianapolis) as part of Noncommutat
ive geometry in NYC\n\n\nAbstract\nIn noncommutative geometry it is often
natural to consider dense *-subalgebras of C*-algebras in particular in co
nnection with cyclic cohomology or with the study of unbounded derivations
on C*-algebras.\nIf C*-algebras are thought of as generalizations of topo
logical spaces\, then dense subalgebras may be regarded as specifying addi
tional structures on the underlying space\, like a smooth structure.\nAt p
resent there is no universally accepted general theory of such smooth suba
lgebras\, however there is a number of "standard" examples defined and stu
died in the literature.\nIn analogy with the algebras of smooth functions
on a compact manifold\, such a smooth subalgebra should have the following
properties:\n(1) It should be closed under holomorphic functional calculu
s of all elements and under smooth-functional calculus of self-adjoint ele
ments\n(2) It should be complete with respect to a locally convex algebra
topology\nThe purpose of the talk is to discuss those concepts on examples
\, including some more recent constructions.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sherry Gong (Texas A&M University)
DTSTART:20220601T190000Z
DTEND:20220601T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/101
DESCRIPTION:Title: The Novikov conjecture\, operator K theory\, and diffeomorphism groups\nby Sherry Gong (Texas A&M University) as part of Noncommutative geomet
ry in NYC\n\n\nAbstract\nIn this talk\, I will discuss some recent work on
a version of the Novikov conjecture for certain subgroups of diffeomorphi
sm groups. This talk will be about joint work with Jianchao Wu\, Zhizhang
Xie\, and Guoliang Yu.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bhishan Jacelon (Czech Academy of Sciences)
DTSTART:20220608T190000Z
DTEND:20220608T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/102
DESCRIPTION:Title: Dynamical applications of C*-classification\nby Bhishan Jacelon (Cze
ch Academy of Sciences) as part of Noncommutative geometry in NYC\n\n\nAbs
tract\nBy the work of many mathematicians\, including Elliott\, Gong\,\nLi
n and Niu\, the class of infinite-dimensional\, simple\, separable\nC*-alg
ebras that have finite nuclear dimension and satisfy the UCT can\nbe class
ified by an invariant based on K-theory and traces. Insofar as\nthe theme
of classification is pervasive throughout science in\ngeneral\, and (nonco
mmutative) topology in particular\, this result is\nan extraordinary feat
of mathematics. What's more\, it provides\npowerful machinery for the anal
ysis of the internal structure of\namenable C*-algebras. In this talk\, I
will explain one such\napplication: In the subclass of classifiable C*-alg
ebras consisting of\nthose for which the simplex of tracial states is none
mpty\, with\nextremal boundary that is compact and has the structure of a
connected\ntopological manifold\, automorphisms can be shown to be generic
ally\ntracially chaotic. Using similar ideas\, I will show how certain sta
bly\nprojectionless C*-algebras can be described as crossed products.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Kuzmin (University of Gothenburg)
DTSTART:20220615T190000Z
DTEND:20220615T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/103
DESCRIPTION:Title: Index theory of hypoelliptic operators on Carnot manifolds\nby Alexe
y Kuzmin (University of Gothenburg) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nWe study the index theory of hypoelliptic operators on
Carnot manifolds -- manifolds whose Lie algebra of vector fields is equipp
ed with a filtration induced from sub-bundles of the tangent bundle. A Hei
senberg pseudodifferential operator\, elliptic in the calculus of van Erp-
Yuncken\, is hypoelliptic and Fredholm. Under some geometric conditions\,
we compute its Fredholm index by means of operator K-theory. These results
extend the work of Baum-van Erp (Acta Mathematica '2014) for co-oriented
contact manifolds to a methodology for solving this index problem geometri
cally on Carnot manifolds. Under the assumption that the Carnot manifold i
s regular\, i.e. has isomorphic osculating Lie algebras in all fibres\, an
d admits a flat coadjoint orbit\, the methodology derived from Baum-van Er
p's work is developed in full detail. In this case\, we develop K-theoreti
cal dualities computing the Fredholm index by means of geometric K-homolog
y a la Baum-Douglas. The duality involves a Hilbert space bundle of flat o
rbit representations. Explicit solutions to the index problem for Toeplitz
operators and operators of the form "ΔH+γT" are computed in geometric K
-homology\, extending results of Boutet de Monvel and Baum-van Erp\, respe
ctively\, from co-oriented contact manifolds to regular polycontact manifo
lds.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhaoting Wei (Texas A&M-Commerce)
DTSTART:20220914T190000Z
DTEND:20220914T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/104
DESCRIPTION:Title: Equivariant K-theory on flag varieties of semisimple Lie groups\nby
Zhaoting Wei (Texas A&M-Commerce) as part of Noncommutative geometry in NY
C\n\n\nAbstract\nLet G be a real semisimple Lie group and X be the flag va
riety of the complexification of G. Kashiwara proposed that there is a dee
p connection between G-equivariant sheaves on X and the representations of
G\, which plays the central role in geometric representation theory. In t
his talk I will discuss a K-theoretic analogue of G-equivariant sheaves\,
namely G-equivariant K-theory on X. I will talk about attempts to compute
such K-theory and its relation with the representation theory of G. I will
do some computation in special cases.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn McCormick (CSU Long Beach)
DTSTART:20220629T190000Z
DTEND:20220629T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/105
DESCRIPTION:Title: Holomorphic subalgebras of $n$-homogeneous $C^*$-algebras\nby Kathry
n McCormick (CSU Long Beach) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nThere is a long tradition of analyzing $C^*$-algebras through
topological invariants. One such result is Tomiyama and Takesaki's 1961 pr
oof that an $n$-homogeneous $C^*$-algebra is determined up to $*$-isomorph
ism by an underlying continuous matrix bundle. Suppose that the base space
of the bundle is a bordered Riemann surface with finitely many smooth bou
ndary components\, and the interior of the bundle is holomorphic. Then for
each such $n$-homogeneous $C^*$-algebra\, one can define a holomorphic su
balgebra. In this talk\, we will describe some progress made towards class
ifying these subalgebras up to complete isometric isomorphism based on the
ir underlying bundles\, including some recent work with Jacob Cornejo.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Alessandrini (Columbia University)
DTSTART:20220921T190000Z
DTEND:20220921T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/106
DESCRIPTION:Title: Non commutative cluster coordinates for Higher Teichmüller Spaces\n
by Daniele Alessandrini (Columbia University) as part of Noncommutative ge
ometry in NYC\n\n\nAbstract\nIn higher Teichmuller theory we study subsets
of the character varieties\nof surface groups that are higher rank analog
s of Teichmuller spaces\,\ne.g. the Hitchin components\, the spaces of max
imal representations and\nthe other spaces of positive representations.\n\
nFock-Goncharov generalized Thurston's shear coordinates and Penner's\nLam
bda-lengths to the Hitchin components\, showing that they have a\nbeautifu
l structure of cluster variety.\n\nWe applied a similar strategy to Maxima
l Representations and we found new\ncoordinates on these spaces that give
them a structure of non-commutative\ncluster varieties\, in the sense defi
ned by Berenstein-Rethak. This is based on a joint\nwork with Guichard\, R
ogozinnikov and Wienhard and one with Berenstein\, Rethak\,\nRogozinnikov
and Wienhard.\n\nIn an project in progress we are generalizing these coord
inates to the other\nsets of positive representations\, using some tools w
e developed.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Etesi (Budapest University of Technology and Economics)
DTSTART:20221026T190000Z
DTEND:20221026T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/107
DESCRIPTION:Title: The universal von Neumann algebra of smooth four-manifolds revisited
\nby Gabor Etesi (Budapest University of Technology and Economics) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nMaking use of its smooth
structure only\, out of a connected\noriented smooth $4$-manifold a von N
eumann algebra is constructed. As a\nspecial four dimensional phenomenon t
his von Neumann algebra contains\nalgebraic (i.e.\, formal or coming from
a metric) curvature tensors of the\nunderlying $4$-manifold and the von Ne
umann algebra itself is a\nhyperfinite factor of ${\\rm II}_1$-type hence
is unique up to abstract\nisomorphisms of von Neumann algebras. Over a fix
ed $4$-manifold this\nuniversal von Neumann algebra admits a particular re
presentation on a\nHilbert space such that its unitary equivalence class i
s preserved by\norientation-preserving diffeomorphisms consequently the Mu
rray--von\nNeumann coupling constant of this representation is well-define
d and gives\nrise to a new and computable real-valued smooth $4$-manifold
invariant.\nIts link with Jones' subfactor theory is noticed as well as co
mputations\nin the simply connected closed case are carried out.\n\nApplic
ation to the cosmological constant problem is also discussed.\nNamely\, th
e aforementioned mathematical construction allows to reformulate\nthe clas
sical vacuum Einstein equation with cosmological constant over a\n$4$-mani
fold as an operator equation over its tracial universal von\nNeumann algeb
ra such that the trace of a solution is naturally identified\nwith the cos
mological constant. This framework permits to use the observed\nmagnitude
of the cosmological constant to estimate by topological means\nthe number
of primordial black holes about the Planck era. This number\nturns out to
be negligable which is in agreement with known density\nestimates based on
the Press--Schechter mechanism.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shirly Geffen (WWU Münster)
DTSTART:20221102T190000Z
DTEND:20221102T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/108
DESCRIPTION:Title: Dynamical comparison of amenable actions by non-amenable groups.\nby
Shirly Geffen (WWU Münster) as part of Noncommutative geometry in NYC\n\
n\nAbstract\nWe pull back boundary-type actions to paradoxical decompositi
ons of the acting group itself. \nIn particular\, we obtain strong paradox
ical structure in non-elementary hyperbolic groups\, in many lattices in L
ie groups\, and in non-elementary Baumslag-Solitar groups.\nThis allows us
to show that whenever such groups admit a minimal amenable topologically
free action on a compact Hausdorff space\, the system has dynamical compar
ison and the attached crossed product is a purely infinite classifiable C*
-algebra.\n\nThis is joint work with Eusebio Gardella\, Julian Kranz\, and
Petr Naryshkin.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Nistor (Université de Lorraine)
DTSTART:20221005T190000Z
DTEND:20221005T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/110
DESCRIPTION:Title: Invariant differential operators acting on quotient spaces and their ind
ex\nby Victor Nistor (Université de Lorraine) as part of Noncommutati
ve geometry in NYC\n\n\nAbstract\nLet $G$ be a compact Lie group acting on
a smooth manifold $M$ (without \nboundary)\,
$E \\to M$ be an equivariant bundle\, and $P$ be a $G$-invariant
\npseudodifferential operator acting on the sections of $
E$. Let $\\alpha$ \nbe an irreducible represen
tation of $G$ and $\\pi_\\alpha(P)$ be the restriction
\nof $P$ to the isotypical component corresponding to $\\alpha$. We stud
y the \nresulting algebra of symbols and we give
a simple\, necessary and sufficient \ncriterion fo
r $\\pi_\\alpha(P)$ to be Fredholm. We also provide a spectral
\nsequence converging to the periodic cyclic homology of t
he corresponding \nalgebra of symbols. This wor
k was done in collaboration with A. Baldare\, \
nM. Benameur\, R. Come\, and M. Lesch.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Kranz (WWU Münster)
DTSTART:20220928T190000Z
DTEND:20220928T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/111
DESCRIPTION:Title: K-theory of noncommutative Bernoulli shifts\nby Julian Kranz (WWU M
ünster) as part of Noncommutative geometry in NYC\n\n\nAbstract\nGiven a
unital C*-algebra A and a discrete group G\, we consider the shift action
of G on the infinite tensor product of G-many copies of A. In many cases\,
we are able to compute the K-theory of the associated reduced crossed pro
duct (for instance when A is finite-dimensional and G is amenable). The to
ols appearing include applications of the Baum-Connes conjecture and eleme
ntary representation theory of finite groups. \nThis is joint work in prog
ress with S. Chakraborty\, S. Echterhoff and S. Nishikawa.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Frei (University of Copenhagen)
DTSTART:20221012T190000Z
DTEND:20221012T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/112
DESCRIPTION:Title: Operator algebras and quantum information: Connes implies Tsirelson and
robust self-testing\nby Alexander Frei (University of Copenhagen) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nWe give a very simpl
e proof of Connes implies Tsirelson\,\nand further advertise a hot topic i
n quantum information: optimal states and robust self-testing. We showcase
here how operator algebraic techniques can be quite fruitful.\n\nFor this
we begin with by recalling quantum strategies in the context of non-local
games\, and their description in terms of the state space on the full gro
up algebra of certain free groups.\n\nWith this description at hand\, we t
hen directly obtain the main result via an elementary lifting result by Ki
m\, Paulsen and Schafhauser:\nthe Connes embedding problem implies the syn
chronous Tsirelson conjecture.\n\nAs such the entire proof is elementary\,
\nand bypasses all versions of Kirchberg's QWEP conjecture and the like\,\
nas well as any reformulation such as in terms of the micro state conjectu
re.\n\nMoreover\, it should be (likely) easier to construct minimal nonloc
al games as counterexamples for the synchronous Tsirelson conjecture (whic
h is equivalent to the full Tsirelson conjecture but in a non-trivial way)
and so also nonamenable traces for above groups\, in other words non-Conn
es embeddable operator algebras.\n\n\n\nAfter this we continue (as much as
time permits) with an advertisement for one of the hottest topics in quan
tum information:\ndevice-independent certification of quantum states\, or
in short ROBUST SELF-TESTING\,\nwhich has tremendous importance for the co
ming era of practical quantum computing.\nand we showcase how operator alg
ebraic techniques can be quite fruitful here.\n\nMore precisely\, we illus
trate these techniques on the following two prominent classes of nonlocal
games:\n\n1) The tilted CHSH game.\nWe showcase here how to compute the qu
antum value using operator algebraic techniques\, and how to use the same
to derive uniqueness for entire optimal states\, including all higher mome
nts as opposed to correlations defined on two-moments only\, where the lat
ter compares to traditional self-testing.\nMoreover\, we report in this ex
ample on previously unknown phase transitions on the uniqueness of optimal
states when varying the parameters for the tilted CHSH game.\n\n2) The Me
rmin--Peres magic square and magic pentagram game.\nAs before\, we also no
te here uniqueness of optimal states\, which in these two examples is a ba
sically familiar result.\n\nThe first part is based on preprint: https://a
rxiv.org/abs/2209.07940\nThe second part on self-testing (and further robu
st self-testing) is based on joint work with Azin Shahiri.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Klisse (TU Delft)
DTSTART:20221019T190000Z
DTEND:20221019T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/113
DESCRIPTION:Title: On the isomorphism class of q-Gaussian C*-algebras\nby Mario Klisse
(TU Delft) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIn 199
1 Bozejko and Speicher introduced a non-commutative version of Brownian mo
tion by defining a family of algebras depending on a parameter −1 ≤ q
≤ 1 that are nowadays commonly known as the q-Gaussian algebras. These a
lgebras interpolate between the extreme Bosonic case q = 1 and the Fermion
ic case q = −1. For q = 0 they coincide with Voiculescu’s free Gaussia
ns. The q-Gaussians can be studied on the level of *-algebras\, on the lev
el of C*-algebras\, and on the level of von Neumann algebras. Whereas it i
s easily seen that in the *-algebraic setting the q-Gaussians all coincide
\, as soon as one passes to the operator algebraic level the question for
the dependence on the parameter q becomes notoriously difficult.\n\nAfter
introducing the necessary background on q-Gaussians\, by considering the s
o-called Akemann-Ostrand property of the canonical inclusion we will discu
ss the dependence of the isomorphism class of q-Gaussian C*-algebras on th
e parameter q. This partially answers a question by Nelson and Zeng.\n\nTh
e talk is baised on joint work with Matthijs Borst\, Martijn Caspers and M
ateusz Wasilewski.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergii Bezuglyi (University of Iowa)
DTSTART:20221115T190000Z
DTEND:20221115T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/114
DESCRIPTION:Title: Dynamics and measures on generalized Bratteli diagrams\nby Sergii Be
zuglyi (University of Iowa) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nIn the talk\, I discuss measures on the path space of\ngeneral
ized Bratteli diagrams. We consider self-similar measures (called\nalso IF
S measures) on the path space of discrete and measurable Bratteli\ndiagram
s. In the literature\, similarity may be defined by systems of\naffine map
s (Sierpinski) or systems of conformal maps (Julia). We study\nnew classes
of iterated function systems associated to stationary generalized\nBratte
li diagrams. For the corresponding iterated function\nsystems\, we further
identify the measures which are also shift-invariant.\nThe talk is based
on joint papers with Palle Jorgensen.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Marciniak (University of Gdansk)
DTSTART:20221109T200000Z
DTEND:20221109T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/115
DESCRIPTION:Title: Positive maps on operator algebras – some problems and some solutions<
/a>\nby Marcin Marciniak (University of Gdansk) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nIn the last decade\, the theory of positive
maps on operator algebras has gained increased importance as it has been
shown to have numerous applications in quantum information theory. We will
present an overview of the basic topics of this theory\, in particular th
e characterization of extreme positive maps or the problem of decomposabil
ity. One of the intensively studied recently problems is the question of t
he existence of entangled PPT states with high Schmidt number. In the lang
uage of positive maps\, this is equivalent to the existence of indecomposa
ble k-positive maps for large values of k.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klaus Thomsen (Aarhus University)
DTSTART:20221130T200000Z
DTEND:20221130T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/116
DESCRIPTION:Title: The structure of KMS states for flows on an AF algebra\nby Klaus Tho
msen (Aarhus University) as part of Noncommutative geometry in NYC\n\n\nAb
stract\nIn a recent work with George Elliott we have obtained a complete d
escription of the configurations of KMS states that occur for flows on a u
nital simple infinite dimensional AF algebra. The answer is that they all
do\, provided only that the simplex of 0-KMS states is affinely homeomorph
ic to the tracial state space of the AF algebra\; a condition which is obv
iously necessary. In the talk I will explain the road to this conclusion\,
which can be seen as the culmination of work and ideas that go back more
than 40 years and has involved very many mathematicians.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andre Kornell (Dalhousie University)
DTSTART:20230125T200000Z
DTEND:20230125T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/117
DESCRIPTION:Title: Categories of Hilbert spaces\nby Andre Kornell (Dalhousie University
) as part of Noncommutative geometry in NYC\n\n\nAbstract\nHilbert spaces
form one category with bounded operators and another category with contrac
tions. I will present axioms for each of these two categories. These axiom
s are interesting because they make no explicit reference to the real numb
er system. The proof appeals to Soler's theorem and to the theory of dagge
r categories\, as well as to a few familiar results from operator theory.\
n
LOCATION:https://researchseminars.org/talk/NYC-NCG/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolai L. Vasilevski (CINVESTAV\, Mexico City)
DTSTART:20230201T200000Z
DTEND:20230201T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/118
DESCRIPTION:Title: Commutative algebras of Toeplitz operators on the disk: Spectral theorem
approach\nby Nikolai L. Vasilevski (CINVESTAV\, Mexico City) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nFor three standard models
of commutative algebras generated by Toeplitz\noperators in the weighted
analytic Bergman space on he unit disk\, we\nfind their representations as
the algebras of bounded functions of\ncertain unbounded self-adjoint oper
ators. We discuss main properties of\nthese representation and\, especiall
y\, describe relations between\nproperties of the spectral function of Toe
plitz operators in the\nspectral representation and properties of the symb
ols.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco D'Andrea (Università di Napoli Federico II)
DTSTART:20230208T200000Z
DTEND:20230208T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/120
DESCRIPTION:Title: CW structures in noncommutative geometry\nby Francesco D'Andrea (Uni
versità di Napoli Federico II) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nI will illustrate some examples and ideas for a theory of C
W complexes in noncommutative geometry. In order to accommodate some impor
tant examples\, instead of diagrams in the category of quantum spaces (dua
l to C*-algebras) one is forced to work with a suitable homotopy category.
In this category\, K-theory computations are made possible through the us
e of a Mayer-Vietoris sequence. The K-theory of a quantum space can be pro
moted from a plain abelian group to an augmented ring (in the sense of Car
tan-Eilenberg)\, giving a finer topological invariant. The construction of
this invariant suggests a notion of "topology" and "continuity" in the qu
antum setting (a kind of Grothendieck topology). This is a work in progres
s in collaboration with P.M. Hajac\, T. Maszczyk\, A. Sheu\, and B. Zielin
ski.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Wulff (University of Göttingen)
DTSTART:20230215T200000Z
DTEND:20230215T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/121
DESCRIPTION:Title: Generalized asymptotic algebras and E-theory for non-separable C*-algebr
as\nby Christopher Wulff (University of Göttingen) as part of Noncomm
utative geometry in NYC\n\n\nAbstract\nMany common ad hoc definitions of b
ivariant K-theory for\nnon-separable C*-algebras have some kind of drawbac
k\, usually that one\ncannot expect the long exact sequences to hold in fu
ll generality. I\nwill present a way to define E-theory for non-separable
C*-algebras\nwithout such disadvantages via a generalized notion of asympt
otic\nalgebras. There is indication that canonical cycles of this new mode
l\nmight arise naturally in index theory on infinite dimensional manifolds
.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shanna Dobson (CSU Los Angeles)
DTSTART:20230105T140000Z
DTEND:20230105T150000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/122
DESCRIPTION:Title: Six Operations on Diamond Topos\nby Shanna Dobson (CSU Los Angeles)
as part of Noncommutative geometry in NYC\n\n\nAbstract\nThis talk is part
of the Special Session on the Langlands Program\, JMM 2023 in Boston\, MA
.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Prokhorova (Technion)
DTSTART:20230222T200000Z
DTEND:20230222T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/123
DESCRIPTION:Title: Index theory of unbounded Fredholm operators\nby Marina Prokhorova (
Technion) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIndex t
heory for norm continuous families of bounded Fredholm operators was devel
oped in the classical work of Atiyah\; its analog for self-adjoint operato
rs was developed in the work of Atiyah and Singer. The index theory of ell
iptic differential operators on closed manifolds is based on these classic
al results: one can pass from operators of positive order to operators of
zeroth order\, and such a transformation is continuous.\n\nHowever\, in ot
her situations one needs to deal with weaker topologies on the space of un
bounded operators. For example\, for elliptic boundary value problems on c
ompact manifolds with boundary\, the graphs of corresponding unbounded ope
rators depend continuously on parameter. The topology determined by passin
g from a closed operator to its graph is called the graph topology. The ho
motopy type of relevant spaces of unbounded Fredholm operators was determi
ned by M. Joachim in 2003.\n\nMy talk is devoted to an index theory of gra
ph continuous families of unbounded Fredholm operators in a Hilbert space.
I will show how this theory is related to the classical index theory of b
ounded Fredholm operators. The talk is based on my recent preprints arXiv:
2110.14359 and arXiv:2202.03337.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feodor Kogan (University of Toronto)
DTSTART:20230301T200000Z
DTEND:20230301T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/124
DESCRIPTION:Title: Overview of Cartan subalgebras in operator algebras\nby Feodor Kogan
(University of Toronto) as part of Noncommutative geometry in NYC\n\n\nAb
stract\nSimilar to the setting of Lie algebras\, a Cartan subalgebra in a
C*-algebra is a maximal abelian subalgebra with some additional properties
. Unlike the setting of Lie algebras Cartan subalgebras might not exist\,
and if they do\, they are rarely unique. I will give an overview of old an
d new results concerning Cartan subalgebras in C*-algebras with an emphasi
s on their relation to groupoids.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Voigt (University of Glasgow)
DTSTART:20230308T200000Z
DTEND:20230308T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/125
DESCRIPTION:Title: Infinite quantum permutations\nby Christian Voigt (University of Gla
sgow) as part of Noncommutative geometry in NYC\n\n\nAbstract\nQuantum sym
metries feature naturally in the study of quantum groups\, subfactors and
quantum information. In this talk I will present an approach to study quan
tum symmetries of infinite graphs. This leads to new examples of discrete
quantum groups\, linking naturally with previous work in the case of finit
e graphs. I will discuss a number of concrete examples\, and also highligh
t some intriguing open problems.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severino T. Melo (Universidade de São Paulo)
DTSTART:20230315T190000Z
DTEND:20230315T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/126
DESCRIPTION:Title: Pseudodifferential operators in strict deformation quantization\nby
Severino T. Melo (Universidade de São Paulo) as part of Noncommutative ge
ometry in NYC\n\n\nAbstract\nMost of the talk will be about old results of
H. O. Cordes\, Marcela Merklen and myself about characterizations of pseu
dodifferential\noperators as smooth vectors for actions of the Heisenberg
group. Then I will announce related results recently obtained with Rodrigo
Cabral and Michael Forger\nabout a class of pseudodifferential operators
with $C^*$-algebra-valued symbols introduced by M. Rieffel in his construc
tion of a "strict deformation\nquantization" for a $C^*$-algebra with an a
ction of $R^n$. We have proven the uniqueness of the $C^*$-norm for Rieffe
l's (non complete) algebra and have\nalso proven a conjecture of Rieffel w
hich characterizes his pseudodifferential operators as the smooth vectors
for an action of the Heisenberg group.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Yu. Pirkovskii (HSE Moscow)
DTSTART:20230329T190000Z
DTEND:20230329T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/127
DESCRIPTION:Title: Nonformal deformations of algebras of holomorphic functions\nby Alex
ei Yu. Pirkovskii (HSE Moscow) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nFormal deformations of associative algebras are by now class
ical and relatively well-studied objects. They were introduced by Gerstenh
aber in 1964\, and they are interesting especially because of their relati
on to deformation quantization. By contrast\, the theory of nonformal defo
rmations is now at a much earlier stage of development. Roughly\, a gener
al feature of all existing approaches to nonformal deformations\, which di
stinguishes them from formal deformations\, is that the role of the "base"
ring is now played by a certain algebra of functions (continuous\, or smo
oth\, or holomorphic...) rather than by the algebra of formal power series
. This makes nonformal deformations quite attractive from the physical poi
nt of view\, because they allow evaluating the deformed star product at co
ncrete nonzero values of the deformation parameter (Planck's constant). In
this talk\, our main objects will be nonformal (or\, more exactly\, holom
orphic) deformations of the algebras of holomorphic functions on the polyd
isc and on the ball in $\\mathbb{C}^n$. We will discuss some properties of
such deformations and their relation to formal deformations. If time perm
its\, we will compare our approach to holomorphic deformations with S. Wal
dmann's approach\, which is better adapted to deformation quantization\, b
ut which applies only to some proper subalgebras of the algebras of holomo
rphic functions.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elias G. Katsoulis (East Carolina University)
DTSTART:20230419T190000Z
DTEND:20230419T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/128
DESCRIPTION:Title: Isomorphisms and stable isomorphisms of non-selfadjoint operator algebra
s\nby Elias G. Katsoulis (East Carolina University) as part of Noncomm
utative geometry in NYC\n\n\nAbstract\nIn this talk we address isomorphism
s and stable isomorphisms of various\nclasses of operator algebras. We sta
te and resolve the isomorphism problem for\ntensor algebras of unital mult
ivariable dynamical systems. Specifically we show\nthat unitary equivalenc
e after a conjugation for multi-variable dynamical systems\nis a complete
invariant for complete isometric isomorphisms between their tensor\nalgebr
as. In particular\, this settles a conjecture of Davidson and Kakariadis r
elating\nto work of Arveson from the sixties\, and extends related work of
Kakariadis and\nKatsoulis.\n\nWe also address stable isomorphism of opera
tor algebras\, in connection with a\nrecent work of Dor-On\, Eilers and Ge
ffen. Among others we show that if $\\mathcal{A}$\n and $\\mathcal{B}$ are
operator algebras with diagonals isomorphic to $c_0$ and \n$\\mathcal{K}$
are the compact\noperators\, then $\\mathcal{A}\\otimes\\mathcal{K}$ and
$\\mathcal{B}\\otimes\\mathcal{K}$\nare isometrically isomorphic if and on
ly if $\\mathcal{A}$ and\n$\\mathcal{B}$ are isometrically isomorphic. If
the algebras $\\mathcal{A}$ and $\\mathcal{B}$ satisfy an extra analyticit
y\ncondition\, a similar result holds with $\\mathcal{K}$ being replaced b
y any operator algebra\ncontaining the compact operators. Time permitting
we will discuss other classes\nof operator algebras and their stable isomo
rphisms\, including tensor algebras of\nmultivariable dynamical systems.\n
\nThe above results come from various projects with C. Ramsey\, E. Kakaria
dis\nand X. Lin.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anar Dosi (Middle East Technical University\, Cyprus)
DTSTART:20230412T170000Z
DTEND:20230412T180000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/129
DESCRIPTION:Title: Projective positivity of the function systems\nby Anar Dosi (Middle
East Technical University\, Cyprus) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nThe present talk is devoted to the projective positivit
y in the category of function systems. It is an operator positivity occurr
ed in the quantization problems of the operator systems. It turns out that
every $∗$-(poly)normed topology compatible with a duality results in th
e (local) projective positivity given by a filter base of the unital cones
with its separated intersection. We describe the (local) projective posit
ivity of the (local) $L^{p}$-spaces given by a bounded (or unbounded) posi
tive Radon measure on a locally compact topological space. The geometry of
the related state spaces is described in the case of $L^{p}$-spaces\, Sch
atten matrix spaces\, and $L^{p}$-spaces of a finite von Neumann algebra.\
n
LOCATION:https://researchseminars.org/talk/NYC-NCG/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitris Gerontogiannis (Leiden University)
DTSTART:20230426T190000Z
DTEND:20230426T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/130
DESCRIPTION:Title: Smale spaces and their dimension theory\nby Dimitris Gerontogiannis
(Leiden University) as part of Noncommutative geometry in NYC\n\n\nAbstrac
t\nSmale spaces were defined by David Ruelle in the 1970's as topological
models for the typically fractal-like hyperbolic nonwandering sets of Step
hen Smale's Axiom A systems. A Smale space is a compact metric space toget
her with a homeomorphism having exponential contraction and expansion beha
viour. Prototype examples are the topological Markov chains\, aperiodic su
bstitution tilings and hyperbolic toral automorphisms. This talk will give
an example-driven introduction to Smale spaces with a focus on their dime
nsion theory\, which can be studied via Markov partitions and Ahlfors regu
lar measures. If time permits\, I will briefly mention how the dimension t
heory of a Smale space is related to fine analytic properties of the opera
tor algebras encoding the stable and unstable foliations on it.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Raad (KU Leuven)
DTSTART:20230517T190000Z
DTEND:20230517T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/131
DESCRIPTION:Title: Inductive Limit Cartan Subalgebras\nby Ali Raad (KU Leuven) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nIn recent years the inter
est for Cartan subalgebras in C*-algebras has risen due to new connections
found with topological dynamics and geometric group theory\, as well as t
he classification programme for C*-algebras. For this\, the study of Carta
n subalgebras in inductive limit C*-algebras is fundamental. I will give a
n overview of this topic as well as provide some new existence and uniquen
ess results for inductive limit Cartan subalgebras.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Bunke (Universität Regensburg)
DTSTART:20230524T190000Z
DTEND:20230524T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/132
DESCRIPTION:Title: A homotopical view on $K$ and $KK$-theory for $C^{*}$-algebras\nby U
lrich Bunke (Universität Regensburg) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nThe goal of this talk is to motivate the consideratio
n of spectrum-valued K-theory for $C^{*}$-algebras. To this end I will dis
cuss some examples where the spectrum-valued functor helps to simplify c
lassical statements and their justification. I will then explain how to co
nstruct a spectrum-valued $K$-theory functor using a homotopical refineme
nt of KK-theory. Accepting the language of $\\infty$-categories\, the latt
er can be obtained in a straightforward way by forcing the desired unive
rsal properties.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Pander Maat (Queen Mary University)
DTSTART:20230913T190000Z
DTEND:20230913T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/133
DESCRIPTION:Title: Hilbert Modules over C*-categories\nby Arthur Pander Maat (Queen Mar
y University) as part of Noncommutative geometry in NYC\n\n\nAbstract\nC*-
categories are a ‘horizontal categorification’ of C*-algebras\, and th
ey have a theory of Hilbert modules which generalizes that over C*-algebra
s. We go through some results about these modules\, culminating in an Eile
nberg-Watts theorem that characterizes which functors between module categ
ories are given by tensor products. We finish with some new work employing
this result\, along with work of Benjamin Duenzinger’s\, to exhibit a l
ocalization of the category of locally small C*-categories at the Morita e
quivalences.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernard Russo (UC Irvine)
DTSTART:20230906T190000Z
DTEND:20230906T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/134
DESCRIPTION:Title: Anti-$C^*$-algebras\nby Bernard Russo (UC Irvine) as part of Noncomm
utative geometry in NYC\n\n\nAbstract\nWe introduce a class of Banach alge
bras that we call\nanti-$C^*$-algebras. We show that the normed standard
embedding of a\n$C^*$-ternary ring is the direct sum of a $C^*$-algebra an
d an\nanti-$C^*$-algebra. We prove that C*-ternary rings and anti-$C^*$-al
gebras are\nsemisimple. We give two new characterizations of $C^*$-ternary
rings which\nare isomorphic to a TRO (ternary ring of operators)\, provid
ing answers\nto a query raised by Zettl in 1983\, and we propose some prob
lems for\nfurther study. (Joint work with Robert Pluta)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gihyun Lee (Ghent University)
DTSTART:20230920T190000Z
DTEND:20230920T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/135
DESCRIPTION:Title: $L_p$-bounds for pseudodifferential operators on curved noncommutative t
ori\nby Gihyun Lee (Ghent University) as part of Noncommutative geomet
ry in NYC\n\n\nAbstract\nIn the theory of pseudodifferential operators\, o
ne of the most essential topics is the study of mapping properties of pseu
dodifferential operators between various kinds of function spaces. The inv
estigation of $L_p$-boundedness of pseudodifferential operators is particu
larly important\, considering its consequences for the regularity and exis
tence of solutions of PDEs.\n\nThe purpose of this talk is to discuss the
counterpart of this problem on noncommutative tori. Noncommutative tori ar
e the most intensively studied noncommutative spaces in noncommutative geo
metry and arise in various parts of mathematics and mathematical physics.
Pseudodifferential calculus on noncommutative tori was introduced in early
1980s by A. Connes\, and it has emerged as an indispensable tool in the r
ecent study of differential geometry of noncommutative tori. Meanwhile\, J
. Rosenberg introduced the notion of Riemannian metric on noncommutative t
ori a decade ago. In this talk\, I will first recall the notion of a curve
d noncommutative torus\, i.e.\, a noncommutative torus endowed with a Riem
annian metric in the sense of J. Rosenberg. I will then show the boundedne
ss of pseudodifferential operators on noncommutative $L_p$-spaces associat
ed with the volume form induced by a Riemannian metric. Based on joint wor
k with V. Kumar.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pawel Sarkowicz (University of Ottawa)
DTSTART:20230927T190000Z
DTEND:20230927T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/136
DESCRIPTION:Title: Tensorially absorbing inclusions of C*-algebras\nby Pawel Sarkowicz
(University of Ottawa) as part of Noncommutative geometry in NYC\n\n\nAbst
ract\nWe introduce the notion of a tensorially absorbing inclusion -- that
is\, when an inclusion absorbs a strongly self-absorbing C*-algebra in a
suitable way. We discuss various properties\, central sequence characteriz
ations\, give examples and non-examples\, and provide some applications an
d natural open questions.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlie Beil (University of Graz)
DTSTART:20231004T190000Z
DTEND:20231004T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/137
DESCRIPTION:Title: Nonnoetherian geometry\, noncommutative desingularizations\, and quantum
theory\nby Charlie Beil (University of Graz) as part of Noncommutativ
e geometry in NYC\n\n\nAbstract\nI will introduce a new kind of geometry t
hat arises from nonnoetherian subalgebras of polynomial rings\, and\, more
generally\, coordinate rings of affine varieties. In this construction\,
points may be 'smeared-out' and have positive dimension. I will then descr
ibe an application of this geometry to a class of noncommutative algebras
defined by oriented graphs in surfaces\, called dimer and ghor algebras. T
he geometry allows these algebras to be viewed as noncommutative desingula
rizations of their centers\, and yields relationships between their repres
entation theory and the surface topology. Finally\, I will sketch an appli
cation of the geometry to a new spacetime model of spin and its wave funct
ion collapse.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joakim Arnlind (Linköping University)
DTSTART:20231011T190000Z
DTEND:20231011T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/138
DESCRIPTION:Title: Noncommutative Riemannian Geometry of Kronecker Algebras\nby Joakim
Arnlind (Linköping University) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nDifferential calculus in noncommutative geometry come in se
veral different flavors\, and one of the more concrete versions goes by th
e name of derivation based differential calculus. This calculus is built f
rom a disinguished Lie algebra of derivations\, and lead to the formulatio
n of differential forms\, cohomology and connections. A fundamental questi
on in noncommutative Riemannian geometry is the existence and uniqueness o
f a torsion free and metric compatible connection\; i.e a Levi-Civita conn
ection. For the moment\, there are no general results addressing this ques
tion in this context\, and I will present a case study based on a simple q
uiver path algebra\, and show how the existence of a Levi-Civita connectio
n depend on the choice of a Lie algebra of derivations.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wade Bloomquist (Morningside University)
DTSTART:20231018T190000Z
DTEND:20231018T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/139
DESCRIPTION:Title: Quantum Traces and Degenerations\nby Wade Bloomquist (Morningside Un
iversity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nSkein a
lgebras of surfaces describe a multiplication for curves on surfaces\, whi
ch remembers the poisson structure on the ring of regular functions of the
character variety of the surface. Quantum trace maps\, introduced by Bon
ahon and Wong\, show how skein algebras of punctured surfaces can be embed
ded into well-behaved algebras called quantum tori. Our discussion will f
ocus on a joint generalization of skein algebras\, which captures the hype
rbolic geometry seen in Roger-Yang skein algebras and the quantum group co
module structure seen in stated skein algebras. This generalization is a
key tool in building a quantum trace map for degenerations (coming from fi
ltrations) of skein algebras of closed surfaces. As time permits we will
discuss some applications. A strong effort will be made to introduce thes
e topics at the expense of some technical details. This work is joint wit
h Thang Le and Hiroaki Karuo.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Peterson (Vanderbilt University)
DTSTART:20231101T190000Z
DTEND:20231101T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/140
DESCRIPTION:Title: Biexact groups and von Neumann algebras\nby Jesse Peterson (Vanderbi
lt University) as part of Noncommutative geometry in NYC\n\n\nAbstract\nTh
e notion of biexactness for groups was introduced by Ozawa in 2004 and has
since become one of the major tools for studying decomposability properti
es for von Neumann algebras. I will survey the development of biexactness
over the last two decades\, and I will discuss a joint project with Changy
ing Ding where we introduce biexact von Neumann algebras and frame many of
these results in this more general setting.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Christopher Phillips (University of Oregon and Fields Institute
for Research in Mathematical Sciences)
DTSTART:20231025T190000Z
DTEND:20231025T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/141
DESCRIPTION:Title: The radius of comparison of C (X) is about half the covering dimension o
f X\nby N. Christopher Phillips (University of Oregon and Fields Insti
tute for Research in Mathematical Sciences) as part of Noncommutative geom
etry in NYC\n\n\nAbstract\nRecall that a C*-algebra $A$ has strict compari
son of projections\nif whenever $p$ and $q$ are projections in matrix alge
bras over $A$\,\nand $\\tau (p) < \\tau (q)$ for all tracial states $\\tau
$ on $A$\,\nthen $p$ is Murray-von Neumann subequivalent to $q$.\nIn conne
ction with the Elliott\nclassification program\, and because many simple C
*-algebras have\nvery few projections\, this has been extended to comparis
on of\ngeneral positive elements.\n(This will be explained in the talk.)\n
Strict comparison holds\nfor unital stably finite classifiable simple C*-a
lgebras.\nThe radius of comparison ${\\mathrm{rc}} (A)$ of a C*-algebra $A
$\nis a numerical measure of the failure of strict comparison.\nIt is zero
if strict comparison holds\,\nand in general is a not so well understood
kind of topological dimension.\n\nLet $X$ be a compact metric space.\nIt h
as been known for some time that ${\\mathrm{rc}} (C (X))$\nis at most abou
t half the covering dimension of $X$.\nIn 2013\, Elliott and Niu proved th
at ${\\mathrm{rc}} (C (X))$ is\,\nup to an additive constant\,\nat least h
alf the rational cohomological dimension of $X$.\nRecently\, we proved tha
t\, up to a slightly worse additive constant\,\n${\\mathrm{rc}} (C (X))$ i
s at least half the covering dimension of $X$\,\nwhich is sometimes much l
arger.\nThis shows that ${\\mathrm{rc}} (A)$\, like stable rank\, roughly\
ncorresponds to covering dimension\, not to rational or integral\ncohomolo
gical dimension\, and not to some previously unknown dimension.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iason Moutzouris (Purdue University)
DTSTART:20231115T200000Z
DTEND:20231115T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/142
DESCRIPTION:Title: When amenable groups have real rank zero $C^*$-algebras?\nby Iason M
outzouris (Purdue University) as part of Noncommutative geometry in NYC\n\
n\nAbstract\nFor every torsion free\, discrete and amenable group $G$\, th
e Kadison-Kaplansky conjecture has been verified\, so $C^*(G)$ has no nont
rivial projections. On the other hand\, every torsion element $g\\in G$\,
of order $n$\, gives rise to a projection $\\frac{1+g+...+g^{n-1}}{n}\\in
C^*(G)$. Actually\, if $G$ is locally finite\, then $C^*(G)$ is an AF-alge
bra\, so it has an abundance of projections. So\, it is natural to ask wh
at happens when the group has both torsion and\nnon-torsion elements. A re
sult on this direction came from Scarparo\, who showed that for every disc
rete\, infinite\, finitely generated elementary amenable group\, $C^*(G)$
cannot have real rank zero. In this talk\, we will explain why if $G$ is
discrete\, amenable and $C^*(G)$ has real rank zero\, then all elementary
amenable normal subgroups with finite Hirsch length must be locally finite
.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Christopher Phillips (University of Oregon)
DTSTART:20240507T190000Z
DTEND:20240507T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/143
DESCRIPTION:Title: Minicourse: An invitation to mean dimension of a dynamical system and
the radius of comparison of its crossed product\, I\nby N. Christophe
r Phillips (University of Oregon) as part of Noncommutative geometry in NY
C\n\n\nAbstract\nPrerequisites (optional): \n\n1. https://sju.webex.com/re
cordingservice/sites/sju/recording/e0819482c399103cbf7c005056812d4c/playba
ck\n\n2. https://sju.webex.com/recordingservice/sites/sju/recording/480a92
c95598103cae68005056819173/playback\n\n\nThe purpose of this minicourse is
to explain the background\n(including the terms below) and some progress
towards the following conjecture\, relating topological dynamics to the st
ructure of the crossed product $C^*$-algebra.\n\nLet $G$ be a countable am
enable group\, let $X$ be a compact metrizable space\,\nand let $T$ be an
action of $G$ on $X$. The mean dimension $mdim ~(T)$ is a \npurely dynamic
al invariant\, designed so that the mean dimension of the shift \non $([0\
, 1]^d)^G$ is equal to $d$. The radius of comparison $rc ~(A)$ of a \nunit
al $C^*$-algebra $A$ is a numerical measure of failure of comparison\nin t
he Cuntz semigroup of $A$\, a generalization of unstable K-theory.\nIt was
introduced to distinguish $C^*$-algebras having no connection\nwith dynam
ics. The conjecture asserts that if $T$ is free and minimal\,\nthen $rc ~(
C^* (G\, X\, T)) = \\frac{1}{2} ~mdim ~(T)$. The inequality\n$rc ~(C^* (G\
, X\, T)) \\leq \\frac{1}{2} ~mdim ~(T)$ is known for \n$G = {\\mathbb{Z}}
^n$\, and progress towards the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\
frac{1}{2} ~mdim ~(T)$ has been made for the known \nclasses of examples o
f free minimal actions with nonzero mean dimension\,\nfor any countable am
enable group $G$. The emphasis will be on the inequality\n$rc ~(C^* (G\, X
\, T)) \\geq \\frac{1}{2} ~mdim ~(T)$\;\nthe results there are joint work
with Ilan Hirshberg.\n\n\nLecture 1. \n\nThis lecture will be mainly about
dynamical systems.\nAfter an introduction\, we will review the crossed pr
oduct $C^*$-algebra associated to a\ndynamical system\, and then describe
the mean dimension of a dynamical system.\nTime permitting\, we will start
the discussion of comparison of projections in \n$C^*$-algebras.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Christopher Phillips (University of Oregon)
DTSTART:20240514T190000Z
DTEND:20240514T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/144
DESCRIPTION:Title: Minicourse: An invitation to mean dimension of a dynamical system and
the radius of comparison of its crossed product\, II\nby N. Christophe
r Phillips (University of Oregon) as part of Noncommutative geometry in NY
C\n\n\nAbstract\nThe purpose of this minicourse is to explain the backgrou
nd\n(including the terms below) and some progress towards the following co
njecture\, relating topological dynamics to the structure of the crossed p
roduct $C^*$-algebra.\n\nLet $G$ be a countable amenable group\, let $X$ b
e a compact metrizable space\,\nand let $T$ be an action of $G$ on $X$. Th
e mean dimension $mdim ~(T)$ is a \npurely dynamical invariant\, designed
so that the mean dimension of the shift \non $([0\, 1]^d)^G$ is equal to $
d$. The radius of comparison $rc ~(A)$ of a \nunital $C^*$-algebra $A$ is
a numerical measure of failure of comparison\nin the Cuntz semigroup of $A
$\, a generalization of unstable K-theory.\nIt was introduced to distingui
sh $C^*$-algebras having no connection\nwith dynamics. The conjecture asse
rts that if $T$ is free and minimal\,\nthen $rc ~(C^* (G\, X\, T)) = \\fra
c{1}{2} ~mdim ~(T)$. The inequality\n$rc ~(C^* (G\, X\, T)) \\leq \\frac{1
}{2} ~mdim ~(T)$ is known for \n$G = {\\mathbb{Z}}^n$\, and progress towar
ds the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\frac{1}{2} ~mdim ~(T)$ h
as been made for the known \nclasses of examples of free minimal actions w
ith nonzero mean dimension\,\nfor any countable amenable group $G$. The em
phasis will be on the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\frac{1}{2
} ~mdim ~(T)$\;\nthe results there are joint work with Ilan Hirshberg.\n\n
Lecture 2.\n\nThis lecture will be mainly about comparison in $C^*$-algebr
as.\nWe will describe comparison properties\, first for projections and th
en for positive elements.\nThen we define the radius of comparison\, and s
how how it is related to ``noncommutative dimension''.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Christopher Phillips (University of Oregon)
DTSTART:20240521T190000Z
DTEND:20240521T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/145
DESCRIPTION:Title: Minicourse: An invitation to mean dimension of a dynamical system and
the radius of comparison of its crossed product\, III\nby N. Christop
her Phillips (University of Oregon) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nThe purpose of this minicourse is to explain the backgr
ound\n(including the terms below) and some progress towards the following
conjecture\, relating topological dynamics to the structure of the crossed
product $C^*$-algebra.\n\nLet $G$ be a countable amenable group\, let $X$
be a compact metrizable space\,\nand let $T$ be an action of $G$ on $X$.
The mean dimension $mdim ~(T)$ is a \npurely dynamical invariant\, designe
d so that the mean dimension of the shift \non $([0\, 1]^d)^G$ is equal to
$d$. The radius of comparison $rc ~(A)$ of a \nunital $C^*$-algebra $A$ i
s a numerical measure of failure of comparison\nin the Cuntz semigroup of
$A$\, a generalization of unstable K-theory.\nIt was introduced to disting
uish $C^*$-algebras having no connection\nwith dynamics. The conjecture as
serts that if $T$ is free and minimal\,\nthen $rc ~(C^* (G\, X\, T)) = \\f
rac{1}{2} ~mdim ~(T)$. The inequality\n$rc ~(C^* (G\, X\, T)) \\leq \\frac
{1}{2} ~mdim ~(T)$ is known for \n$G = {\\mathbb{Z}}^n$\, and progress tow
ards the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\frac{1}{2} ~mdim ~(T)$
has been made for the known \nclasses of examples of free minimal actions
with nonzero mean dimension\,\nfor any countable amenable group $G$. The
emphasis will be on the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\frac{1}
{2} ~mdim ~(T)$\;\nthe results there are joint work with Ilan Hirshberg.\n
\n\nLecture 3.\n\nIn this lecture\, we state some known results towards th
e conjecture \n$rc ~(C^* (G\, X\, T)) = \\frac{1}{2} ~mdim ~(T)$\,\nand sa
y something about the ideas which go into the results\ntowards the inequal
ity $rc ~(C^* (G\, X\, T)) \\geq \\frac{1}{2} ~mdim ~(T)$.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Skeide (Università degli Studi del Molise)
DTSTART:20231129T200000Z
DTEND:20231129T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/146
DESCRIPTION:Title: Partial Isometries Between Hilbert Modules\nby Michael Skeide (Unive
rsità degli Studi del Molise) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nHilbert modules are Banach spaces and share\, of course\, al
l their good properties. But geometrically they behave - as opposed with t
he very well-behaved Hilbert spaces - very much like pre-Hilbert spaces.\n
\nAs a common root of most problems - if not all - one may highlight the
fact that Hilbert modules need not be self-dual\; one of the most striking
consequences of missing self-duality is the fact that not all bounded mod
ules maps need to possess an adjoint. (Intimately related: not all closed
submodules are the range of a projection.) This raises the question how to
define isometries\, cosisometries\, and partial isometries between Hilber
t modules\, without requiring explicitly in the definition that these maps
are adjointable.\n\nWhile the definition of isometries (as inner product
preserving maps) is rather natural and well-known since long (they need no
t be adjointable)\, our definitions (proposed with Orr Shalit) of coisomet
ries (they turn out to be adjointable) and partial isometries (they need n
ot be adjointable) are rather recent.\n\nAs a specific problem\, we will a
ddress the question how to find a (reasonable) composition law among parti
al isometries (making them the morphisms of a category). It turns out that
for Hilbert spaces the problem can be solved\, while for Hilbert modules
we have to pass to the *partially defined* isometries. The proofs of some
of the intermediate statements explore typical features of proofs in Hilbe
rt module theory: Some are like those for Hilbert spaces\; some reduce the
proof (by means of a well-known technical tool) to that for Hilbert space
s\; and some are simply ``different''. (Of course\, the latter also for wo
rk Hilbert spaces\; but they are ``different'' from what you would write d
own with all you arsenal of Hilbert space methods at your disposal.)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Manuilov (Moscow State University)
DTSTART:20231122T200000Z
DTEND:20231122T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/147
DESCRIPTION:Title: Metrics on doubles as an inverse semigroup\nby Vladimir Manuilov (Mo
scow State University) as part of Noncommutative geometry in NYC\n\n\nAbst
ract\nUsually metrics do not form an algebraic structure. I was interested
in various metrics on two copies (double) of a metric space $(X\,d)$ such
that the metric on each copy is $d$\, and only distances between points o
n different copies of $X$ may vary. To my surprise\, if one passes from me
trics to their equivalence classes (either quasi-equivalence or coarse equ
ivalence) then the metrics on the double of $X$ form an inverse semigroup.
Inverse semigroups are similar to sets of partial isometries on a Hilbert
space\, and one may define a C*-algebra of an inverse semigroup along the
same guidelines as group C*-algebras. I shall speak about some results on
these inverse semigroups\, e.g. when they are commutative\, and when they
have a kind of finiteness property\, i.e. when the unit is Murray-von Neu
mann equivalent to a proper projection.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Steinberg (City College of New York)
DTSTART:20231206T200000Z
DTEND:20231206T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/148
DESCRIPTION:Title: Simplicity of inverse semigroup and etale groupoid algebras\nby Benj
amin Steinberg (City College of New York) as part of Noncommutative geomet
ry in NYC\n\n\nAbstract\nWe survey some of the results on simplicity of al
gebras of ample groupoids over fields\, culminating with the definitive re
sults of the speaker and Szakacs. We indicate some applications to an old
question of Munn from the 70s on simplicity of inverse semigroups algebra
s and to Nekrashevych algebras of self-similar groups.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Francis (University of Western Ontario)
DTSTART:20240124T200000Z
DTEND:20240124T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/149
DESCRIPTION:Title: Holonomy and the Newlander-Nirenberg theorem in $b^k$-geometry\nby M
ichael Francis (University of Western Ontario) as part of Noncommutative g
eometry in NYC\n\n\nAbstract\nMelrose introduced $b$-geometry as a paradig
m for studying operators on a manifold that suffer a first-order degenerac
y along a hypersurface. Scott considered higher-order degeneracies\, intro
ducing $b^k$-geometry for $k>1$. In this talk we consider two different as
pects of (a slight variation of) Scott's $b^k$-geometry: one global and on
e local. Firstly\, we discuss the classification of $b^k$-geometries by a
holonomy invariant (similar results were obtained independently by Bischof
f-del Pino-Witte). We also discuss the Newlander-Nirenberg for complex $b^
k$-manifolds. Complex $b$-manifolds ($k=1$) were defined by Mendoza the Ne
wlander-Nirenberg theorem for $b$-manifolds was obtained by Francis-Barron
.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damián Ferraro (Departamento de Matemática y Estadística del Li
toral\, Uruguay)
DTSTART:20240207T200000Z
DTEND:20240207T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/150
DESCRIPTION:Title: Cross-sectional C*-algebras of Fell bundles\nby Damián Ferraro (Dep
artamento de Matemática y Estadística del Litoral\, Uruguay) as part of
Noncommutative geometry in NYC\n\n\nAbstract\nA Fell bundle (or C*-algebra
ic bundle) $B=\\{B_t\\}_{t\\in G}$ may be thought of as a kind of action o
f the base group $G$ on the C*-algebra $B_e$\, $e$ being the unit of $G.$
When doing so\, the full and reduced cross-sectional C*-algebras of $B$\,
$C^*(B)$ and $C^*_r(B)$ respectively\, become the full and reduced crossed
products of the action.\n\nIt is implicit in Exel-Ng's construction/chara
cterization of $C^*_r(B)$ that the induction of representations from $H:=\
\{e\\}$ to $G\,$ $U\\mapsto Ind_{H\\uparrow G}(U)\,$ and from $B_e$ to $B\
,$ $T\\mapsto Ind_{B_e\\uparrow B}(T)\,$ are intimately related and that b
oth can be used to define/describe $C^*_r(B).$ If $B$ is saturated\, the e
quivalence of the definitions is a straightforward consequence of Fell's a
bsorption principle.\n\nThe situation is not so clear when one considers c
losed subgroups $H$ of $G$ other than $\\{e\\}$ (even if $B$ is saturated)
.\nThe reduction of $B$ to $H\,$ $B_H:=\\{B_t\\}_{t\\in H}\,$ is a Fell bu
ndle and one has induction processes $U\\mapsto Ind_{H\\uparrow G}(U)$ and
$T\\mapsto Ind_{B_H\\uparrow B}(T)\,$ where $U$ and $T$ stand for represe
ntations of $H$ and $B_H\,$ respectively. In this talk we use $U\\mapsto I
nd_{H\\uparrow G}(U)$ and $T\\mapsto Ind_{B_H\\uparrow B}(T)$ to construct
two candidates for the "reduced $H$-cross-sectional C*-algebra of $B$". W
e also give conditions implying they are isomorphic.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt McBride (Mississippi State University)
DTSTART:20240131T200000Z
DTEND:20240131T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/151
DESCRIPTION:Title: Crossed Product C*-algebras Associated with p-Adic Multiplication\nb
y Matt McBride (Mississippi State University) as part of Noncommutative ge
ometry in NYC\n\n\nAbstract\nI will discuss some basics of p-adic numbers\
, some examples of $C^*$-algebras that naturally arise from the crossed pr
oduct of the continuous functions on $Z_p$ with automorphisms and endomorp
hisms coming from the action of p-adic multiplication. I will also discus
s some basic structure\, including identifying ideals\, short exact sequen
ces and if time allows some K-Theory.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Christensen (University of Copenhagen)
DTSTART:20240214T200000Z
DTEND:20240214T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/152
DESCRIPTION:Title: From spectral triples in NCG to Grothendieck's inequalities in the theor
y of finite rank matrices\nby Erik Christensen (University of Copenhag
en) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWhile studyin
g properties of a spectral triple\, I realized that the Schur product - or
entry wise product of infinite matrices -- has a nice Stinespring repre
sentation as a completely bounded bilinear operator. On the other hand it
is well known that Grothendieck's inequality on bilinear forms has a dual
counterpart\, which describes certain properties of Schur multipliers. It
turned out that the theory of operator spaces and completely bounded multi
linear maps form a nice background to present some classical and some new
results on both the Schur product and on Grothendieck's inequalities. Part
of this will be extended to the non commutative Grothendieck inequality t
oo.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Krajczok (Vrije Universiteit Brussel)
DTSTART:20240228T200000Z
DTEND:20240228T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/153
DESCRIPTION:Title: Approximation properties of discrete quantum groups\nby Jacek Krajcz
ok (Vrije Universiteit Brussel) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nIt is a classical result in abstract harmonic analysis\, th
at discrete group G is amenable if and only if its group von Neumann algeb
ra vN(G) has weak* CPAP (completely positive approximation property). Ther
e is also a variant of this result for weak amenability: G is weakly amena
ble if and only if vN(G) has weak* CBAP (completely bounded approximation
property). These equivalences remain true also for unimodular discrete qua
ntum groups\, which form a class of objects strictly containing discrete g
roups. It is however an open question\, whether approximation properties o
f vN(G) imply analogous one for G\, if G is a non-unimodular quantum group
. During the talk I will discuss how one can obtain positive results by co
nsidering vN(G) not just as a von Neumann algebra\, but as an operator mod
ule over $L^1(\\hat{G})$. If time permits\, I will also discuss a recent r
esult about multiplicativity of Cowling-Haagerup (weak amenability) consta
nt.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt McBride (Mississippi State University)
DTSTART:20240327T190000Z
DTEND:20240327T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/154
DESCRIPTION:Title: Derivations on Smooth Subalgebras\nby Matt McBride (Mississippi Stat
e University) as part of Noncommutative geometry in NYC\n\n\nAbstract\nI w
ill discuss some basics about smooth subalgebras in various algebras inclu
ding the Toeplitz algebra and the Hensel-Steinitz algebra. I will also d
iscuss classifying derivations on those smooth algebras.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilnur Baibulov (St Petersburg State University)
DTSTART:20240221T200000Z
DTEND:20240221T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/155
DESCRIPTION:Title: The spectrum of the C*-algebra of singular integral operators with semi-
almost periodic coefficients\nby Ilnur Baibulov (St Petersburg State U
niversity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nThe $C
^*$-algebra generated by one-dimensional singular integral operators in $L
_2(\\mathbb{R})$ is studied. The coefficients are assumed to be continuous
and stabilizing at infinity to almost periodic functions. In this talk I
will describe the primitive spectrum of this algebra. The talk is based on
collaborative work with O.V. Sarafanov.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Thiel (Chalmers University of Technology and University of
Gothenburg)
DTSTART:20240313T190000Z
DTEND:20240313T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/156
DESCRIPTION:Title: A gentle introduction to Cuntz semigroups\, I\nby Hannes Thiel (Chal
mers University of Technology and University of Gothenburg) as part of Non
commutative geometry in NYC\n\n\nAbstract\nThe Cuntz semigroup is a geomet
ric refinement of K-theory that was\nintroduced by Cuntz in the 1970s in h
is pioneering work on the structure\nof simple C*-algebras. This powerful
invariant has seen many\napplications in the structure and classification
theory of C*-algebras.\nRecently\, it has also become clear that Cuntz sem
igroups are interesting\nobjects of study in their own right.\n\nIn these
lectures\, I will give a short introduction to Cuntz semigroups\,\nand pre
sent some examples and applications.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Thiel (Chalmers University of Technology and University of
Gothenburg)
DTSTART:20240320T190000Z
DTEND:20240320T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/157
DESCRIPTION:Title: A gentle introduction to Cuntz semigroups\, II\nby Hannes Thiel (Cha
lmers University of Technology and University of Gothenburg) as part of No
ncommutative geometry in NYC\n\n\nAbstract\nThe Cuntz semigroup is a geome
tric refinement of K-theory that was\nintroduced by Cuntz in the 1970s in
his pioneering work on the structure\nof simple C*-algebras. This powerful
invariant has seen many\napplications in the structure and classification
theory of C*-algebras.\nRecently\, it has also become clear that Cuntz se
migroups are interesting\nobjects of study in their own right.\n\nIn these
lectures\, I will give a short introduction to Cuntz semigroups\,\nand pr
esent some examples and applications.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús A. Álvarez López (University of Santiago de Compostela)
DTSTART:20240306T200000Z
DTEND:20240306T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/158
DESCRIPTION:Title: A trace formula for foliated flows\nby Jesús A. Álvarez López (Un
iversity of Santiago de Compostela) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nIn the lecture\, I will try to explain the ideas of a r
ecent paper on the trace formula for foliated flows\, written in collabora
tion with Yuri Kordyukov and Eric Leichtnam. Let $\\mathcal{F}$ be a trans
versely oriented foliation of codimension one on a closed manifold $M$\, a
nd let $\\phi=\\{\\phi^t\\}$ be a foliated flow on $(M\,\\mathcal{F})$ (it
maps leaves to leaves). Assume the closed orbits of $\\phi$ are simple an
d its preserved leaves are transversely simple. In this case\, there are f
initely many preserved leaves\, which are compact. Let $M^0$ denote their
union\, $M^1=M\\setminus M^0$ and $\\mathcal{F}^1=\\mathcal{F}|_{M^1}$. We
consider two locally convex Hausdorff spaces\, $I(\\mathcal{F})$ and $I'(
\\mathcal{F})$\, consisting of the leafwise currents on $M$ that are conor
mal and dual-conormal to $M^0$\, respectively. They become topological com
plexes with the differential operator $d_{\\mathcal{F}}$ induced by the de
~Rham derivative on the leaves\, and they have an $\\mathbb{R}$-action $\\
phi^*=\\{\\phi^{t\\\,*}\\}$ induced by $\\phi$. Let $\\bar H^\\bullet I(\\
mathcal{F})$ and $\\bar H^\\bullet I'(\\mathcal{F})$ denote the correspond
ing leafwise reduced cohomologies\, with the induced $\\mathbb{R}$-action
$\\phi^*=\\{\\phi^{t\\\,*}\\}$. $\\bar H^\\bullet I(\\mathcal{F})$ and $\\
bar H^\\bullet I'(\\mathcal{F})$ are shown to be the central terms of shor
t exact sequences in the category of continuous linear maps between locall
y convex spaces\, where the other terms are described using Witten's pertu
rbations of the de~Rham complex on $M^0$ and leafwise Witten's perturbatio
ns for $\\mathcal{F}^1$. This is used to define some kind of Lefschetz dis
tribution $L_{\\rm dis}(\\phi)$ of the actions $\\phi^*$ on both $\\bar H^
\\bullet I(\\mathcal{F})$ and $\\bar H^\\bullet I'(\\mathcal{F})$\, whose
value is a distribution on $\\mathbb{R}$. Its definition involves several
renormalization procedures\, the main one is the b-trace of some smoothing
b-pseudodifferential operator on the compact manifold with boundary obtai
ned by cutting $M$ along $M^0$. We also prove a trace formula describing $
L_{\\rm dis}(\\phi)$ in terms of infinitesimal data from the closed orbits
and preserved leaves. Some term of the formula is related with Connes' No
n-Commutative Geometry of foliations with a transverse measure. This solve
s a conjecture of C. Deninger involving two leafwise reduced cohomologies
instead of a single one.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gisela Tartaglia (Universidad Nacional de La Plata)
DTSTART:20240403T190000Z
DTEND:20240403T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/159
DESCRIPTION:Title: Induction of coactions for algebraic quantum groups\nby Gisela Tarta
glia (Universidad Nacional de La Plata) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nGiven G a discrete group and H a subgroup\, it is k
nown how to\ninduce G-algebras from H-algebras. In this talk\, we will pre
sent a\ngeneralization of this construction in terms of coactions of algeb
raic\nquantum groups. We will start by recalling the basic definitions of\
nalgebraic quantum groups\, comodule algebras and cotensor product. Given\
nan a.q.g. A\, we will show how to obtain an A-comodule algebra starting\n
from a B-comodule algebra\, where B is a compact quantum subgroup of A.\nF
inally\, we will prove that under some hypothesis\, we obtain a Morita\neq
uivalence between the crossed products of the corresponding dual\nactions.
\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Hochs (Radboud University)
DTSTART:20240424T190000Z
DTEND:20240424T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/160
DESCRIPTION:Title: The equivariant Fried conjecture for suspension flow\nby Peter Hochs
(Radboud University) as part of Noncommutative geometry in NYC\n\n\nAbstr
act\nRay-Singer analytic torsion is a topological invariant of compact man
ifolds\, which can be used to distinguish between homotopy equivalent mani
folds that are not homeomorphic. The Ruelle dynamical zeta function is a p
roperty of flows on compact manifolds\, which encodes information on perio
dic flow curves. Interestingly\, the absolute value of this function at ze
ro is often equal to the analytic torsion of the manifold\, even though th
e latter does not involve the flow at all. Fried’s conjecture is the pro
blem to determine when this equality holds. With Saratchandran\, we constr
ucted equivariant versions of analytic torsion and the Ruelle zeta functio
n for proper group actions\, and posed the question when an equivariant ve
rsion of Fried’s conjecture holds. With Pirie\, we are investigating thi
s conjecture for a specific type of flows: suspension flows of diffeomorph
isms.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Shulman (University of Gothenburg)
DTSTART:20240410T190000Z
DTEND:20240410T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/161
DESCRIPTION:Title: On almost commuting matrices\nby Tatiana Shulman (University of Goth
enburg) as part of Noncommutative geometry in NYC\n\n\nAbstract\nQuestions
of whether almost commuting matrices are necessarily close to commuting o
nes are old. They are reformulated using $C^*$-algebra theory and have som
ewhat topological nature. We investigate which relations for families of c
ommuting matrices are stable under small perturbations and give some appli
cations. Joint work with Dominic Enders.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitch Hamidi (Embry‑Riddle Aeronautical University)
DTSTART:20240417T190000Z
DTEND:20240417T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/162
DESCRIPTION:Title: $C^*$-extensions of non-self-adjoint dynamics\nby Mitch Hamidi (Embr
y‑Riddle Aeronautical University) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nGiven the action of a group G on a non-self-adjoint ope
rator algebra A\, the crossed product of A by G can be realized as the sub
algebra of a $C^*$-crossed product when the dynamics of G acting on A can
be extended to self-adjoint dynamics of G acting on a $C^*$-algebra. In th
is talk\, we characterize the existence of such a dynamical extension in t
erms of the boundary ideal structure for A in its maximal representation.
We define a lattice structure for an operator algebra’s completely isome
tric representation theory and discuss how one might recover the crossed p
roduct of an operator algebra in a representation lacking a self-adjoint d
ynamical extension.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changying Ding (UCLA)
DTSTART:20240501T190000Z
DTEND:20240501T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/163
DESCRIPTION:Title: On Cartan subalgebras of $II_1$ factors arising from Bernoulli actions o
f weakly amenable groups\nby Changying Ding (UCLA) as part of Noncommu
tative geometry in NYC\n\n\nAbstract\nA conjecture of Popa states that the
$II_1$ factor arising from a Bernoulli action of a nonamenable group has
a unique (group measure space) Cartan subalgebra\, up to unitary conjugacy
. In this talk\, I will discuss this conjecture and show that it holds for
weakly amenable groups with constant $1$ among algebraic actions. The pro
of involves the notion of properly proximal groups introduced by Boutonnet
\, Ioana\, and Peterson.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Meyer (Georg-August-Universität Göttingen)
DTSTART:20240529T190000Z
DTEND:20240529T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/164
DESCRIPTION:Title: Classification of Purely Infinite Graph C*-Algebras\nby Ralf Meyer (
Georg-August-Universität Göttingen) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nI will explain how purely infinite graph $C^*$-algebr
as may be classified up to stable isomorphism using an invariant of K-theo
retic nature. This is contained in my recent preprint with Rasmus Bentman
n. The key idea is to classify $C^*$-correspondences from a graph $C^*$-a
lgebra to another $C^*$-algebra up to homotopy\, using some projections an
d unitaries in the target $C^*$-algebra. Since we classify correspondence
s up to homotopy\, we also classify general graph $C^*$-algebras up to hom
otopy equivalence. The relevant homotopies will automatically preserve ga
uge-invariant ideals\, and we may improve this to also preserve the ideals
that are not gauge invariant\, if these are present.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alcides Buss (Federal University of Santa Catarina\, Brazil)
DTSTART:20240911T190000Z
DTEND:20240911T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/165
DESCRIPTION:Title: P-adic Operator Algebras\nby Alcides Buss (Federal University of San
ta Catarina\, Brazil) as part of Noncommutative geometry in NYC\n\n\nAbstr
act\nIn this talk we present the of p-adic operator algebras\, which are n
onarchimedean analogues of $C^*$-algebras. We demonstrate that various cla
ssical examples of operator algebras - such as group(oid) algebras - have
a nonarchimedean counterpart. The category of p-adic operator algebras exh
ibits a similar flavor to the category of real and complex $C^*$-algebras\
, featuring limits\, colimits\, tensor products\, crossed products and an
enveloping construction permitting us to construct p-adic operator algebra
s from involutive algebras over $Z_p$. Finally\, we briefly discuss an ana
logue of topological K-theory for Banach $Z_p$-algebras\, and compute it i
n basic examples\, like Cuntz algebras and rotation algebras.\n\nThis is j
oint work with Luiz Felipe Garcia and Devarshi Mukherjee.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojan Kuzma (University of Primorska\, Slovenia)
DTSTART:20240918T190000Z
DTEND:20240918T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/167
DESCRIPTION:Title: Birkhoff-James orthogonality in normed vector spaces\nby Bojan Kuzma
(University of Primorska\, Slovenia) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nBirkhoff-James orthogonality generalizes the classica
l orthogonality from Hilbert to general normed spaces. It can be a useful
tool for finding the best approximation of a vector within a given subspa
ce. However\, unlike the classical one\, it is in general not symmetric.
In fact (in dimensions greater than 2) it is symmetric if and only if the
norm is induced by the inner product. This early classification of inner-
product spaces goes back to James (for real Banach spaces) with an aid of
Bohnenblust (for complex ones). One can visualize this relation as an inf
inite directed graph (called ortho-digraph)\, where vertices are all the
vectors from a normed space (or all points in its projectivisation) and tw
o vertices x\, y form a directed edge if x is Birkhoff-James orthogonal t
o y .We will show that this digraph contains a lot of information about th
e normed space: It knows how to calculate the dimension of the underlying
space\, knows if the norm is rotund or smooth\, knows how to find smooth p
oints and in some special cases even knows if the underlying field is real
or complex. At least for smooth spaces in can even completely characteriz
e them\, modulo (conjugate) linear isometry.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bora Yalkinoglu (Université de Strasbourg\, CNRS)
DTSTART:20240925T190000Z
DTEND:20240925T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/168
DESCRIPTION:Title: On the discrete periodic Toda flow\nby Bora Yalkinoglu (Université
de Strasbourg\, CNRS) as part of Noncommutative geometry in NYC\n\n\nAbstr
act\nThe discrete periodic Toda flow is a very interesting integrable syst
em. The goal of our talk is to explain how it can be linearized in terms o
f Gauß composition law for quadratic forms. \nFurther\, we will indicate
how the periodic box-ball flow\, a famous tropical integrable system\,\nca
n naturally be embedded into the Toda system and from there point to some
intriguing relations with number theory.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valerio Proietti (University of Oslo)
DTSTART:20241002T190000Z
DTEND:20241002T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/169
DESCRIPTION:Title: Elliott invariant in a geometric context\nby Valerio Proietti (Unive
rsity of Oslo) as part of Noncommutative geometry in NYC\n\n\nAbstract\nGi
ven a class of topological dynamical systems\, we study the associated map
ping torus from the point of view of foliated spaces. By studying the inte
raction between the leafwise Dirac operator and the invariant transverse m
easures\, we reframe in a geometric fashion the Elliott invariant for the
crossed product of the dynamical system\, and prove a rigidity result for
the mapping torus\, lifting leafwise homotopy equivalences to isomorphism
of the noncommutative leaf space. Joint work with Hao Guo and Hang Wang.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Miller (University of Southern Denmark)
DTSTART:20241009T190000Z
DTEND:20241009T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/170
DESCRIPTION:Title: Homology and K-theory for self-similar group actions\nby Alistair Mi
ller (University of Southern Denmark) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nSelf-similar groups are groups of automorphisms of in
finite rooted trees obeying a simple but powerful rule. Under this rule\,
groups with exotic properties can be generated from very basic starting da
ta\, most famously the Grigorchuk group which was the first example of a g
roup with intermediate growth.\n\nNekrashevych introduced a groupoid and a
$C^*$-algebra for a self-similar group action on a tree as models for som
e underlying noncommutative space for the system. Our goal is to compute t
he K-theory of the $C^*$-algebra and the homology of the groupoid. Our mai
n theorem provides long exact sequences which reduce the problems to group
theory. I will demonstrate how to apply this theorem to fully compute hom
ology and K-theory through the example of the Grigorchuk group.\n\nThis is
joint work with Benjamin Steinberg.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Yuncken (Université de Lorraine)
DTSTART:20250129T200000Z
DTEND:20250129T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/171
DESCRIPTION:Title: Crystallizing the algebra of functions on a compact semisimple Lie group
\nby Robert Yuncken (Université de Lorraine) as part of Noncommutativ
e geometry in NYC\n\n\nAbstract\nThe theory of crystal bases is a means of
simplifying the representation theory of semisimple Lie algebras by passi
ng through quantum groups. Varying the parameter q of the quantized envel
oping algebras\, we pass from the classical theory at q=1 through the Drin
feld-Jimbo algebras at 0 < q < 1 to the crystal limit at q=0. At this poi
nt\, the main features of the representation theory crystallize into purel
y combinatorial data described by crystal graphs. In this talk\, we will
describe what happens to the algebra of continuous functions on a compact
semisimple Lie group under the crystallization process\, yielding higher-r
ank graph algebras. This is joint work with Marco Matassa.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Goldbring (University of California\, Irvine)
DTSTART:20241016T190000Z
DTEND:20241016T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/172
DESCRIPTION:Title: What is…model theory of operator algebras?\nby Isaac Goldbring (Un
iversity of California\, Irvine) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nModel theory is the area of logic that studies mathematica
l structures through the lens of first-order logic\, examining what proper
ties of a structure are expressible by first-order sentences and analyzing
what subsets of the structure can be defined using first-order formulae.
In the last 15 years or so\, the model theory of operator algebras has be
en a very active field with exciting interactions taking place between the
model theoretic and operator algebraic communities. In this talk\, I wil
l survey some of the main themes being pursued in the model theory of trac
ial von Neumann algebras. No prior knowledge of logic or model theory wil
l be assumed.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela Di Donato (University of Pavia)
DTSTART:20241023T190000Z
DTEND:20241023T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/173
DESCRIPTION:Title: Rectifiability in Carnot groups\nby Daniela Di Donato (University of
Pavia) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIntrinsic
regular surfaces in Carnot groups play the same role as $C^1$ surfaces in
Euclidean spaces. As in Euclidean spaces\, intrinsic regular surfaces can
be locally defined in different ways: e.g. as non critical level sets or
as continuously intrinsic differentiable graphs. The equivalence of these
natural definitions is the problem that we are studying. Precisely our aim
is to generalize some results proved by Ambrosio\, Serra Cassano\, Vitton
e valid in Heisenberg groups to the more general setting of Carnot groups.
This is joint work with Antonelli\, Don and Le Donne\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jintao Deng (SUNY at Buffalo)
DTSTART:20241030T190000Z
DTEND:20241030T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/174
DESCRIPTION:Title: Twisted Roe Algebras and the Coarse Baum-Connes Conjecture\nby Jinta
o Deng (SUNY at Buffalo) as part of Noncommutative geometry in NYC\n\n\nAb
stract\nThe coarse Baum-Connes conjecture claims that certain topological
K-homology and the K-theory of Roe algebras associated to metric spaces ar
e isomorphic via the index map. It provides algorithm to compute the highe
r indices for elliptic operators on non-compact Riemannian manifolds. The
higher index is an element of the K-theory of the Roe algebra. To underst
and Roe algebras\, we introduced a notion of twisted Roe algebras and a tw
isted coarse Baum-Connes conjecture. In the talk\, I will cover basic prop
erties of the twisted Roe algebras and the K-theory for the twisted algebr
as associated with metric spaces with a coarsely embeddable fibration stru
cture. As an application\, the coarse Baum-Connes conjecture holds for a f
initely generated group which is an extension of coarsely embeddable group
s. This is based on a joint work with Liang Guo.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meenakshi McNamara (Perimeter Institute)
DTSTART:20241127T210000Z
DTEND:20241127T220000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/175
DESCRIPTION:Title: The exact quantum chromatic number of Hadamard graphs and their products
\nby Meenakshi McNamara (Perimeter Institute) as part of Noncommutativ
e geometry in NYC\n\n\nAbstract\nQuantum chromatic numbers are defined via
non-local games on classical graphs. Very few exact computations of the q
uantum chromatic number of graphs are known. In this talk\, we will give a
proof of the exact quantum chromatic number of Hadamard graphs. As oppose
d to prior results on this problem\, this approach uses results on conjuga
cy class graphs which allows us to consider products of Hadamard graphs as
well. Specifically\, we compute the exact quantum chromatic number of cat
egorical products of Hadamard graphs.\n\nThroughout this work\, we use sev
eral results for the quantum chromatic numbers of quantum graphs\, an oper
ator algebraic generalization of classical graphs that appears in connecti
on to quantum information theory. In particular\, we also discuss results
on products of quantum graphs appearing in joint work with Rolando de Sant
iago.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Scarparo (Federal University of Pelotas\, Brazil)
DTSTART:20250205T200000Z
DTEND:20250205T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/176
DESCRIPTION:Title: A tracial characterization of Furstenberg's x p\, x q conjecture\nby
Eduardo Scarparo (Federal University of Pelotas\, Brazil) as part of Nonc
ommutative geometry in NYC\n\n\nAbstract\nFurstenberg's conjecture about x
p\, xq\, invariant measures on $[0\,1)$\, where p and q are multiplicative
ly independent integers\, is one of the most fundamental open problems in
ergodic theory. We will see how the topological counterpart of this conjec
ture\, which is a theorem due to Furstenberg\, implies the uniqueness of t
he $C^*$-norm on the complex group ring of a certain metabelian group $G$.
\n\nFurthermore\, we will present a characterization of the xp\,xq conject
ure in terms of the traces of $C^*(G)$\, and discuss the primitive ideal s
pace and K-theory of $C^*(G)$. This is based on joint work with Chris Bruc
e.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Goldbring (University of California\, Irvine)
DTSTART:20250507T190000Z
DTEND:20250507T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/177
DESCRIPTION:Title: Minicourse: Applications of model theory to operator algebras\, I\nb
y Isaac Goldbring (University of California\, Irvine) as part of Noncommut
ative geometry in NYC\n\n\nAbstract\nIn these three talks\, I will outline
several applications of model theory to operator algebras. In the first
talk\, I will explain how model theory sheds light on the recent resolutio
n of the Connes Embedding Problem from the quantum complexity result known
as MIP*=RE. In the second talk\, I will explain how the ideas from the f
irst talk also give information about the class of QWEP C*-algebras introd
uced by Kirchberg in the 1990s. In the final talk\, I will discuss two pr
oblems centered around relative commutants of tracial von Neumann algebras
in ultrapowers and how they are intimately connected with model theoretic
ideas. These talks will be independent of each other and from the talk I
gave in this seminar in the fall.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Goldbring (University of California\, Irvine)
DTSTART:20250514T190000Z
DTEND:20250514T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/178
DESCRIPTION:Title: Minicourse: Applications of model theory to operator algebras\, II\
nby Isaac Goldbring (University of California\, Irvine) as part of Noncomm
utative geometry in NYC\n\n\nAbstract\nIn these three talks\, I will outli
ne several applications of model theory to operator algebras. In the firs
t talk\, I will explain how model theory sheds light on the recent resolut
ion of the Connes Embedding Problem from the quantum complexity result kno
wn as MIP*=RE. In the second talk\, I will explain how the ideas from the
first talk also give information about the class of QWEP C*-algebras intr
oduced by Kirchberg in the 1990s. In the final talk\, I will discuss two
problems centered around relative commutants of tracial von Neumann algebr
as in ultrapowers and how they are intimately connected with model theoret
ic ideas. These talks will be independent of each other and from the talk
I gave in this seminar in the fall.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Goldbring (University of California\, Irvine)
DTSTART:20250521T190000Z
DTEND:20250521T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/179
DESCRIPTION:Title: Minicourse: Applications of model theory to operator algebras\, III\
nby Isaac Goldbring (University of California\, Irvine) as part of Noncomm
utative geometry in NYC\n\n\nAbstract\nIn these three talks\, I will outli
ne several applications of model theory to operator algebras. In the firs
t talk\, I will explain how model theory sheds light on the recent resolut
ion of the Connes Embedding Problem from the quantum complexity result kno
wn as MIP*=RE. In the second talk\, I will explain how the ideas from the
first talk also give information about the class of QWEP C*-algebras intr
oduced by Kirchberg in the 1990s. In the final talk\, I will discuss two
problems centered around relative commutants of tracial von Neumann algebr
as in ultrapowers and how they are intimately connected with model theoret
ic ideas. These talks will be independent of each other and from the talk
I gave in this seminar in the fall.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Ponge (Sichuan University)
DTSTART:20241106T200000Z
DTEND:20241106T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/180
DESCRIPTION:Title: Noncommutative geometry and semiclassical analysis\nby Raphael Ponge
(Sichuan University) as part of Noncommutative geometry in NYC\n\n\nAbstr
act\nIn this talk\, I will present new results regarding semiclassical Wey
l’s laws in the setup of Connes’ noncommutative geometry. They provide
precise asymptotics for the counting functions of Schroedinger operators
under the semiclassical limit. This improves and simplifies previous resul
ts of McDonald-Sukochev-Zanin. This provides a bridge between semiclassica
l analysis and noncommutative geometry. Thanks to the Birman-Scwhinger pri
nciple and old results of Birman-Solomyak this reduces to establishing var
ious weak Schatten class properties for the operators at stake. This has a
number of applications. We shall present two of them. First\, we recover
previously known semiclassical Weyl’s laws on Euclidean domains and clos
ed manifolds. These results were proved in 60s and 70s. However\, thanks
to our setup\, they can be deduced results of Minakshisundaram and Pleijel
on short time heat kernel asymptotics for Laplacians that were establishe
d in the late 40s. Second\, we obtain semiclassical Weyl laws for noncommu
tative tori for any dimension. These laws were conjectured by Ed McDonald
and the speaker.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuoxing Zhou (École Normale Supérieure)
DTSTART:20241113T200000Z
DTEND:20241113T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/181
DESCRIPTION:Title: Noncommutative topological boundaries and amenable invariant intermediat
e subalgebras\nby Shuoxing Zhou (École Normale Supérieure) as part o
f Noncommutative geometry in NYC\n\n\nAbstract\nAs an analogue of the topo
logical boundary of discrete groups $\\Gamma$\, we define the noncommutati
ve topological boundary of tracial von Neumann algebras $(M\,\\tau)$ and a
pply it to generalize a recent result by Amrutam-Hartman-Oppelmayer\, show
ing that for a trace preserving action $\\Gamma \\curvearrowright (A\,\\ta
u_A)$ on an amenable tracial von Neumann algebra\, any $\\Gamma$-invariant
amenable intermediate subalgebra between $A$ and $\\Gamma\\ltimes A$ is n
ecessarily a subalgebra of $\\mathrm{Rad}(\\Gamma) \\ltimes A$. By taking
$(A\,\\tau_A)=L^\\infty(X\,\\nu_X)$ for a free pmp action $\\Gamma \\curve
arrowright (X\,\\nu_X)$\, we obtain a similar result for invariant subequi
valence relations of $\\mathcal{R}_{\\Gamma \\curvearrowright X}$.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Kettner (Czech Academy of Sciences)
DTSTART:20241204T200000Z
DTEND:20241204T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/182
DESCRIPTION:Title: Cuntz–Pimsner algebras of twisted partial automorphisms\nby Aaron
Kettner (Czech Academy of Sciences) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nWe will discuss how to construct a $C^*$-algebra from a
vector bundle\nand a partial action of the integers on the base space of
the bundle\,\nusing the machinery of Cuntz–Pimsner algebras. Despite bei
ng much more\ngeneral\, the resulting algebras share many properties with
partial\ncrossed products by the integers. They also generalise the\n$C^*$
-algebras constructed from homeomorphisms twisted by vector bundles\nrecen
tly introduced by\nAdamo–Archey–Forough–Georgescu–Jeong–Strung
–Viola. Under natural\nconditions on the action and the space\, classifi
ability of the\n$C^*$-algebras is shown. In particular\, we obtain both st
ably finite as\nwell as purely infinite classifiable $C^*$-algebras from t
he same\ndynamical framework.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Tageddine (McGill University)
DTSTART:20241211T200000Z
DTEND:20241211T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/183
DESCRIPTION:Title: Noncommutative geometry on the Berkovich projective line\nby Damien
Tageddine (McGill University) as part of Noncommutative geometry in NYC\n\
n\nAbstract\nThe Berkovich projective line is an analytic space over a non
-Archimedean field. It can also be constructed as an inverse limit of fini
te rooted trees. \nWe find how to associate $C^*$-algebras generated by pa
rtial isometries to the Berkovich line. This allows us to construct severa
l spectral triples on this space. \nFinally\, we show that invariant measu
res\, such as the Patterson-Sullivan measure\, can be obtained as certain
KMS-states of the crossed product algebra with a subgroup of $PGL_2(C_p)$.
\n\nThis is a joint work with Masoud Khalkhali.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Yang (Harvard)
DTSTART:20250212T200000Z
DTEND:20250212T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/184
DESCRIPTION:Title: The Jacquet-Langlands correspondence of von Neumann dimensions over arit
hmetic groups\nby Jun Yang (Harvard) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nWe first show the local-global compatibility of Ta
magawa measures and Plancherel measures under the local/global Jacquet-Lan
glands correspondence. We then prove that the global Jacquet-Langlands cor
respondence preserves von Neumann dimensions over arithmetic groups.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noemie Combe (University of Warsaw)
DTSTART:20250219T200000Z
DTEND:20250219T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/185
DESCRIPTION:Title: Quantum Information Geometry and the Connes–Araki–Haagerup Cones
\nby Noemie Combe (University of Warsaw) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nThe profound interplay between von Neumann algebra
s and quantum field theory has increasingly highlighted their importance i
n higher category theory and topology. A central insight emerges from Tomi
ta–Takesaki theory\, which studies the modular automorphism groups of vo
n Neumann algebras. Using techniques from affine differential geometry\, w
e establish an explicit connection between the Connes–Araki–Haagerup c
ones—objects invariant under modular operators—and geometric structure
s intrinsic to the axiomatization of 2D topological quantum field theory (
TQFT).\n\nWe demonstrate that these strictly convex symmetric cones posses
s a pre-Frobenius structure and contain a submanifold satisfying the Witte
n–Dijkgraaf–Verlinde–Verlinde (WDVV) equation\, thereby forming a Fr
obenius submanifold. This result reveals new and concrete relationships be
tween objects invariant under modular operators and low-dimensional TQFTs\
, with additional implications for quantum information geometry.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Etesi (Budapest University of Technology and Economics)
DTSTART:20250312T190000Z
DTEND:20250312T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/186
DESCRIPTION:Title: The four dimensional smooth Poincare conjecture from the viewpoint of Ne
umann algebra representations\nby Gabor Etesi (Budapest University of
Technology and Economics) as part of Noncommutative geometry in NYC\n\n\nA
bstract\nIn this talk we outline the construction and basic properties of\
na new smooth 4-manifold invariant obtained by the aid of the rich\nrepres
entation theory of the hyperfinite II_1 factor von Neumann algebra.\nThis
invariant gives rise to a unital Abelian semigroup homomorphism from\n(the
category of) connected compact oriented smooth 4-manifold equipped\nwith
the connected sum operation into the semi-open interval [0\,1) with\nAbeli
an semigroup operation $(s\,t)\\mapsto s+t-st$. This invariant has the\nin
teresting property that its range is appropriately restricted by the\nposs
ible values of Jones' indices of subfactors within the II_1\nhyperfinite f
actor hence consists of a discrete and a continuous part. It\nis then obse
rved that (i) the invariant is not injective on its continuous\nrange part
\; (ii) when evaluated on the standard 4-sphere its value falls\nwithin th
e discrete part of the range and its injectivity at this specific\nvalue i
s equivalent to the validity of the 4 dimensional smooth Poincare\nconject
ure. Moreover\, as the punch line of this talk\, it is expected that\nthis
invariant possesses a sort of continuity hence non-invertability at\nits
specifec values in the continuous range will imply non-invartability\nat n
earby values\; however such argument cannot be applied to study the 4\ndim
ensional smooth Poincare conjecture because of the aforementioned\ndiscret
eness hence the conjecture's difficulty might be related with\nthe isolati
on of the 4-sphere in this sense from the rest of smooth\n4-manifolds.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bazlov (University of Manchester)
DTSTART:20250226T200000Z
DTEND:20250226T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/187
DESCRIPTION:Title: Cocycle twists of algebras\, representations and orders\nby Yuri Baz
lov (University of Manchester) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nA way to deform an associative algebra $A$ is to twist the\n
multiplication by a 2-cocycle on a group or a Hopf algebra acting on\n$A$.
I am interested to know to what extent the representations (and\nring-the
oretic and homological properties) of the twist are determined\nby those o
f $A$. My case in point will be rational Cherednik algebras\nover complex
reflection groups: twists of these well-studied objects\ngive algebras\, w
ith similar PBW bases\, over "mystic reflection groups"\,\nand for some of
them we can give an explicit combinatorial description\nof standard modul
es(arXiv:2501.06673\, with Jones-Healey). Twists\ndescend to finite-dimens
ional quotients of Cherednik algebras at $t=0$\,\nand over number fields\,
seem to produce their forms (in the sense that\nthe twist trivializes ove
r a field extension). This hints at an\ninterplay between twists and arith
metic\; if time permits\, I will mention\na possible connection to Hopf-Ga
lois structures on fields.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bruce (Newcastle University)
DTSTART:20250326T190000Z
DTEND:20250326T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/188
DESCRIPTION:Title: On the C*-algebra of Connes’ adele class space\nby Chris Bruce (Ne
wcastle University) as part of Noncommutative geometry in NYC\n\n\nAbstrac
t\nThe multiplicative group of an algebraic number field acts by multiplic
ation on the adele ring of the field\, and the quotient space for this act
ion is Connes’ adele class space. I will give an overview of joint work
with Takuya Takeishi in which we prove that the crossed product $C^*$-alge
bra associated with the adele class space completely remembers the number
field. Precisely\, we prove that two such crossed product C*-algebras are
*-isomorphic if and only if the underlying number fields are isomorphic. P
rimitive ideals and subquotients play a central role in our proof.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Reyes (University of California\, Irvine)
DTSTART:20250319T190000Z
DTEND:20250319T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/189
DESCRIPTION:Title: Searching for noncommutative spectrum functors\nby Manuel Reyes (Uni
versity of California\, Irvine) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nIn the classical algebra-geometry correspondences\, the ass
ignment turning an algebra into a space is a type of spectrum. Thus spectr
a of noncommutative algebras have been of interest for a long time in both
algebra and noncommutative geometry. Because the spectrum typically provi
des a functor from commutative algebras to spaces\, it is natural to ask w
hether we can extend it to a noncommutative spectrum functor. I will discu
ss this problem\, along with negative and partial positive results toward
its resolution.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pitts (University of Nebraska-Lincoln)
DTSTART:20250416T190000Z
DTEND:20250416T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/190
DESCRIPTION:Title: Pseudo-Cartan Inclusions and their Cartan Envelopes\nby David Pitts
(University of Nebraska-Lincoln) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nI will discuss the class of pseudo-Cartan inclusions\,\n
which are a class of regular inclusions of $C^*$-algebras\n $\\mathcal D\
\subseteq \\mathcal C$ where $\\mathcal D$ is abelian.\n This class inclu
des several previously studied classes such as:\n Cartan inclusions\, wea
k Cartan inclusions and virtual Cartan\n inclusions.\n\n The class of ps
eudo-Cartan inclusions coincides with the class of regular\n inclusions h
aving a Cartan envelope. Roughly speaking\, a Cartan\n envelope for a r
egular inclusion is a minimal Cartan inclusion into\n which the inclusio
n regularly embeds.\n\n Pseudo-Cartan inclusions and their Cartan envelop
es have desirable\n properties: for example\, they\n behave well under s
uitable inductive limits and under minimal tensor\n products.\n \n Time
permitting\, I will describe some applications. Here is a\n sample Appl
ication: Suppose for $i=1\,2$\,\n $(\\mathcal C_i\,\\mathcal D_i)$ are p
seudo-Cartan inclusions and\n $\\mathcal A_i$ are intermediate Banach alg
ebras\,\n\\[\\mathcal D_i\\subseteq \\mathcal A_i\\subseteq \\mathcal C_i.
\\] If $\\theta: \\mathcal A_1\\rightarrow\n\\mathcal A_2$ is an isometri
c isomorphism\, then $\\theta$ uniquely extends to a\n$*$-isomorphism of t
he $C^*$-subalgebras of $\\mathcal C_i$ generated by \n$\\mathcal A_i$\,\n
\\[\\tilde\\theta: C^*(\\mathcal A_1)\\rightarrow C^*(\\mathcal A_2).\\]\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Frank (HTWK Leipzig)
DTSTART:20250402T190000Z
DTEND:20250402T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/191
DESCRIPTION:Title: Multiplier modules of Hilbert $C^*$-modules revisited\nby Michael Fr
ank (HTWK Leipzig) as part of Noncommutative geometry in NYC\n\n\nAbstract
\nFollowing the approach to multiplier modules of Hilbert $C^*$-modules in
troduced by D. Bakić and \nB. Guljaš (2003) we reconsider key definition
s and facts to get deeper insights into related structures. The independen
t approach by M. Daws (2010) and by A. Buss\, B. Kwaśniewski\, A. McKee\,
A. Skalski (2024) via Banach $C^*$-modules serves as an alternative point
of view on which we comment and give facts to interrelate these two theor
ies. \nThe property of a Hilbert $C^*$-module to be a multiplier $C^*$-mod
ule is shown to be an invariant with respect to the consideration as a lef
t or right Hilbert C*-module in the sense of a $C^*$-correspondence in str
ong Morita equivalence theory. The interrelation of the C*-algebras of "co
mpact" operators\, the Banach algebras of bounded module operators and the
Banach spaces of bounded module operators of a Hilbert $C^*$-module to it
s $C^*$-dual Banach $C^*$-module are characterized for pairs of Hilbert $C
^*$-modules and their respective multiplier modules. The structures on the
latter are always isometrically embedded into the respective structures o
n the former. Examples for which continuation of these kinds of bounded mo
dule operators from the initial Hilbert $C^*$-module to its multiplier mod
ule fails are given\, however existing continuations turn out to be always
unique. Similarly\, bounded modular functionals from both kinds of Hilber
t $C^*$-modules to their respective $C^*$-algebras of coefficients are com
pared\, and eventually existing continuations are shown to be unique.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itamar Vigdorovich (University of California\, San Diego)
DTSTART:20250409T190000Z
DTEND:20250409T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/192
DESCRIPTION:Title: Structural properties of reduced $C^∗$-algebras associated with higher
-rank lattices\nby Itamar Vigdorovich (University of California\, San
Diego) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe present
the first examples of higher-rank lattices whose reduced $C^*$-algebras s
atisfy strict comparison\, stable rank one\, selflessness\, uniqueness of
embeddings of the Jiang--Su algebra\, and allow explicit computations of t
he Cuntz semigroup. This resolves a question raised in recent groundbreaki
ng work of Amrutam\, Gao\, Kunnawalkam Elayavalli\, and Patchell\, in whic
h they exhibited a large class of finitely generated non-amenable groups s
atisfying these properties. Our proof relies on quantitative estimates in
projective dynamics\, crucially using the exponential mixing for diagonali
zable flows. As a result\, we obtain an effective mixed-identity-freeness
property\, which\, combined with V. Lafforgue's rapid decay theorem\, yiel
ds the desired conclusions.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Alpeev (Ecole Normale Supérieure)
DTSTART:20250910T190000Z
DTEND:20250910T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/193
DESCRIPTION:Title: C*-simplicity and the Poisson boundary\nby Andrei Alpeev (Ecole Norm
ale Supérieure) as part of Noncommutative geometry in NYC\n\n\nAbstract\n
A connection between the Furstenberg boundary and $C^*$-simplicity of grou
ps was a major breakthrough of the previous decade by Kalantar and Kennedy
.\nThe furstenberg boundary is a topological object associated with a grou
p. The Poisson boundary is a measurable object\, associated with a pair of
a group and a probability measure on the group\, that describes the asymp
totic behaviour of the random walk on the group.\nI will talk about a conn
ection between $C^*$-simplicity and the Poisson boundary\, namely\, that a
countable group is $C^*$-simple iff its natural action on the Poisson bou
ndary is essentially free for a generic measure on the group.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Hamilton (Texas Tech University)
DTSTART:20250917T190000Z
DTEND:20250917T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/194
DESCRIPTION:Title: Noncommutative geometry in effective field theory and large N phenomena<
/a>\nby Alastair Hamilton (Texas Tech University) as part of Noncommutativ
e geometry in NYC\n\n\nAbstract\nIn this talk I will discuss the notion of
an effective field theory\, as formally introduced by Costello\, and its
manifestation in the framework of noncommutative geometry introduced by Ko
ntsevich. Noncommutative geometry arises within this context from replacin
g ordinary Feynman diagrams with diagrams of interacting open strings\, an
d I will explain how the large N phenomena first discovered by ‘t Hooft
arises in this framework. Here a connection can be made between these open
string type theories that arise in noncommutative geometry and large N ga
uge theories using the Loday-Quillen-Tsygan theorem from algebraic K-theor
y. If time permits\, I may discuss the treatment of the Batalin-Vilkovisky
formalism within this context and the connection with moduli spaces of Ri
emann surfaces.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250609T140000Z
DTEND:20250609T150000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/195
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 1\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250609T150000Z
DTEND:20250609T160000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/196
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 2\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250610T133000Z
DTEND:20250610T143000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/197
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 3\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250610T150000Z
DTEND:20250610T160000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/198
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 4\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250611T133000Z
DTEND:20250611T143000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/199
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 5\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250611T150000Z
DTEND:20250611T160000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/200
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 6\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250612T133000Z
DTEND:20250612T143000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/201
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 7\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250612T150000Z
DTEND:20250612T160000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/202
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 8\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/202/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250613T133000Z
DTEND:20250613T143000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/203
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 9\nby Anne-Marie Aubert (CNRS\, Sorbonne Universi
té - Université de Paris) as part of Noncommutative geometry in NYC\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250613T150000Z
DTEND:20250613T160000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/204
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncommutative
geometry"\, Lecture 10\nby Anne-Marie Aubert (CNRS\, Sorbonne Univers
ité - Université de Paris) as part of Noncommutative geometry in NYC\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/204/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jananan Arulseelan (Iowa State University)
DTSTART:20250924T190000Z
DTEND:20250924T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/205
DESCRIPTION:Title: Model Theory and an Ocneanu Ultraproduct for General Von Neumann Algebra
s\nby Jananan Arulseelan (Iowa State University) as part of Noncommuta
tive geometry in NYC\n\n\nAbstract\nThe model theories of tracial von Neum
ann algebras and\, more recently\, sigma-finite von Neumann algebras have
led to a large body of work and applications in operator algebras. I will
discuss recent work removing the sigma-finiteness condition\, yielding a c
ompletely general model theory of von Neumann algebras. After reviewing ex
isting ultraproduct constructions in von Neumann algebras\, I will introdu
ce and characterize the ultraproduct corresponding to this new framework a
nd show how it generalizes important properties of the Ocneanu ultraproduc
t. I will also discuss potential future work. Partially joint work with Go
ldbring\, Hart\, and Sinclair.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/205/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Neagu (KU Leuven)
DTSTART:20251001T190000Z
DTEND:20251001T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/206
DESCRIPTION:Title: Noncommutative coloured entropy\nby Robert Neagu (KU Leuven) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nBuilding on the classica
l noncommutative entropy for automorphisms of nuclear C*-algebras\, I will
introduce a formally different notion of entropy which uses the more refi
ned cpc approximations given by finite nuclear dimension or finite decompo
sition rank. In the sequel\, I will explore the typical values of this ent
ropy. This is joint work with Bhishan Jacelon.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/206/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Toyota (Texas A&M)
DTSTART:20251008T190000Z
DTEND:20251008T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/207
DESCRIPTION:Title: Twisted coarse Baum-Connes conjecture and relatively hyperbolic groups.<
/a>\nby Ryo Toyota (Texas A&M) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nCoarse Baum-Connes conjecture claims an algorithm to compute
the higher index and which has applications to important problems in geom
etry\, topology and operator algebras. To verify this conjecture for a lar
ger class of metric spaces\, we introduce twisted coarse Baum–Connes con
jecture with stable coarse algebras\, which can be viewed as a geometric a
nalogue of the Baum–Connes conjecture with coefficients. We show that th
is twisted version has stronger permanence properties than the classical c
oarse Baum–Connes conjecture\, particularly with respect to unions and s
ubspaces. Then\, we apply this framework to relatively hyperbolic groups.
For a finitely generated group $G$ that is hyperbolic relative to $\\{H_1
\,\\cdots\,H_n\\}$\, it is known that $G$ satisfies coarse Baum-Connes con
jecture if each $H_i$ does and $H_i$ admits finite-dimensional simplicial
model of the universal space for proper actions. As a consequence of the p
ermanence properties\, we can remove the topological condition of $H_i$ in
the aforementioned theorem. Namely\, we show that $G$ satisfies twisted c
oarse Baum-Connes conjecture with stable coefficients\, if and only if eac
h $H_i$ does. This is a joint work with Jintao Deng.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/207/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Hume (Carleton University)
DTSTART:20251015T190000Z
DTEND:20251015T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/208
DESCRIPTION:Title: Characterization of zero singular ideal in non-Hausdorff groupoid C*-alg
ebras\nby Jeremy Hume (Carleton University) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nNon-Hausdorff etale groupoids arise natural
ly from interesting dynamical systems and as models of important classes o
f $C^*$-algebras. One of the main obstacles in understanding the associate
d $C^*$-algebras in terms of their groupoids is the existence of a possibl
y non-zero ideal consisting of functions supported on meagre sets which\,
for instance\, obstructs characterizing simplicity in terms of the usual g
roupoid properties in the Hausdorff setting. In this talk\, I discuss my r
esult characterizing when this "singular" ideal is zero in terms of a grou
poid property. I will discuss the methods I use in the proofs\, including
the use of the Hausdorff cover of a non-Hausdorff groupoid\, introduced by
Timmermann\, and a new concept of "compressing" linear maps to *-homomorp
hisms. This talk is based on my preprint https://arxiv.org/abs/2509.07262.
\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/208/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrique Pardo Espino (Universidad de Cádiz)
DTSTART:20251029T190000Z
DTEND:20251029T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/209
DESCRIPTION:Title: Categorical models for ample groupoids and their algebras\nby Enriqu
e Pardo Espino (Universidad de Cádiz) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nA decade ago\, Spielberg described a new method for
defining $C^*$-algebras from oriented combinatorial data\, generalizing th
e construction of algebras from directed graphs\, higher-rank graphs\, and
(quasi-)ordered groups. To do so\, he introduced left cancellative small
categories\, and endowed any such category with a $C^*$-algebra encoding c
ategorical information\; he showed that this algebra is the groupoid algeb
ra of a (sort of) Deaconu-Renault étale groupoid. \n\n"In this talk\, we
explain the relevance of these algebras. Furthermore\, we show that they a
re Exel's groupoid $C^*$-algebras associated to a suitable inverse semigro
up $\\mathcal{S}_\\Lambda$\; this would allow us characterize their proper
ties\, like being Hausdorff\, effective and minimal\, and thus simplicity
for these algebras. We the study groupoid actions on left cancellative sma
ll categories and their associated Zappa-Szép products\, by reducing them
to Spielberg's model.\n\nThe contents of this talk are joint work with Ed
uard Ortega (NTNU Trondheim\, Norway)."\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/209/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Forrest Glebe (University of Hawai'i\, Mānoa)
DTSTART:20251105T200000Z
DTEND:20251105T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/210
DESCRIPTION:Title: Characters of Bundles Associated to Almost Representations of Discrete G
roups\nby Forrest Glebe (University of Hawai'i\, Mānoa) as part of No
ncommutative geometry in NYC\n\n\nAbstract\nA group is said to be matricia
lly stable if every function from the group to unitary matrices that is "a
lmost multiplicative" in the point-operator norm topology is "close\," in
the same topology\, to a genuine representation. A result of Dadarlat show
s that even cohomology obstructs matricial stability. The obstruction in h
is proof can be realized as follows. To each almost-representation\, we ma
y associate a vector bundle. This vector bundle has topological invariants
\, called Chern characters\, which lie in the even cohomology of the group
. If any of these invariants are nonzero\, the almost-representation is fa
r from a genuine representation. The first Chern character can be computed
with the "winding number argument" of Kazhdan\, Exel\, and Loring\, but t
he other invariants are harder to compute explicitly. In this talk\, I wil
l discuss results that allow us to compute higher invariants in specific c
ases: when the failure to be multiplicative is scalar (joint work with Mar
ius Dadarlat) and when the failure to be multiplicative is small in a Scha
tten p-norm.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/210/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naihuan Jing (North Carolina State University)
DTSTART:20251022T190000Z
DTEND:20251022T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/211
DESCRIPTION:Title: q-Immanants and Higher Quantum Capelli Identities\nby Naihuan Jing (
North Carolina State University) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nImminents are generalizations of determinants and permanen
ts. In this talk I will explain how to construct the family of polynomial
s $S_{\\mu}(z)$ indexed by standard Young tableaux whose coefficients are
central elements in the quantized algebra $U_q(gl(n))$. For another specia
l value of $z$\, they coincide with Okounkov's quantum immanant for the en
veloping algebra gl(n). We show that the Harish-Chandra image of $S_{\\mu
}(z)$ are the factorial Schur functions. We also obtain the quantum analog
ues of the higher Capelli identities and Newton-type identities\nfor the q
uantum enveloping algebra. This is joint work with Ming Liu and Alexander
Molev.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/211/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Ivanescu (MacEwan University\, Edmonton)
DTSTART:20251119T200000Z
DTEND:20251119T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/212
DESCRIPTION:Title: Remarks on the Cuntz Semigroup\nby Cristian Ivanescu (MacEwan Univer
sity\, Edmonton) as part of Noncommutative geometry in NYC\n\n\nAbstract\n
The Cuntz semigroup was introduced by J. Cuntz in the late 1970s as a refi
nement of K-theory for C*-algebras. Around 2000\, A. Toms discovered examp
les of simple $C^*$-algebras that share the same Elliott invariant\, given
by K-theory\, traces\, and their pairings\, but differ in their Cuntz sem
igroups. This showed that the Cuntz semigroup captures additional structur
e beyond the classical invariants and renewed interest in its study.\nIn t
his talk\, I will give an overview of the Cuntz semigroup\, explain its ba
sic ideas\, and discuss some recent developments related to it. Topics wil
l include the way-below relation and the notion of Cu-nuclearity.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/212/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Boersema (Seattle University)
DTSTART:20260506T190000Z
DTEND:20260506T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/214
DESCRIPTION:Title: Minicourse: Real C*-algebras and K-theory\, I\nby Jeff Boersema (Sea
ttle University) as part of Noncommutative geometry in NYC\n\nAbstract: TB
A\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/214/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Boersema (Seattle University)
DTSTART:20260513T190000Z
DTEND:20260513T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/215
DESCRIPTION:Title: Minicourse: Real C*-algebras and K-theory\, II\nby Jeff Boersema (Se
attle University) as part of Noncommutative geometry in NYC\n\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/215/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Boersema (Seattle University)
DTSTART:20260520T190000Z
DTEND:20260520T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/216
DESCRIPTION:Title: Minicourse: Real C*-algebras and K-theory\, III\nby Jeff Boersema (S
eattle University) as part of Noncommutative geometry in NYC\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/216/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvid Siqveland (Universitetet i Sørøst-Norge)
DTSTART:20251210T200000Z
DTEND:20251210T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/217
DESCRIPTION:Title: Localization in Associative Rings and Associative Schemes\nby Arvid
Siqveland (Universitetet i Sørøst-Norge) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nWe start with the argument for doing associative
algebraic geometry: We need schemes of associative algebras to parametriz
e (find moduli of) noncommutative objects.\n\nLet $A$ be a commutative rin
g. Then we can define the sheaf of rings on $X=Spec ~A$ by letting $O_X(U)
=im A\\subseteq %\\underset{m\\in U\\text{ maximal}}\n\\prod A_m\,$ and to
generalize this to rings that are not necessarily commutative\, we need a
replacement for the local rings $A_m.$\nWe change our view: The interesti
ng point about $A_m$ is not that it is local\, but rather that it is local
ly representing\, i.e. that in the category of pointed rings\, $mor( m\\su
bset A\,-)$ is represented by $A_m.$\n\nLet $A$ be an Associative (not nec
essarily commutative) ring. and let $M$ be a simple right $A$-module. We p
rove that in the category of pointed associative rings there is a pointed
associative ring $A_M$ representing $mor((A\,M)\,-).$ Moreover\, we prove
that for any set of $r>0$ simple modules $M=\\{M_i\\}_{i=1}^r\,$ the cate
gorical product $A_M=\\prod_{i=1}^r A_{M_i}$ exists. (When $A$ is noncommu
tative\, this is certainly not the Cartesian product). Given this\, we can
define $aspec ~A$ as the set of simple right $A$-modules\, together with
the contractions of such\, and we give $X=aspec ~A$ the topology generated
by $\\{D(f)\\}_{f\\in A}\,$ defined in such a way that if $A$ is commutat
ive\, this is the ordinary Zariski topology. Then $O_X(U)=im A\\subseteq%\
\underset{M\\in\\simp A\\cap U}\n\\prod A_M$ is a sheaf\, and an associati
ve scheme is a ringed space $X$ covered by affine open sets.\n\nWe end by
defining A Noncommutative Geometry. Let $Y=\\mathbb R^3\\times\\mathbb R^3
=\\{(\\text{observer}\,\\text{observed})\\}.$ We let $\\mathbb U$ be the n
oncommutative blowup of $\\Delta\\subseteq\\mathbb R^3\\times\\mathbb R^3$
which is adding a tangent direction to each $(x\,x)\\in\\Delta.$ Choose a
Riemannian metric on $\\mathbb R^3.$ Then the maximal velocity is the len
gth of the tangent vector on one side of the diagonal\, and we also get a
n opposite tangent vector on the dark side of the diagonal.\n\nEverything
in this lecture are Turing computable\, and so everything can be computed
by infinitesimally deformation theory. See O.A. Laudal's book [2] for th
e study of this model.\n\n\nBibliography\n\n\n\n1. E. Eriksen\, O. A. Laud
al\, A. Siqveland\,\nNoncommutative Deformation Theory. Monographs and Res
earch Notes in Mathematics. CRC Press\, Boka Raton\, FL\, 2017\n\n\n\n2. O
. A. Laudal\, Mathematical models in science\, World Scientific Publishing
Co. Pte. Ltd.\, Hackensack\, NJ\, 2021\n\n\n\n3. A. Siqveland\, \nAssocia
tive Algebraic Geometry\,\nWorld Scientific Publishing Co. Pte. Ltd.\, Hac
kensack\, NJ\, 2023\nISBN: 977-1-80061-354-6\n\n\n4. A. Siqveland\,\nAssoc
iative Schemes\,\\\\\nhttps://doi.org/10.48550/arXiv.2302.13843\,\n2024\n\
n\n5. A. Siqveland\,\nCountably Generated Matrix Algebras\,\\\\\nhttps://d
oi.org/10.48550/arXiv.2408.01034\,\n2024\n\n\n6. A. Siqveland\,\nShemes of
Associative Algebras\,\\\\\nhttps://doi.org/10.48550/arXiv.2410.17703\,\n
2024\n\n\n7. A. Siqveland\,\nAssociative Local Function Rings\,\\\\\nhttps
://doi.org/10.48550/arXiv.2410.16819\,\n2024\n\n\n8. A. Siqveland\,\nCateg
orical Construction of Schemes\,\\\\\nhttps://arxiv.org/abs/2511.03433\,\n
2025\n\n\n9. A. Siqveland\,\nSchemes of Object in abelian Categories\,\\\\
\nhttp://arxiv.org/abs/2511.04191\,\n2025\n\n\n10. A. Siqveland\,\nLocaliz
ation in Associative Rings\,\\\\\nhttp://arxiv.org/abs/2511.07900\,\n2025\
n\n\n11. A. Siqveland\,\nAssociative Schemes and Subschemes\,\\\\\nhttp://
arxiv.org/abs/2511.09176\,\n2025\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/217/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Handelman (University of Ottawa)
DTSTART:20260128T200000Z
DTEND:20260128T210000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/218
DESCRIPTION:Title: Random walks on groups from a dimension group perspective\nby David
Handelman (University of Ottawa) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nLet G be a finitely generated infinite discrete group\, an
d let S\, containing 1\, be a finite\nsubset of G that generates it as a s
emigroup (that is\, $U_{n=0}^{\\infty}S^n = G$). Let P be an element of\nt
he group algebra AG (where A is either the integers or the reals)\, whose
support is S\, and\nall of whose nonzero coefficients are positive. Then l
eft multiplication by P is a positive\nhomomorphism $AG \\to AG$\, and ite
rating it leads to an unnormalized random walk on G.\nWe can associate in
the obvious way the structure of a dimension group (a direct limit of\nsim
plicially ordered torsion-free abelian groups/finite-dimensional vector sp
aces).\n\nWe are interested in space-time cones associated to this constru
ction\, and the harmonic\nfunctions thereon (generalizing from the case of
abelian groups\, a method of proving even-\ntual positivity for repeated
multiplication by P)\, that reflect properties of the random\nwalk. A natu
ral cone arises by setting $L_n$ to be the subset of G that can be reached
by n\niterates of S starting at 1\, i.e.\, $L_n = S^n$\, and this has the
advantage that at each stage\, we\nare dealing with finite-dimensional ve
ctor spaces. However\, this is still quite complicated\nand massively redu
ndant\; so we define Ln to be Sn with all points reached in fewer than n\n
steps deleted. This is better from the dimension group point of view\, but
there is now the\npossibility of dead-ends\, that is\, g in $L_n$ with $g
· S\\subset S^n$ (so no gs—with s in S—belongs\nto $L_{n+1} · S
$)\, and these occur almost ubiquitously.\n\nWe first describe how we can
refine $L_n$ to avoid dead-ends without loss of information\,\nand then st
udy properties of the random walk that are naturally suggested by behaviou
r\nof these new (almost-) partitions of G. Then we apply them to torsion-f
ree abelian by\nfinite groups\, and show that some are much better behaved
than others\, by considering\nthe induced integral action. Then we discus
s other groups\, and in some cases\, determine\nthe pure (= extremal = ind
ecomposable = ergodic) unfaithful finite harmonic functions on\nthem\, in
particular\, for the simplest discrete Heisenberg group and the lamplighte
r group.\nFinally\, we show that the quotients by the maximal order ideals
of the resulting dimension\ngroups are always ordinary stationery dimensi
on groups (and if A is the integers\, every\nsuch can be obtained for some
free group and choice of P)\, so in particular\, have unique\ntrace. In t
he case of the lamplighter group\, this exhausts the unfaithful pure harmo
nic\nfunctions\, but in the case of the Heisenberg group\, don’t even am
ount to a hill of traces.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/218/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvid Siqveland (Universitetet i Sørøst-Norge)
DTSTART:20260415T190000Z
DTEND:20260415T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/219
DESCRIPTION:Title: Minicourse: Riemannian Geometry on Associative Varieties\, I\nby Arv
id Siqveland (Universitetet i Sørøst-Norge) as part of Noncommutative ge
ometry in NYC\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/219/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvid Siqveland (Universitetet i Sørøst-Norge)
DTSTART:20260422T190000Z
DTEND:20260422T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/220
DESCRIPTION:Title: Minicourse: Riemannian Geometry on Associative Varieties\, II\nby Ar
vid Siqveland (Universitetet i Sørøst-Norge) as part of Noncommutative g
eometry in NYC\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/220/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvid Siqveland (Universitetet i Sørøst-Norge)
DTSTART:20260429T190000Z
DTEND:20260429T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/221
DESCRIPTION:Title: Minicourse: Riemannian Geometry on Associative Varieties\, III\nby A
rvid Siqveland (Universitetet i Sørøst-Norge) as part of Noncommutative
geometry in NYC\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/221/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Vignati (Université de Paris Cité)
DTSTART:20260408T190000Z
DTEND:20260408T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/222
DESCRIPTION:Title: Rigidity of Roe-like algebras\nby Alessandro Vignati (Université de
Paris Cité) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIn
the late 80s John Roe defined a family of C*-algebras capable of detecting
coarse geometric properties of metric spaces in operator algebraic terms\
; these are called Roe-like algebras. It is fairly elementary to show that
if two metric spaces look the same in coarse geometric terms\, that is\,
if they are (bijectively) coarsely equivalent\, then the associated Roe-li
ke algebras are isomorphic. In this talk\, we investigate the converse imp
lications\, trying to extract geometric information from algebraic data.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/222/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Arhancet (University of Franche-Comté)
DTSTART:20260401T190000Z
DTEND:20260401T200000Z
DTSTAMP:20260420T021021Z
UID:NYC-NCG/223
DESCRIPTION:Title: Classical harmonic analysis viewed through the prism of noncommutative g
eometry\nby Cédric Arhancet (University of Franche-Comté) as part of
Noncommutative geometry in NYC\n\n\nAbstract\nThis talk aims to connect n
oncommutative geometry with classical harmonic analysis on Banach spaces\,
with a particular emphasis on both classical and noncommutative $L^p$-spa
ces. The overarching goal is to show how the study of operators on $L^p$-s
paces can be naturally integrated into the broader framework of noncommuta
tive geometry\, thereby opening new perspectives in analysis.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/223/
END:VEVENT
END:VCALENDAR