BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Floris Elzinger
DTSTART;VALUE=DATE-TIME:20200714T130000Z
DTEND;VALUE=DATE-TIME:20200714T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/1
DESCRIPTION:Title: Fre
e orthogonal quantum groups and strong 1-boundedness\nby Floris Elzing
er as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbstra
ct\nThe free orthogonal quantum groups\, depending on a parameter matrix Q
\, form an accessible class of examples of compact quantum groups\, which
can be viewed as analogues of both the real orthogonal groups and certain
free product groups. In fact\, a particularly well-behaved subclass\, wher
e the parameter matrix is conjugate to either an identity $I_M$ or standar
d symplectic $J_{2N}$\, shares many von Neumann algebraic properties with
the free groups. A natural question is then whether these objects are dist
inguishable on the von Neumann algebraic level. Recently\, Brannan and Ver
gnioux managed to show that in case $Q = I_M$ these operator algebras sati
sfy a free-probabilistic property called strong 1-boundedness\, which the
free group factors do not. Their proof employs techniques from the theory
of compact quantum groups\, free probability\, and the quantum analogue of
Cayley graphs. We will review the necessary notions and explain how the t
echniques of Brannan and Vergnioux can be extended to also cover the missi
ng case $Q = J_{2N}$.\n
LOCATION:https://researchseminars.org/talk/GOBA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrik Wirzenius
DTSTART;VALUE=DATE-TIME:20200721T130000Z
DTEND;VALUE=DATE-TIME:20200721T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/2
DESCRIPTION:Title: The
quotient algebra of compact-by-approximable operators.\nby Henrik Wir
zenius as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAb
stract\nLet $K(X)$ denote the Banach algebra of compact operators acting o
n a Banach space $X$ and $A(X)$ the uniform closure of the bounded finite
rank operators. In this talk I will describe joint work with Hans-Olav Tyl
li (University of Helsinki) on the quotient algebra $K(X)/A(X)$ of compact
-by-approximable operators. This is a radical Banach algebra that is poorl
y understood\, mainly because $K(X)/A(X)$ is non-trivial only within the c
lass of Banach spaces $X$ failing the approximation property. I will focus
on the size and algebraic structure of $K(X)/A(X)$.\n
LOCATION:https://researchseminars.org/talk/GOBA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simeng Wang
DTSTART;VALUE=DATE-TIME:20200728T130000Z
DTEND;VALUE=DATE-TIME:20200728T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/3
DESCRIPTION:Title: Ind
ividual ergodic theorems on von Neumann algebras\nby Simeng Wang as pa
rt of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbstract\nBirk
hoff’s celebrated individual ergodic theorem asserts that for a measure-
preserving ergodic transformation on a measure space\, the time average is
equal to the space average almost everywhere. Since the theory of von Neu
mann algebras is a quantum analogue of the classical measure theory\, it i
s natural to study similar individual ergodic theorems in the setting of v
on Neumann algebras. The study was exactly initiated by Lance in 1970s\, a
nd witnessed fruitful progress in recent decades with the help of modern t
ools from the operator space theory\, such as the noncommutative vector-va
lued $L^p$-spaces studied by Pisier\, Junge and Xu. This talk aims to give
a gentle introduction to the aforementioned topic\, and if time permits\,
we may also present some recent results in this direction\, in particular
ergodic theorems for some group actions on von Neumann algebras and for p
ositive contractions on $L^p$-spaces\, which is joint work with Guixiang H
ong\, Ben Liao and Samya Ray.\n
LOCATION:https://researchseminars.org/talk/GOBA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Gotfredsen
DTSTART;VALUE=DATE-TIME:20200804T130000Z
DTEND;VALUE=DATE-TIME:20200804T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/4
DESCRIPTION:Title: The
quantised interval as a quantum metric space\nby Thomas Gotfredsen as
part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbstract\nT
he study of metrics on state spaces arising from semi-norms dates back to
Connes and was formalised as the notion of a compact quantum metric space
by Rieffel\, whose notion of quantum Gromov-Hausdorff distance on the clas
s of compact quantum metric spaces\, has established a new famework for th
e study of approximations of C*-algebras. \n\nIn a recent paper\, Aguilar
and Kaad have shown that the standard Podleś sphere\, originally introduc
ed as the homogeneous space for Woronowicz' quantum SU(2)\, is in fact a c
ompact quantum metric space\, and they posed the rather natural question\,
whether the standard Podleś sphere converges to the standard 2-sphere in
the quantum analogues of the Gromov-Hausdorff distance as the deformation
parameter tends to 1 . \nIn my talk based on joint work with Jens Kaad an
d David Kyed\, I will present some new developments to the above question.
In particular we have shown that the commutative C*-subalgebras generated
by the self-adjoint generator of the standard Podleś sphere\, converge t
o the interval of length \\pi as one would expect if the more general conv
ergence result is true\, and that the spaces in fact vary continuously. Th
is provides some evidence that the convergence result for the Podles spher
es may hold true as well (this is currently work in progress).\n
LOCATION:https://researchseminars.org/talk/GOBA/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Orendain
DTSTART;VALUE=DATE-TIME:20200811T130000Z
DTEND;VALUE=DATE-TIME:20200811T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/5
DESCRIPTION:Title: For
mal Haagerup standard form on infinite index morphisms of factors\nby
Juan Orendain as part of Groups\, Operators\, and Banach Algebras Webinar\
n\n\nAbstract\nThe Haagerup $L^2$-space construction\, introduced by Haage
rup in the 70's\, associates a standard form to every von Neumann algebra\
, without any reference to weights\, and is thus regarded as a coordinate
free version of the GNS construction. The Haagerup standard form and the C
onnes fusion tensor product organize von Neumann algebras and their repres
entations into a bicategory. The main interest on this bicategory comes fr
om the fact that it encodes weak Morita equivalence as a formal homotopy r
elation.\n\nBicategories are a specific type of categorical structure of s
econd order\, corresponding to globular sets. The second order categorical
structures corresponding to cubical sets are double categories. Results s
tudying relations between cubical and globular categories have been obtain
ed continually since the 60's\, mainly in nonabelian homotopy theory\, but
more recently in areas ranging from algebraic geometry to network theory.
I will explain results of this type regarding the existence of two non-eq
uivalent double categories of representations of factors\, and how these s
tructures relate to questions of functoriality of the Haagerup standard fo
rm and the Connes fusion tensor product.\n\nThis program builds on work of
Bartels\, Douglas and Hénriques on the theory of coordinate free conform
al nets and their relation to the Stolz-Teichner program.\n
LOCATION:https://researchseminars.org/talk/GOBA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aasaimani Thamizhazhagan
DTSTART;VALUE=DATE-TIME:20200818T130000Z
DTEND;VALUE=DATE-TIME:20200818T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/6
DESCRIPTION:Title: On
the structure of invertible elements in Fourier-Stieltjes algebras\nby
Aasaimani Thamizhazhagan as part of Groups\, Operators\, and Banach Algeb
ras Webinar\n\n\nAbstract\nFor a locally compact abelian group $G$\, J. L.
Taylor (1971) gave a complete characterization of invertible elements in
the measure algebra $M(G)$. Using the Fourier-Stieltjes transform\, this c
haracterization can be carried out in the context of Fourier-Stieltjes alg
ebras $B(G)$. We generalise this characterization to the setting of the Fo
urier-Stieltjes algebra $B(G)$ of certain classes of locally compact group
s\, in particular\, many totally minimal groups and the $ax+b$-group.\n
LOCATION:https://researchseminars.org/talk/GOBA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Kim
DTSTART;VALUE=DATE-TIME:20200825T130000Z
DTEND;VALUE=DATE-TIME:20200825T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/7
DESCRIPTION:Title: Why
MIP* = RE implies not-CEP and Blackadar-Kirchberg's MF problem\nby Sa
m Kim as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbs
tract\nIn this expository talk\, we explain a direct route to why the resu
lts of Ji\, Natarajan\, Vidick\, Wright\, and Yuen give us a II$_1$-factor
that cannot embed into a tracial ultrapower of the separable hyperfinite
II$_1$-factor $\\mathcal{R}$. More specifically\, we define a class of fin
itely generated unital C*-algebras $C^*(\\mathcal{G})$ for a fixed paramet
er $\\mathcal{G}$ with the following property: there exist extremal traces
$\\tau$ on $C^*(\\mathcal{G})$ such that the II$_1$-factor $\\mathcal{M}_
\\tau$ generated by $C^*(\\mathcal{G})$ in the GNS representation of $\\ta
u$ has the property that there cannot exist a unital *-homomorphism from $
\\mathcal{M}_\\tau$ into a tracial ultrapower of $\\mathcal{R}$. We descri
be ways in which convex geometry over $\\mathbb{R}^n$ will give us such pa
rameters $\\mathcal{G}$ and extremal traces $\\tau$. As a consequence of o
ur construction\, we have a separable counter-example of Blackadar-Kirchbe
rg's MF problem\, which asks whether every stably finite C*-algebra embeds
into a norm ultrapower of the UHF algebra $\\mathcal{Q}$. Questions relat
ed to the refinement of both the MF conjecture and the refutation of CEP a
re raised at the end.\n
LOCATION:https://researchseminars.org/talk/GOBA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Klisse
DTSTART;VALUE=DATE-TIME:20201116T150000Z
DTEND;VALUE=DATE-TIME:20201116T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/8
DESCRIPTION:Title: Top
ological boundaries of connected graphs and Coxeter groups\nby Mario K
lisse as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbs
tract\nIn this talk we will present a method which allows to associate cer
tain topological spaces with connected rooted graphs. These spaces reflect
combinatorial and order theoretic properties of the underlying graph and
are particularly tractable in the case of Cayley graphs of finite rank Cox
eter groups. In that context we speak of the compactification and the boun
dary of the Coxeter group. They have some desirable properties and nicely
relate to various other important constructions such as Gromov's hyperboli
c compactification\, the Higson compactification and Furstenberg boundarie
s of Coxeter groups.\n\nThe study of (certain) compactifications and bound
aries of groups has lots of interesting operator algebraic applications. F
or instance\, they play a role in the rigidity theory of von Neumann algeb
ras and are crucial in Kalantar-Kennedy's solution of the simplicity quest
ion for group C*-algebras. Our construction turns out to be closely relate
d to Hecke C*-/ and Hecke von Neumann algebras. These are operator algebra
s associated with (Iwahori) Hecke algebras. We will discuss some implicati
ons of this connection.\n
LOCATION:https://researchseminars.org/talk/GOBA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sanaz Pooya
DTSTART;VALUE=DATE-TIME:20201123T150000Z
DTEND;VALUE=DATE-TIME:20201123T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/9
DESCRIPTION:Title: Hig
her Kazhdan projections and Baum-Connes conjectures\nby Sanaz Pooya as
part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbstract\nT
he Baum-Connes conjecture\, if it holds for a certain group\, provides top
ological tools to compute the K-theory of its reduced group C*-algebra. Th
is conjecture has been confirmed for large classes of groups\, such as ame
nable groups\, but also for some Kazhdan's property (T) groups. Property (
T) and its strengthening are driving forces in the search for potential co
unterexamples to the conjecture. Having property (T) for a group is charac
terised by the existence of a certain projection in the universal group C*
-algebra of the group\, known as the Kazhdan projection. It is this projec
tion and its analogues in other completions of the group ring\, which obst
ruct known methods of proof for the Baum-Connes conjecture. In this talk\,
I will introduce a generalisation of Kazhdan projections. Employing these
projections we provide a link between surjectivity of the Baum-Connes map
and the l²-Betti numbers of the group. A similar relation can be obtaine
d in the context of the coarse Baum-Connes conjecture. This is based on jo
int work with Kang Li and Piotr Nowak.\n
LOCATION:https://researchseminars.org/talk/GOBA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bruce (Queen Mary University of London and the University of
Glasgow)
DTSTART;VALUE=DATE-TIME:20201130T160000Z
DTEND;VALUE=DATE-TIME:20201130T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/10
DESCRIPTION:Title: C*
-algebras from actions of congruence monoids\nby Chris Bruce (Queen Ma
ry University of London and the University of Glasgow) as part of Groups\,
Operators\, and Banach Algebras Webinar\n\n\nAbstract\nI will give an ove
rview of recent results for semigroup C*-algebras associated with number f
ields. These results are already interesting in the case where the field i
s the rational numbers\, and I will focus mostly on this case to make ever
ything more explicit and accessible.\nC*-algebras of full ax+b-semigroups
over rings of algebraic integers were first studied by Cuntz\, Deninger\,
and Laca\; their construction has since been generalized by considering ac
tions of congruence monoids. Semigroup C*-algebras obtained this way provi
de an example class of unital\, separable\, nuclear\, strongly purely infi
nite C*-algebras which\, in many cases\, completely characterize the initi
al number-theoretic data. They also carry canonical time evolutions\, and
the associated C*-dynamical systems exhibit intriguing phenomena. For inst
ance\, the striking similarity between the K-theory formula and the parame
terization space for the low temperature KMS states\, observed by Cuntz in
the case of the full ax+b-semigroup\, persists in the more general settin
g.\nPart of this work is joint with Xin Li\, and part is joint with Marcel
o Laca and Takuya Takeishi.\n
LOCATION:https://researchseminars.org/talk/GOBA/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Stella Adamo (Mathematical Research Institute of Oberwolfach
)
DTSTART;VALUE=DATE-TIME:20201207T150000Z
DTEND;VALUE=DATE-TIME:20201207T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/11
DESCRIPTION:Title: Th
e problem of continuity for representable functionals on Banach quasi *-al
gebras\nby Maria Stella Adamo (Mathematical Research Institute of Ober
wolfach) as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\n
Abstract\nA way to study problems concerning quantum statistical mechanics
is to consider locally convex quasi *-algebras\, for which Banach quasi *
-algebras constitute a special class. For example\, Banach quasi *-algebra
s can be obtained by taking the completion of a *-algebra $A_0$ with respe
ct to a norm $|| \\cdot ||$ for which the multiplication is (only) separat
ely continuous.\nIn the (locally convex) quasi *-algebras setting\, a rele
vant role is played by representable functionals. Roughly speaking\, a lin
ear functional will be called representable if it allows a GNS-like constr
uction.\n\nIn this talk\, we discuss the problem of continuity for these f
unctionals and some related results. We begin our discussion by looking at
the properties of representable (and continuous) functionals\, especially
in the simplest case of Hilbert quasi *-algebras. This discussion leads n
aturally to look at the problem of continuity for these functionals. Hence
\, we examine the approaches to study this problem. If time permits\, we w
ill discuss some applications.\nThe first part of the talk is joint work w
ith C. Trapani. The second part is joint work with M. Fragoulopoulou.\n
LOCATION:https://researchseminars.org/talk/GOBA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Arnott (University of Lancaster)
DTSTART;VALUE=DATE-TIME:20201214T150000Z
DTEND;VALUE=DATE-TIME:20201214T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/12
DESCRIPTION:Title: Ke
rnels of bounded operators on transfinite Banach sequence spaces\nby M
ax Arnott (University of Lancaster) as part of Groups\, Operators\, and Ba
nach Algebras Webinar\n\n\nAbstract\nFor a Banach space $E$\, we ask the f
ollowing question: "Is it true that for every closed subspace $Y$ of $E$\,
there exists some bounded linear operator $T : E \\to E$ for which $Y= \\
ker T$?"\n\nIn a recent paper by Niels Laustsen and Jared White\, it was p
roved that every separable Banach space answers the question in the positi
ve\, and that there exists a reflexive Banach space which answers the ques
tion in the negative.\n\nLet $\\Gamma$ be an uncountable cardinal. In this
talk we will investigate the above question for the transfinite Banach se
quence spaces $\\ell_p(\\Gamma)$ for $1\\leq p <\\infty$\, and $c_0(\\Gamm
a)$. The question is answered in the negative for $\\ell_1(\\Gamma)$\, and
in the positive for $\\ell_p(\\Gamma)$ for $1 < p <\\infty$ and $c_0(\\Ga
mma)$.\n
LOCATION:https://researchseminars.org/talk/GOBA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eusebio Gardella
DTSTART;VALUE=DATE-TIME:20210111T150000Z
DTEND;VALUE=DATE-TIME:20210111T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/15
DESCRIPTION:Title: Gr
oup representations on $L^p$-spaces\nby Eusebio Gardella as part of Gr
oups\, Operators\, and Banach Algebras Webinar\n\n\nAbstract\nFor a given
locally compact group\, we study group representations\n(by invertible iso
metries) on $L^p$-spaces\, for $p \\in [1\,\\infty)$\, and the associated
\nBanach algebras. For example\, the algebra associated to the left regula
r \nrepresentation was first studied by Herz in the 70's\, and has receive
d renewed \nattention in the past two decades. There is also a "universal"
$L^p$-operator group\nalgebra. For $p=2$ one obtains the group C*-algebra
s\, and the behaviour of these \nobjects for other values of p tend to exh
ibit a mixture between the case p=2 and \nthe much more rigid case of $L^1
(G)$. I will give an overview of what is known and \nwhat questions remain
open.\n
LOCATION:https://researchseminars.org/talk/GOBA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eirik Berge
DTSTART;VALUE=DATE-TIME:20210118T150000Z
DTEND;VALUE=DATE-TIME:20210118T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/16
DESCRIPTION:Title: Qu
antization on the affine group\nby Eirik Berge as part of Groups\, Ope
rators\, and Banach Algebras Webinar\n\n\nAbstract\nThe classical notion o
f quantization in Euclidean space -- using time and frequency shifts -- ha
s traditionally been of interest to people in classical analysis and theor
etical physics. However\, it has become more apparent in recent years that
understanding geometric and algebraic aspects of quantization is essentia
l. In this talk\, I will review (a version of) classical quantization befo
re moving on to the more recent phenomenon of quantization with time shift
s and dilations. As probably suspected\, this will naturally involve the a
ffine group. I will show that the theory here is heavily influenced by the
non-unimodularity of the affine group. If time permits\, I will talk abou
t some recent work and open problems that are left in this setting. The ma
terial presented is based on joint work with Stine M. Berge\, Franz Luef\,
and Eirik Skrettingland.\n
LOCATION:https://researchseminars.org/talk/GOBA/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Priyanga Ganesan
DTSTART;VALUE=DATE-TIME:20210125T150000Z
DTEND;VALUE=DATE-TIME:20210125T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/17
DESCRIPTION:Title: Qu
antum graphs\nby Priyanga Ganesan as part of Groups\, Operators\, and
Banach Algebras Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOBA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samya Kumar Ray
DTSTART;VALUE=DATE-TIME:20210201T150000Z
DTEND;VALUE=DATE-TIME:20210201T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/18
DESCRIPTION:Title: Is
ometries between Schatten-$p$ classes\nby Samya Kumar Ray as part of G
roups\, Operators\, and Banach Algebras Webinar\n\n\nAbstract\nIsometries
between commutative and non-commutative $L_p$-spaces have a long history w
hich starts from the seminal work of Banach himself. However\, despite man
y remarkable results and characterization theorems not much is known when
finite dimensional Schatten-$p$ classes embed between each other. In this
direction\, together with my collaborators\, I have some rigidity results
about the isometric embeddability of finite dimensional Schatten-$p$ class
. For example\, if $2 < p<\\infty$ and $T:\\ell_p^2\\to B(\\ell_2)$ is an
isometry\, then $T (e_1)\,T(e_2) \\in B(\\ell_2) K(\\ell_2)$. We also have
applications in the direction of operator spaces. Interestingly\, our met
hods are completely new and use various concepts such as Birkhoff-James or
thogonality\, norm parallelism\, multiple operator integral and Kato-Relli
ch theorem in the perturbation of a linear operator.\n
LOCATION:https://researchseminars.org/talk/GOBA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnendu Khan
DTSTART;VALUE=DATE-TIME:20210208T150000Z
DTEND;VALUE=DATE-TIME:20210208T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/19
DESCRIPTION:Title: Fu
ndamental group of certain property (T) factors\nby Krishnendu Khan as
part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbstract\nC
alculation of fundamental group of type $II_1$ factor is\, in general\, an
extremely hard and central problem in the field of von Neumann algebras.
In this direction\, a conjecture due to A. Connes states that the fundamen
tal group of the group von Neumann algebra associated to any icc property
(T) group is trivial. Up to now there was no single example of property (T
) factor satisfying the conjecture. In this talk\, I shall provide the fir
st examples of property (T) group factors (arising from group theoretic co
nstructions) with trivial fundamental group. This talk is based on a joint
work with Ionut Chifan\, Sayan Das and Cyril Houdayer.\n
LOCATION:https://researchseminars.org/talk/GOBA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrios Gerontogiannis
DTSTART;VALUE=DATE-TIME:20210215T150000Z
DTEND;VALUE=DATE-TIME:20210215T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/20
DESCRIPTION:Title: Sm
ooth algebras associated to Smale spaces and extensions by Schatten ideals
\nby Dimitrios Gerontogiannis as part of Groups\, Operators\, and Bana
ch Algebras Webinar\n\n\nAbstract\nIn the 1980's\, Douglas initiated the s
tudy of smooth extensions of C*-algebras\; C*-algebraic extensions by the
ideal of compact operators that on certain dense *-subalgebras (in cases B
anach) reduce to algebraic extensions by Schatten ideals. Douglas studied
smooth extensions of C(X)\, for X being a finite complex. Shortly after\,
Douglas and Voiculescu studied the case of sphere extensions. In the nonco
mmutative setting\, examples of C*-algebras with a pervading presence of s
mooth extensions include the Cuntz-Krieger algebras (Goffeng-Mesland)\, an
d crossed product C*-algebras formed by Gromov hyperbolic groups acting on
their boundary (Emerson-Nica). In this talk I will present the notion of
smoothness in C*-algebras and that the smooth extensions of Ruelle algebra
s (higher dimensional analogues of Cuntz-Krieger algebras) associated to S
male spaces\, are generic in some sense. The smoothness of Ruelle algebras
has interesting connections with the Hausdorff dimension of the underlyin
g Smale space. This research is part of my PhD thesis.\n
LOCATION:https://researchseminars.org/talk/GOBA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Emma Mikkelsen
DTSTART;VALUE=DATE-TIME:20210222T150000Z
DTEND;VALUE=DATE-TIME:20210222T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/21
DESCRIPTION:Title: On
the quantum twistor bundle\nby Sophie Emma Mikkelsen as part of Group
s\, Operators\, and Banach Algebras Webinar\n\n\nAbstract\nThe concept of
a quantum principal bundle is well established by now. However\, general (
locally trivial) fiber bundles are much less understood in the noncommutat
ive setting.\nWe investigate a noncommutative sphere bundle from what we
call the quantum twistor bundle.It is constructed as a quotient of the qua
ntum instanton bundle of Bonechi\, Ciccoli and Tarlini $SU_q(2)\\to S_q^7\
\to S_q^4$ for a suitable circle action on the Vaksmann-Soibelman quantum
sphere $S_q^7$. It is an example of a locally trivial noncommutative bund
le fulfilling conditions of the framework proposed by Brzeziski and Szyman
ski.\n
LOCATION:https://researchseminars.org/talk/GOBA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Raad
DTSTART;VALUE=DATE-TIME:20210301T150000Z
DTEND;VALUE=DATE-TIME:20210301T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/22
DESCRIPTION:Title: Ex
istence and Uniqueness of Canonical Cartan Subalgebras in Inductive Limit
C*-algebras\nby Ali Raad as part of Groups\, Operators\, and Banach Al
gebras Webinar\n\n\nAbstract\nCartan subalgebras of C*-algebras have witne
ssed major breakthroughs recently\, becoming the cornerstone of how to bui
ld a bridge between C*-algebras on the one hand\, and geometric group theo
ry and topological dynamics on the other. As such\, existence and uniquene
ss questions become crucial. \n\nIn this talk I will introduce the notion
of a Cartan subalgebra and discuss the question of existence and uniquenes
s in the setting of inductive limit C*-algebras. Indeed Stratila and Voicu
lescu show in 1975 that AF-algebras admit a canonical Cartan subalgebra. I
will provide a novel uniqueness result for the uniqueness of these subalg
ebras in AF-algebras\, and also completely settle the question of existenc
e and uniqueness of canonical Cartan subalgebras in AI-algebras and AT-alg
ebras. If time permits\, I will generalize a theorem of Renault's that giv
es a correspondence between Cartan pairs and C*-algebras of twisted étale
groupoids.\n
LOCATION:https://researchseminars.org/talk/GOBA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Favre (University of Stockholm)
DTSTART;VALUE=DATE-TIME:20210315T150000Z
DTEND;VALUE=DATE-TIME:20210315T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/23
DESCRIPTION:Title: An
Algebraic Characterization of the Type I Property for Ample Groupoids
\nby Gabriel Favre (University of Stockholm) as part of Groups\, Operators
\, and Banach Algebras Webinar\n\n\nAbstract\nI will discuss the type I pr
operty for second countable locally compact Hausdorff ample groupoids. Loo
sely speaking\, the type I property says that the von Neumann algebras gen
erated by unitary representations are the simplest possible kind of von Ne
umann algebras to understand.\nAfter developing a feel for this property\,
the discussion will shift towards the noncommutative Stone duality betwee
n ample groupoids and Boolean inverse semigroups. This duality is used in
a new characterization of the type I property for groupoids\, that we obta
ined. This characterization will appear as the semigroup counterpart to a
result of van Wyk. If time permits\, I will apply our result to algebraica
lly characterize discrete inverse semigroups of type I.\nThis is joint wor
k with S. Raum.\n
LOCATION:https://researchseminars.org/talk/GOBA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blake Green (University of Lancaster)
DTSTART;VALUE=DATE-TIME:20210322T150000Z
DTEND;VALUE=DATE-TIME:20210322T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/24
DESCRIPTION:by Blake Green (University of Lancaster) as part of Groups\, O
perators\, and Banach Algebras Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOBA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Krajczok (IMPAN\, Warsaw)
DTSTART;VALUE=DATE-TIME:20210426T140000Z
DTEND;VALUE=DATE-TIME:20210426T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/25
DESCRIPTION:Title: On
the von Neumann algebra of class functions on a compact quantum group
\nby Jacek Krajczok (IMPAN\, Warsaw) as part of Groups\, Operators\, and B
anach Algebras Webinar\n\n\nAbstract\nA famous result of Pytlik states tha
t the radial subalgebra in the group von Neumann algebra of a free group o
n n>=2 generators is maximal abelian (MASA). One can study an analogue of
this subalgebra - the von Neumann algebra generated by characters - in a m
ore general context of discrete quantum groups. By a result of Freslon and
Vergnioux\, it is known that this algebra is MASA for the discrete quantu
m group dual to the Kac-type orthogonal quantum group. I will show that th
e situation is quite different when our compact quantum group is not of Ka
c type (equivalently\, the discrete dual is non-unimodular). The crucial n
otion for our work is that of quasi-split inclusions.\nThis is a joint wor
k with Mateusz Wasilewski.\n
LOCATION:https://researchseminars.org/talk/GOBA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Manor (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20210503T140000Z
DTEND;VALUE=DATE-TIME:20210503T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/26
DESCRIPTION:Title: No
nunital operator systems and noncommutative convexity\nby Nick Manor (
University of Waterloo) as part of Groups\, Operators\, and Banach Algebra
s Webinar\n\n\nAbstract\nThe recent work on nc convex sets of Davidson-Ken
nedy and Kennedy-Shamovich show that there is a rich interplay between the
category of operator systems and the category of compact nc convex sets\,
leading to new insights even in the case of C*-algebras. The category of
nc convex sets are a generalization of the usual notion of a compact conve
x set that provides meaningful connections between convex theoretic notion
s and notions in operator system theory. In this talk\, we present a relat
ed duality theorem for norm closed self-adjoint subspaces of $B(H)$. Using
this duality\, we will describe various C*-algebraic and operator system
theoretic notions\, as well as a rich class of examples arising as duals o
f well-understood operator systems. This is joint work with Matthew Kenned
y and Se-Jin Kim.\n
LOCATION:https://researchseminars.org/talk/GOBA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Frei
DTSTART;VALUE=DATE-TIME:20210517T140000Z
DTEND;VALUE=DATE-TIME:20210517T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/27
DESCRIPTION:Title: Re
lative Cuntz-Pimsner algebras: a complete description of their lattice of
gauge-invariant ideals\nby Alex Frei as part of Groups\, Operators\, a
nd Banach Algebras Webinar\n\n\nAbstract\nWe give a new\, systematic appro
ach to the gauge-invariant uniqueness theorem describing all relative Cunt
z-Pimsner algebras\,\nand whence revealing a complete description of their
gauge-invariant ideal lattice.\n\nFor this we start with a swift introduc
tion to C*-correspondences\, in particular drawing a comparison to Fell bu
ndles.\n\nContinuing\, we provide a slightly deeper analysis of covariance
s as well as their relation to kernels and quotients. With these observati
ons at hand\, we introduce the relevant reduction leading us to a suitable
parametrization of relative Cuntz-Pimsner algebras\, and so revealing a c
omplete description of their gauge-invariant ideal lattice.\nOur parametri
zation is a heuristic analog of Katsura's originally obtained one.\n\nWith
this at hand\, we arrive at the gauge-invariant uniqueness theorem\, for
all arbitrary gauge-equivariant representations.\n\nFrom here we move on t
o the analysis part of the program. We compute the covariances in the case
of the Fock representation and its quotients. As a result\, we derive tha
t the parametrization of relative Cuntz-Pimsner algebras introduced above
is also classifying. In other words\, we obtain a complete and intrinsic p
icture of the lattice of quotients\, and equivalently of their lattice of
gauge-invariant ideals.\n\nIf time permits\, we finish off with the next c
hapter on their induced Fell bundles and dilations\, as already investigat
ed by Schweizer.\n
LOCATION:https://researchseminars.org/talk/GOBA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordy van Velthoven
DTSTART;VALUE=DATE-TIME:20210524T140000Z
DTEND;VALUE=DATE-TIME:20210524T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/28
DESCRIPTION:Title: Co
mpleteness of coherent systems associated to lattices\nby Jordy van Ve
lthoven as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nA
bstract\nThe talk considers the relation between the spanning properties o
f a lattice orbit of a square-integrable projective representation and the
associated lattice co-volume. Under a suitable compatibility condition be
tween the cocycle and the lattice\, the density theorem provides a trichot
omy that precisely describes the spanning properties of a given lattice or
bit. For classes of Lie groups\, the interplay between the density theorem
and Perelomov’s completeness problem will be considered.\n
LOCATION:https://researchseminars.org/talk/GOBA/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitch Haslehurst
DTSTART;VALUE=DATE-TIME:20210607T140000Z
DTEND;VALUE=DATE-TIME:20210607T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/29
DESCRIPTION:Title: Re
lative K-theory for C*-algebras and factor groupoids\nby Mitch Haslehu
rst as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbstr
act\nIt is a reasonable question to ask\, given some K-theory data\, wheth
er or not there is a groupoid whose C*-algebra has this K-theory data. The
re has been substantial recent progress on this question\, notably Xin Li'
s construction of Cartan subalgebras in classifiable C*-algebras as well a
s work of Robin Deeley\, Ian Putnam\, and Karen Strung via minimal dynamic
al systems. In this talk I will discuss an approach to this problem using
factor groupoids. I will begin with an overview of relative K-theory\, whi
ch is essential for computational purposes\, and proceed to describe some
constructions of factor groupoids which provide a degree of control over t
he K-theory of their C*-algebras.\n
LOCATION:https://researchseminars.org/talk/GOBA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Przemyslaw Ohrysko
DTSTART;VALUE=DATE-TIME:20210531T140000Z
DTEND;VALUE=DATE-TIME:20210531T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/30
DESCRIPTION:by Przemyslaw Ohrysko as part of Groups\, Operators\, and Bana
ch Algebras Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOBA/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Przemyslaw Ohrysko (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20210614T140000Z
DTEND;VALUE=DATE-TIME:20210614T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T233856Z
UID:GOBA/31
DESCRIPTION:Title: In
version problem in measure and Fourier-Stieltjes algebras\nby Przemysl
aw Ohrysko (University of Warsaw) as part of Groups\, Operators\, and Bana
ch Algebras Webinar\n\n\nAbstract\nLet $G$ be a locally compact Abelian gr
oup with its dual $\\widehat{G}$ and let $M(G)$ denote the\nBanach algebra
of complex-valued measures on $G$. The classical Wiener-Pitt phenomenon\n
asserts that the spectrum of a measure may be strictly larger than the clo
sure of the range\nof its Fourier-Stieltjes transform. In particular\, if
$G$ is non-discrete\, there exists µ ∈ $M(G)$\nsuch that |$\\widehat{\\
mu}$(γ)| > c > 0 for every γ ∈ $\\widehat{G}$ but µ is not invertible
. In the paper [N]\, N.\nNikolski suggested the following problem.\n\nProb
lem 1. Let µ ∈ $M(G)$ satisfy $\\|\\mu\\|$ ≤ 1 and |$\\widehat{\\mu}$
(γ)| ≥ δ for every γ ∈ $\\widehat{G}$. What is\nthe minimal value o
f $\\delta_0$ assuring the invertibility of µ for every δ > $\\delta_0$?
What can be said\nabout the inverse (in terms of δ)?\n\nIn my talk I sho
w that $\\delta_0 =1/2$\nis the optimal value for the first question (for
non-discrete\n$G$). Also\, I will present a partial solution for the quant
itative variant of the problem\n(second question): if all elements of G (e
xcept the unit) are of infinite order then we can\ncontrol the norm of the
inverse for every δ > $\\frac{-1+\\sqrt{33}}{8}$. This improves the orig
inal\nresult of Nikolski: δ > $\\frac{1}{\\sqrt{2}}$.\nIf time permits I
will present some generalizations of the aformentioned results for Fourier
Stieltjes algebras built on non-commutative groups.\nThe talk is based on
a paper [OW] written in collaboration with Mateusz Wasilewski.\n
LOCATION:https://researchseminars.org/talk/GOBA/31/
END:VEVENT
END:VCALENDAR