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BEGIN:VEVENT
SUMMARY:Mehrdad Kalantar (University of Houston\, USA)
DTSTART;VALUE=DATE-TIME:20201109T150000Z
DTEND;VALUE=DATE-TIME:20201109T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/1
DESCRIPTION:Title: Furs
tenberg boundary of a discrete quantum group\nby Mehrdad Kalantar (Uni
versity of Houston\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbs
tract\nThe notion of topological boundary actions has recently found strik
ing applications in the study of operator algebras associated to discrete
groups. We will discuss the analogue concept for discrete quantum groups\,
show that in this generalization there still always exists a maximal boun
dary action - the so-called Furstenberg boundary. We discuss applications
in problems of C*-simplicity and uniqueness of the Haar state of the dual.
\n\nThis is joint work with Pawel Kasprzak\, Adam Skalski and Roland Vergn
ioux.\n
LOCATION:https://researchseminars.org/talk/QGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuki Arano (Kyoto University\, Japan)
DTSTART;VALUE=DATE-TIME:20201116T150000Z
DTEND;VALUE=DATE-TIME:20201116T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/2
DESCRIPTION:Title: On t
he Baum-Connes conjecture for discrete quantum groups with torsion and the
quantum Rosenberg Conjecture\nby Yuki Arano (Kyoto University\, Japan
) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe give a decompo
sition of the equivariant Kasparov category for a discrete quantum group w
ith torsions. This formulates the Baum-Connes assembly map for general dis
crete quantum groups possibly with torsion. As an application\, we show th
at the group C*-algebra of a discrete quantum group in a certain class sat
isfies the UCT.\n
LOCATION:https://researchseminars.org/talk/QGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenny De Commer (Vrije Universiteit Brussel\, Belgium)
DTSTART;VALUE=DATE-TIME:20201123T150000Z
DTEND;VALUE=DATE-TIME:20201123T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/3
DESCRIPTION:Title: A qu
antization of Sylvester's law of inertia\nby Kenny De Commer (Vrije Un
iversiteit Brussel\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\
nAbstract\nSylvester's law of inertia states that two self-adjoint matrice
s A and B are related as $A = X^*BX$ for some invertible complex matrix $X
$ if and only if $A$ and $B$ have the same signature $(N_+\,N_-\,N_0)$\, i
.e. the same number of positive\, negative and zero eigenvalues. In this t
alk\, we will discuss a quantized version of this law: we consider the ref
lection equation *-algebra (REA)\, which is a quantization of the *-algebr
a of polynomial functions on self-adjoint matrices\, together with a natur
al adjoint action by quantum $GL(N\,\\mathbb{C})$. We then show that to ea
ch irreducible bounded *-representation of the REA can be associated an ex
tended signature $(N_+\,N_-\,N_0\,[r])$ with $[r]$ in $\\mathbb{R}/\\mathb
b{Z}$\, and we will explain in what way this is a complete invariant of th
e orbits under the action by quantum $GL(N\,\\mathbb{C})$. This is part of
a work in progress jointly with Stephen Moore.\n
LOCATION:https://researchseminars.org/talk/QGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivo Dell'Ambrogio (Université de Lille\, France)
DTSTART;VALUE=DATE-TIME:20201130T150000Z
DTEND;VALUE=DATE-TIME:20201130T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/4
DESCRIPTION:Title: The
spectrum of equivariant Kasparov theory for cyclic groups of prime order\nby Ivo Dell'Ambrogio (Université de Lille\, France) as part of Quantu
m Groups Seminar [QGS]\n\n\nAbstract\nIn 2006\, Ralf Meyer and Ryszard Nes
t proved that the G-equivariant Kasparov category of a locally compact gro
up G carries the structure of a tensor-triangulated category. This structu
re conveniently handles the usual homological algebra\, bootstrap construc
tions and assembly maps involved in many KK-theoretical calculations\, e.g
. in connection with the Baum-Connes conjecture. As with any tensor trian
gulated category\, we can also associate to the G-equivariant Kasparov cat
egory its spectrum in the sense of Paul Balmer. This is a topological spac
e (similar to the Zariski spectrum of a commutative ring) which allows us\
, as it were\, to re-inject some genuinely geometric ideas in non-commutat
ive geometry. It turns out that the spectrum contains enough information t
o prove the Baum-Connes conjecture for G\, hence we should expect the ques
tion of its computation to be very hard. In this talk\, after discussing
such preliminaries and motivation\, I will present joint work with Ralf Me
yer providing the state of the art on this subject. Although more general
partial results are known\, a complete answer is only known so far for fin
ite groups of prime order and for algebras in the bootstrap category.\n
LOCATION:https://researchseminars.org/talk/QGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martijn Caspers (TU Delft\, Netherlands)
DTSTART;VALUE=DATE-TIME:20201207T150000Z
DTEND;VALUE=DATE-TIME:20201207T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/5
DESCRIPTION:Title: Ries
z transforms on compact quantum groups and strong solidity\nby Martijn
Caspers (TU Delft\, Netherlands) as part of Quantum Groups Seminar [QGS]\
n\n\nAbstract\nThe Riesz transform is one of the most important and classi
cal examples of a Fourier multiplier on the real numbers. It may be descri
bed as the operator $\\nabla_j \\Delta^{-1/2}$ where $\\nabla_j = d/dx_j$
is the derivative and $\\Delta$ is the Laplace operator. In a more general
context the Riesz transform may always be defined for any diffusion semig
roup on the reals. In case the generator of this semi-group is the Laplace
operator the classical Riesz transform is retrieved. In quantum probabili
ty the quantum Markov semi-groups play the role of the diffusion semi-grou
ps and again a suitable notion of Riesz transform can be described.\n\nWe
show that the Riesz transform may be used to prove rigidity properties of
von Neumann algebras. We focus in particular on examples from compact quan
tum groups. Using these tools we show that a class of quantum groups admit
s rigidity properties. The class has the following properties:\n\n(1) $\\t
ext{SU}_q(2)$ is contained in it.\n\n(2) The class is stable under monoida
l equivalence\, free products\, dual quantum subgroups and wreath products
with $S^+_N$.\n\nThe rigidity properties include the Akemann-Ostrand prop
erty and strong solidity. Part of this talk is based on joint work with Ma
teusz Wasilewski and Yusuke Isono.\n
LOCATION:https://researchseminars.org/talk/QGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Kyed (University of Southern Denmark\, Denmark)
DTSTART;VALUE=DATE-TIME:20201214T150000Z
DTEND;VALUE=DATE-TIME:20201214T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/6
DESCRIPTION:Title: Dyna
mics of compact quantum metric spaces\nby David Kyed (University of So
uthern Denmark\, Denmark) as part of Quantum Groups Seminar [QGS]\n\n\nAbs
tract\nThe classical Gelfand correspondence justifies the slogan that C*-
algebras are to be thought of as "non-commutative Hausdorff spaces"\, and
Rieffel's theory of compact quantum metric spaces provides\, in the same
vein\, a non-commutative counterpart to the theory of compact metric space
s. The aim of my talk is to introduce the basics of this theory\, and expl
ain some new results on dynamical systems of compact quantum metric spaces
. If time permits\, I will also touch upon another recent result\, whic
h shows how quantized intervals approximate a classical interval in the q
uantum version of the Gromov-Hausdorff distance. This is based on joint wo
rks with Jens Kaad and Thomas Gotfredsen.\n
LOCATION:https://researchseminars.org/talk/QGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Penneys (The Ohio State University\, USA)
DTSTART;VALUE=DATE-TIME:20210111T150000Z
DTEND;VALUE=DATE-TIME:20210111T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/7
DESCRIPTION:Title: Disc
rete subfactors\, realization of algebra objects\, and Q-system completion
\nby David Penneys (The Ohio State University\, USA) as part of Quantu
m Groups Seminar [QGS]\n\n\nAbstract\nIn recent decades\, we have seen tha
t quantum symmetries of quantum\nmathematical objects\, like non-commutati
ve spaces and quantum field\ntheories\, are best described by quantum grou
ps\, subfactors\, and\nunitary tensor categories. Subfactor classification
has led to\ndiscovery of interesting "exotic" quantum symmetries and to i
mportant\nconstructions for unitary tensor categories. For example\, Q-sys
tems\n(special C* Frobnius algebra objects) were introduced by Longo to\nc
haracterize the canonical endomorphism for type III subfactors\, which\nis
the analog of Jones' basic construction for type $II_1$ and Kosaki's\nver
sion for type III. We will use this perspective to discuss some\nsubfactor
results which go beyond small index classification\, making\nconnections
to quantum groups along the way. We'll then discuss a\nversion of a unitar
y higher idempotent completion for C*/W*\n2-categories based on Gaiotto-Jo
hnson-Freyd's theory of condensations\nin higher categories.\n
LOCATION:https://researchseminars.org/talk/QGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Bichon (Université Clermont Auvergne\, France)
DTSTART;VALUE=DATE-TIME:20210118T150000Z
DTEND;VALUE=DATE-TIME:20210118T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/8
DESCRIPTION:Title: Abou
t the monoidal invariance of cohomological dimension of Hopf algebras\
nby Julien Bichon (Université Clermont Auvergne\, France) as part of Quan
tum Groups Seminar [QGS]\n\n\nAbstract\nI will discuss the question whethe
r Hopf algebras having monoidally equivalent category of comodules have th
e same cohomological dimension\, and I will present a new positive answer.
\n
LOCATION:https://researchseminars.org/talk/QGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Voigt (University of Glasgow\, UK)
DTSTART;VALUE=DATE-TIME:20210125T150000Z
DTEND;VALUE=DATE-TIME:20210125T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/9
DESCRIPTION:Title: Quan
tum Cuntz-Krieger algebras\nby Christian Voigt (University of Glasgow\
, UK) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nThe notion of
a quantum graph\, a concept going back to work of Erdos-Katavolos-Shulman
and Weaver\, provides a noncommutative generalisation of finite graphs. Q
uantum graphs play an intriguing role in the analysis of quantum symmetrie
s of graphs via monoidal equivalences\, and\nnaturally appear also in quan
tum information theory.\n\nIn this talk\, I will discuss the construction
of certain C*-algebras associated with directed quantum graphs\, in analog
y to the definition of Cuntz-Krieger algebras\, and illustrate this with s
ome examples. (Joint work with M. Brannan\, K. Eifler\, M. Weber.)\n
LOCATION:https://researchseminars.org/talk/QGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amaury Freslon (Université Paris-Saclay\, France)
DTSTART;VALUE=DATE-TIME:20210215T150000Z
DTEND;VALUE=DATE-TIME:20210215T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/10
DESCRIPTION:Title: How
to (badly) quantum shuffle cards\nby Amaury Freslon (Université Pari
s-Saclay\, France) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\n
Card shuffles can be thought of as random walks on the symmetric group\, a
nd the study of these random walks has been a subject of interest to proba
bilists for more than forty years. Even for one of the simplest examples\,
the random transposition walk\, precise results concerning the convergenc
e to equilibrium were only very recently obtained. After briefly describin
g that setting\, I will report on a joint work with L. Teyssier and S. Wan
g where we study an analogue of the random transposition walk on the quant
um symmetric group\, therefore a kind of "quantum card shuffle". In partic
ular\, we obtain a similar asymptotic description of the convergence to eq
uilibrium\, called the "limit profile"\, involving the free Poisson distri
bution while the classical case involved the usual Poisson distribution.\n
LOCATION:https://researchseminars.org/talk/QGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Nakano (University of Georgia\, USA)
DTSTART;VALUE=DATE-TIME:20210222T150000Z
DTEND;VALUE=DATE-TIME:20210222T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/11
DESCRIPTION:Title: Non
commutative Tensor Triangular Geometry\nby Daniel Nakano (University o
f Georgia\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn
this talk\, I will show how to develop a general noncommutative version o
f Balmer's tensor triangular geometry that is applicable to arbitrary mono
idal triangulated categories (M$\\Delta$C). Insights from noncommutative r
ing theory is used to obtain a framework for prime\, semiprime\, and compl
etely prime (thick) ideals of an M$\\Delta$C\, $\\mathbf K $\, and then to
associate to $\\mathbf K$ a topological space --the Balmer spectrum $\\te
xt{Spc }{\\mathbf K}$.\n\nWe develop a general framework for (noncommutati
ve) support data\, coming in three different flavors\, and show that $\\te
xt{Spc }{\\mathbf K}$ is a universal terminal object for the first two not
ions (support and weak support). The first two types of support data are t
hen used in a theorem that gives a method for the explicit classification
of the thick (two-sided) ideals and the Balmer spectrum of an M$\\Delta$C.
The third type (quasi support) is used in another theorem that provides a
method for the explicit classification of the thick right ideals of $\\ma
thbf K$\, which in turn can be applied to classify the thick two-sided ide
als and $\\text{Spc }{\\mathbf K}$.\n\nIf time permits applications will b
e given for quantum groups and non-cocommutative finite-dimensional Hopf a
lgebras studied by Benson and Witherspoon.\n\nThis is joint and ongoing wo
rk with Milen Yakimov and Kent Vashaw\n
LOCATION:https://researchseminars.org/talk/QGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnaud Brothier (University of New South Wales\, Australia)
DTSTART;VALUE=DATE-TIME:20210308T080000Z
DTEND;VALUE=DATE-TIME:20210308T090000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/13
DESCRIPTION:Title: Fro
m subfactors to actions of the Thompson group\nby Arnaud Brothier (Uni
versity of New South Wales\, Australia) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nIn his quest in constructing conformal field theories
from subfactors Vaughan Jones found an efficient machine to construct act
ions of groups like the Thompson groups. I will briefly explain the story
of this discovery. I will then present a general overview of those Jones a
ctions providing explicit examples. Some of the results presented come fro
m joint works with Vaughan Jones and with Valeriano Aiello and Roberto Con
ti.\n
LOCATION:https://researchseminars.org/talk/QGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Réamonn Ó Buachalla (Charles University\, Czech Republic)
DTSTART;VALUE=DATE-TIME:20210315T150000Z
DTEND;VALUE=DATE-TIME:20210315T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/14
DESCRIPTION:Title: Qua
ntum Root Vectors and a Dolbeault Double Complex for the A-Series Quantum
Flag Manifolds\nby Réamonn Ó Buachalla (Charles University\, Czech R
epublic) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn the 200
0s a series of seminal papers by Heckenberger and Kolb introduced an essen
tially unique covariant $q$-deformed de Rham complex for the irreducible q
uantum flag manifolds. In the years since\, it has become increasingly cle
ar that these differential graded algebras have a central role to play in
the noncommutative geometry of Drinfeld-Jimbo quantum groups. Until now\,
however\, the question of how to extend Heckenberger and Kolb's constructi
on beyond the irreducible case has not been examined. Here we address this
question for the $A$-series Drinfeld-Jimbo quantum groups $U_q(\\frak{sl}
_{n+1})$\, and show that for precisely two reduced decompositions of the l
ongest element of the Weyl group\, Lusztig's associated space of quantum r
oot vectors gives a quantum tangent space for the full quantum flag manifo
ld $\\mathcal{O}_q(F_{n+1})$ with associated differential graded algebra o
f classical dimension. Moreover\, its restriction to the quantum Grassmann
ians recovers the $q$-deformed complex of Heckenberger and Kolb\, giving a
conceptual explanation for their origin. Time permitting\, we will discus
s the noncommutative Kähler geometry of thesespaces and the proposed exte
nsion of the root space construction to the other series. (Joint work with
P. Somberg)\n
LOCATION:https://researchseminars.org/talk/QGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Appel (University of Parma\, Italy)
DTSTART;VALUE=DATE-TIME:20210322T150000Z
DTEND;VALUE=DATE-TIME:20210322T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/15
DESCRIPTION:Title: Qua
ntum affine algebras and spectral k-matrices\nby Andrea Appel (Univers
ity of Parma\, Italy) as part of Quantum Groups Seminar [QGS]\n\n\nAbstrac
t\nThe Yang-Baxter equation (YBE) and the reflection equation (RE) are two
fundamental\nsymmetries in mathematics arising from particles moving alon
g a line or a half-line.\nThe quest for constant solutions of YBE (R-matri
ces) is at the very origin of the Drinfeld-Jimbo\nquantum groups and their
universal R-matrix. Similarly\, constant solutions of RE (k-matrices)\nna
turally appear in the context of quantum symmetric pairs (QSP).\n\nIn join
t work with Bart Vlaar\, we construct a discrete family of universal k-mat
rices associated to\nan arbitrary quantum symmetric Kac-Moody pair as oper
ators on category O integrable\nrepresentations. This generalises previous
results by Balagovic-Kolb and Bao-Wang valid\nfor finite-type QSP. In thi
s talk\, I will explain how\, in affine type\, this construction gives ris
e to\nparameter-dependent operators (spectral k-matrices) on finite-dimens
ional representations of\nquantum loop algebras solving the same RE introd
uced by Cherednik and Sklyanin in the 1980s\nin the context of quantum int
egrability near a boundary.\n
LOCATION:https://researchseminars.org/talk/QGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debashish Goswami (Indian Statistical Institute\, India)
DTSTART;VALUE=DATE-TIME:20210329T140000Z
DTEND;VALUE=DATE-TIME:20210329T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/16
DESCRIPTION:Title: Qua
ntum Galois Group of Subfactors\nby Debashish Goswami (Indian Statisti
cal Institute\, India) as part of Quantum Groups Seminar [QGS]\n\n\nAbstra
ct\n(joint work with Suvrajit Bhattacharjee and Alex Chirvasitu) \n\nIn th
is talk\, I prove the existence of a universal (terminal) object in a numb
er of categories of Hopf algebras acting on a given subfactor $N \\subset
M$ (finite index\, type $\\text{II}_1$) such that $N$ is in the fixed poin
t subalgebra of the action. These universal Hopf algebras can be interpret
ed as a quantum group version of Galois group of the subfactor. We compute
such universal quantum groups for certain class of subfactors\, notably t
hose coming from outer actions of finite dimensional Hopf $\\ast$ algebras
.\n
LOCATION:https://researchseminars.org/talk/QGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Reutter (Max Planck Institute for Mathematics\, Germany)
DTSTART;VALUE=DATE-TIME:20210412T140000Z
DTEND;VALUE=DATE-TIME:20210412T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/17
DESCRIPTION:Title: On
fusion 2-categories\nby David Reutter (Max Planck Institute for Mathem
atics\, Germany) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nI
will revisit and categorify concepts from the theory of fusion categories
— including idempotent completeness and semi-simplicity\, ultimately lea
ding to a notion of `fusion 2-category’. I will highlight structural sim
ilarities and differences between fusion 1- and 2-categories and discuss s
everal concrete examples. If time permits\, I will discuss the role of fus
ion 2-categories as a natural building block for 4-dimensional topological
field theories.\n
LOCATION:https://researchseminars.org/talk/QGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Chirvasitu (University at Buffalo\, USA)
DTSTART;VALUE=DATE-TIME:20210419T140000Z
DTEND;VALUE=DATE-TIME:20210419T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/18
DESCRIPTION:Title: Non
-commutative balls and quantum group structures\nby Alexandru Chirvasi
tu (University at Buffalo\, USA) as part of Quantum Groups Seminar [QGS]\n
\n\nAbstract\nThe Toeplitz algebra attached to the unit disk is the univer
sal C∗-algebra generated by an\nisometry\, and is a non-commutative anal
ogue of the unit disk. Similarly\, one can attach algebras to non-commutat
ive counterparts of non-compact Hermitian symmetric spaces. I will discuss
results to the effect that such quantum spaces cannot admit quantum group
structures\, i.e. their attached non-commutative “function algebras”
do not admit reasonable Hopf algebra structures.\n\n(joint w/ Jacek Krajcz
ok and Piotr Soltan)\n
LOCATION:https://researchseminars.org/talk/QGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Schapiro (UC Berkeley\, USA)
DTSTART;VALUE=DATE-TIME:20210426T140000Z
DTEND;VALUE=DATE-TIME:20210426T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/19
DESCRIPTION:Title: Clu
ster realization of spherical DAHA\nby Alexander Schapiro (UC Berkeley
\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nSpherical s
ubalgebra of Cherednik's double affine Hecke algebra of type A admits a po
lynomial representation in which its generators act via elementary symmetr
ic functions and Macdonald operators. Recognizing the elementary symmetric
functions as eigenfunctions of quantum Toda Hamiltonians\, and applying (
the inverse of) the Toda spectral transform\, one obtains a new representa
tion of spherical DAHA. In this talk\, I will discuss how this new represe
ntation gives rise to an injective homomorphism from the spherical DAHA in
to a quantum cluster algebra in such a way that the action of the modular
group on the former is realized via cluster transformations.\n\nThe talk i
s based on a joint work in progress with Philippe Di Francesco\, Rinat Ked
em\, and Gus Schrader.\n
LOCATION:https://researchseminars.org/talk/QGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corey Jones (North Carolina State University\, USA)
DTSTART;VALUE=DATE-TIME:20210503T140000Z
DTEND;VALUE=DATE-TIME:20210503T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/20
DESCRIPTION:Title: Act
ions of fusion categories on topological spaces\nby Corey Jones (North
Carolina State University\, USA) as part of Quantum Groups Seminar [QGS]\
n\n\nAbstract\nFusion categories are algebraic objects which generalize th
e representation categories of finite quantum groups. We define an action
of a (unitary) fusion category C on a compact Hausdorff space X to be a C
module category structure on Hilb(X)\, the category of finite dimensional
Hilbert bundles over a compact Hausdorff space X. When X is connected\, w
e discuss obstructions to the existence of such actions and describe techn
iques for building examples.\n
LOCATION:https://researchseminars.org/talk/QGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rémi Boutonnet (Institut de Mathématiques de Bordeaux\, France)
DTSTART;VALUE=DATE-TIME:20210510T140000Z
DTEND;VALUE=DATE-TIME:20210510T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/21
DESCRIPTION:Title: Non
-commutative ergodic theory of semi-simple lattices\nby Rémi Boutonne
t (Institut de Mathématiques de Bordeaux\, France) as part of Quantum Gro
ups Seminar [QGS]\n\n\nAbstract\nIn the late 90's\, Nevo and Zimmer wrote
a series of papers describing the general structure of stationnary actions
of higher rank semi-simple Lie groups G on probability spaces. With Cyril
Houdayer we extended this result in two ways: first we upgraded it to act
ions on non-commutative spaces (von Neumann algebras)\, and we also manage
d to study actions of lattices in G. I will explain this non-commutative e
rgodic theorem and the main ingredients of proof\, and give striking conse
quences on the unitary representations of these lattices and their charact
ers.\n
LOCATION:https://researchseminars.org/talk/QGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Mančiska (University of Copenhagen\, Denmark)
DTSTART;VALUE=DATE-TIME:20210524T140000Z
DTEND;VALUE=DATE-TIME:20210524T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/23
DESCRIPTION:Title: Qua
ntum groups and nonlocal games\nby Laura Mančiska (University of Cope
nhagen\, Denmark) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nI
n this talk I will explain how quantum groups arise in quantum information
theory via a class of graph based nonlocal games. Our point of departure
will be an interactive protocol (nonlocal game) where two provers try to c
onvince a verifier that two graphs are isomorphic. Allowing provers to tak
e advantage of shared quantum mechanical resources will then allow us to d
efine quantum isomorphism of graphs as the ability of quantum players to w
in the corresponding game with certainty. We will see that quantum isomorp
hism can be naturally reformulated in the language of quantum groups.\n
LOCATION:https://researchseminars.org/talk/QGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Saracco (Université Libre de Bruxelles\, Belgium)
DTSTART;VALUE=DATE-TIME:20210531T140000Z
DTEND;VALUE=DATE-TIME:20210531T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/30
DESCRIPTION:Title: Glo
balization for Geometric Partial Comodules\nby Paolo Saracco (Universi
té Libre de Bruxelles\, Belgium) as part of Quantum Groups Seminar [QGS]\
n\n\nAbstract\n(based on a joint work [2] with Joost Vercruysse)\n\nThe st
udy of partial symmetries (partial actions and coactions\, partial represe
ntations and corepresentations\, partial comodule algebras) is a relativel
y recent field in continuous expansion and\, therein\, one of the relevant
questions is the existence and uniqueness of a so-called globalization (o
r enveloping action). \nFor instance\, in the framework of partial actions
of groups any global action of a group $G$ on a set induces a partial act
ion of the group on any subset by restriction. The idea behind the concept
of globalization of a given partial action is to find a (universal) $G$-s
et such that the initial partial action can be realized as the restriction
of this global one.\n\nWe propose here a categorical approach to partial
symmetries and the globalization question\, explaining several of the exis
ting results and\, at the same time\, providing a procedure to construct g
lobalizations in concrete contexts of interest. Our approach relies on the
notion of geometric partial comodules\, recently introduced by Hu and Ver
cruysse [1] in order to describe partial actions of algebraic groups from
a Hopf-algebraic point of view.\n\nUnlike classical partial actions\, whic
h exist only for (topological) groups and Hopf algebras\, geometric partia
l comodules can be defined over any coalgebra in a monoidal category with
pullbacks and they allow to describe phenomena that are out of the reach o
f the theory of partial (co)actions\, even in the Hopf algebra framework.
At the same time\, geometric partial comodules allow to approach in a unif
ied way partial actions of groups on sets\, partial coactions of Hopf alge
bras on algebras and partial (co)actions of Hopf algebras on vector spaces
.\nThus\, the question of studying the existence (and uniqueness) of globa
lization for geometric partial comodules naturally arises as a unifying wa
y to address the issue.\n\nReferences:\n\n[1] J. Hu\, J.Vercruysse - Geome
trically partial actions. Trans. Amer. Math. Soc. 373 (2020)\, no. 6\, 408
5-4143.\n\n[2] P. Saracco\, J. Vercruysse - Globalization for geometric pa
rtial comodules. Part I: general theory. Preprint (2021).\n
LOCATION:https://researchseminars.org/talk/QGS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aryan Ghobadi (Queen Mary University of London\, UK)
DTSTART;VALUE=DATE-TIME:20210607T140000Z
DTEND;VALUE=DATE-TIME:20210607T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/31
DESCRIPTION:Title: Hop
f algebras in SupLat and set-theoretical YBE solutions\nby Aryan Ghoba
di (Queen Mary University of London\, UK) as part of Quantum Groups Semina
r [QGS]\n\n\nAbstract\nSkew braces have recently attracted attention as a
method to study set-theoretical solutions of the Yang-Baxter equation. In
this talk\, we will present a new approach for studying these solutions\,
by looking at Hopf algebras in the category of complete lattices and join-
preserving morphisms\, denoted by SupLat. Any Hopf algebra\, H in SupLat\,
has a corresponding group\, R(H)\, which we call its remnant and a co-qua
sitriangular structure on H induces a brading operator on R(H)\, which ind
uces a skew brace structure on R(H). From this correspondence\, we will re
cover several aspects of the theory of skew braces. In particular\, we wil
l construct the universal skew brace of a set-theoretical YBE solution\, a
s the remnant of an FRT-type reconstruction in SupLat.\n
LOCATION:https://researchseminars.org/talk/QGS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satyajit Guin (Indian Institute of Technology Kanpur\, India)
DTSTART;VALUE=DATE-TIME:20210614T140000Z
DTEND;VALUE=DATE-TIME:20210614T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/32
DESCRIPTION:Title: Equ
ivariant spectral triple for the compact quantum group $U_q(2)$ for comple
x deformation parameters\nby Satyajit Guin (Indian Institute of Techno
logy Kanpur\, India) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract
\nLet $q=|q|e^{i\\pi\\theta}$ be a nonzero complex number such that $|q|\\
neq 1$\, and consider the compact quantum group $U_q(2)$. In this talk\, w
e discuss a complete list of inequivalent irreducible representations of $
U_q(2)$ and its Peter-Weyl decomposition. Then\, for $\\theta\\notin\\math
bb{Q}\\setminus\\{0\,1\\}$\, we discuss the $K$-theory of the underlying $
C^*$-algebra $C(U_q(2))$\, and a spectral triple which is equivariant unde
r its own comultiplication action. The spectral triple obtained here is ev
en\, $4^+$-summable\, non-degenerate\, and the Dirac operator acts on two
copies of the $L^2$-space of $U_q(2)$. The Chern character of the associat
ed Fredholm module is nontrivial.\n
LOCATION:https://researchseminars.org/talk/QGS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moritz Weber (Saarland University\, Germany)
DTSTART;VALUE=DATE-TIME:20210621T140000Z
DTEND;VALUE=DATE-TIME:20210621T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/33
DESCRIPTION:Title: Ort
hogonal vs unitary in the case of "easy" quantum groups\nby Moritz Web
er (Saarland University\, Germany) as part of Quantum Groups Seminar [QGS]
\n\n\nAbstract\nWe consider quantum subgroups of Wang’s free orthogonal
quantum group on the one hand and of his free unitary quantum group on the
other. In the first case\, the generators of the underlying C*-algebras a
re selfadjoint which is dropped in the latter case. We compare these two c
ases along the lines of so called "easy" quantum groups and we observe tha
t the step from the orthogonal to the unitary case is huge. This is a surv
ey talk on the landscape of "easy" quantum groups with a particular emphas
is on the differences between the orthogonal and the unitary case.\n
LOCATION:https://researchseminars.org/talk/QGS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shintaro Nishikawa (University of Münster\, Germany)
DTSTART;VALUE=DATE-TIME:20210920T140000Z
DTEND;VALUE=DATE-TIME:20210920T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/34
DESCRIPTION:Title: Cro
ssed products of representable localization algebras\nby Shintaro Nish
ikawa (University of Münster\, Germany) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nLet X be a locally compact\, Hausdorff space. The re
presentable localization algebra for X was introduced and studied by Wille
tt and Yu. The K-theory of the algebra serves as the representable K-homol
ogy of the space X.\n\nNow let G be a second countable\, locally compact g
roup and suppose that X is a proper G-space. It turns out that the K-theor
y of the crossed product by G of the representable localization algebra fo
r X serves as the representable G-equivariant K-homology of the proper G-s
pace X.\n\nThe goal of this talk is to describe these facts and roles of t
he representable localization algebras in the study of the Baum--Connes co
njecture.\n
LOCATION:https://researchseminars.org/talk/QGS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Verdon (University of Bristol\, UK)
DTSTART;VALUE=DATE-TIME:20210927T140000Z
DTEND;VALUE=DATE-TIME:20210927T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/35
DESCRIPTION:Title: A c
ovariant Stinespring theorem\nby Dominic Verdon (University of Bristol
\, UK) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe will intr
oduce a finite-dimensional covariant Stinespring theorem for compact quant
um groups. Let G be a compact quantum group\, and let T:= Rep(G) be the ri
gid C*-tensor category of finite-dimensional continuous unitary representa
tions of G. Let Mod(T) be the rigid C*-2-category of cofinite semisimple f
initely decomposable T-module categories. We show that finite-dimensional
G-C*-algebras (a.k.a C*-dynamical systems) can be identified with equivale
nce classes of 1-morphisms out of the object T in Mod(T). For 1-morphisms
X: T -> M1\, Y: T -> M2\, we show that covariant channels between the corr
esponding G-C*-algebras can be 'dilated' to isometries t: X -> Y \\otimes
E\, where E: M2 -> M1 is some 'environment' 1-morphism. Dilations are uniq
ue up to partial isometry on the environment\; in particular\, the dilatio
n minimising the quantum dimension of the environment is unique up to a un
itary. When G is a compact group this implies and generalises previous cov
ariant Stinespring-type theorems.\n\nWe will also discuss some results rel
ating to rigid C*-2-categories\, including that any connected semisimple r
igid C*-2-category is equivalent to Mod(T) for some rigid C*-tensor catego
ry T. (Here semisimple means not just semisimplicity of Hom-categories but
also idempotent splitting for 1-morphisms\, direct sums for objects\, etc
.)\n\nThis talk is based on the paper arXiv:2108.09872.\n
LOCATION:https://researchseminars.org/talk/QGS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Skalski (IMPAN\, Poland)
DTSTART;VALUE=DATE-TIME:20211004T140000Z
DTEND;VALUE=DATE-TIME:20211004T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/36
DESCRIPTION:Title: Gau
ssian states and Gaussian parts of compact quantum groups\nby Adam Ska
lski (IMPAN\, Poland) as part of Quantum Groups Seminar [QGS]\n\n\nAbstrac
t\nI will motivate and explain the notion of a Gaussian state on a compact
quantum group G\, as introduced by Michael Schürmann. This concept leads
to the idea of the Gaussian part of G\, understood as the smallest quantu
m subgroup of G which supports all the Gaussian states of G. I will discus
s properties of Gaussian states and compute Gaussian parts for several exa
mples. This turns out to be related to quantum connectedness and certain t
opological generation questions for quantum subgroups. The talk will be ba
sed on joint work with Uwe Franz and Amaury Freslon.\n
LOCATION:https://researchseminars.org/talk/QGS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Kranz (University of Münster\, Germany)
DTSTART;VALUE=DATE-TIME:20211011T140000Z
DTEND;VALUE=DATE-TIME:20211011T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/37
DESCRIPTION:Title: Ame
nability and weak containment for étale groupoids\nby Julian Kranz (U
niversity of Münster\, Germany) as part of Quantum Groups Seminar [QGS]\n
\n\nAbstract\nA famous theorem of Hulanicki says that a locally compact gr
oup is amenable if and only if its full and reduced C*-algebras coincide.
For groupoids\, the situation is more delicate: While amenability implies
equatility of the full and reduced C*-algebra\, the converse fails accordi
ng to examples by Willett. The behavior of Willett's groupoids can be expl
ained by their non-exactness. We show that if an étale groupoid satisfies
a certain exactness condition\, then equality of its full and reduced C*-
algebra is equivalent to amenability of the groupoid.\n
LOCATION:https://researchseminars.org/talk/QGS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Wahl (Hausdorff Center of Mathematics\, Germany)
DTSTART;VALUE=DATE-TIME:20211025T140000Z
DTEND;VALUE=DATE-TIME:20211025T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/39
DESCRIPTION:Title: An
introduction to diagram algebras\nby Jonas Wahl (Hausdorff Center of M
athematics\, Germany) as part of Quantum Groups Seminar [QGS]\n\n\nAbstrac
t\nIn this talk\, I will introduce the notion of a diagram algebra and exp
lain their connection to the representation theory of compact quantum grou
ps. I will also describe the role that they play for loop models in statis
tical physics as well as the correspondence between their traces and rando
m walks on graphs.\n
LOCATION:https://researchseminars.org/talk/QGS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jordan (University of Edinburgh\, UK)
DTSTART;VALUE=DATE-TIME:20211101T150000Z
DTEND;VALUE=DATE-TIME:20211101T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/40
DESCRIPTION:Title: Clu
ster quantization from factorization homology\nby David Jordan (Univer
sity of Edinburgh\, UK) as part of Quantum Groups Seminar [QGS]\n\n\nAbstr
act\nThe character variety of a manifold is its moduli space of flat G-bun
dles. These moduli spaces and their quantizations appear in a number of pl
aces in mathematics\, representation theory\, and quantum field theory. Fa
mously\, Fock and Goncharov showed that a certain "decorated" variant of c
haracter varieties carries the structure of a cluster variety -- that is\,
the moduli space contains a distinguished set of toric charts\, with comb
inatorially defined transitions functions (called mutations). This led the
m to a now-famous quantization of their decorated character varieties.\n\n
In this talk I'll explain that the by-hands construction of these charts b
y Fock and Goncharov can in fact be extracted from a more general framewor
k called stratified factorization homology\, and I'll outline how this all
ows us to extend the Fock-Goncharov story from surfaces to 3-manifolds.\n
LOCATION:https://researchseminars.org/talk/QGS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apurva Seth (Indian Institute of Science Education and Research -
Bhopal\, India)
DTSTART;VALUE=DATE-TIME:20211108T150000Z
DTEND;VALUE=DATE-TIME:20211108T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/41
DESCRIPTION:Title: $C(
X)$-Algebras and their K-Stability\nby Apurva Seth (Indian Institute o
f Science Education and Research - Bhopal\, India) as part of Quantum Grou
ps Seminar [QGS]\n\n\nAbstract\nNon-stable K-theory is the study of the ho
motopy groups of the group of (quasi-) unitaries of a $C^{*}$-algebra. We
will give an overview of the theory\, and discuss a special class of $C^{*
}$-algebras\, termed as K-stable $C^{*}$-algebras along with its rational
analogue. We shall give a permanence property related to K-stability (rati
onal K-stability) concerning continuous $C(X)$-algebras. We will end with
an application of the aforementioned result to crossed product $C^{*}$-alg
ebras.\n
LOCATION:https://researchseminars.org/talk/QGS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Floris Elzinga (University of Oslo\, Norway)
DTSTART;VALUE=DATE-TIME:20211123T100000Z
DTEND;VALUE=DATE-TIME:20211123T110000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/43
DESCRIPTION:Title: Str
ongly 1-Bounded Quantum Group von Neumann Algebras\nby Floris Elzinga
(University of Oslo\, Norway) as part of Quantum Groups Seminar [QGS]\n\n\
nAbstract\nStrong $1$-boundedness is a property for a tracial von Neumann
algebra $M$ that was introduced by Jung that allows one to distinguish $M$
from the (interpolated) free group factors. Many examples came from group
von Neumann algebras\, such as those from certain groups having property
(T). For quantum group von Neumann algebras\, Brannan and Vergnioux showed
in a landmark paper that those coming from the orthogonal free quantum gr
oups are strongly $1$-bounded\, despite sharing many structural properties
with the free group factors. We first review these developments\, and the
n report on recent progress concerning permanence of strong $1$-boundednes
s under finite index subfactors and applications to quantum automorphism g
roups such as the quantum permutation group $S_{N^2}^+$. This last part is
based on ongoing joint work with Brannan\, Harris\, and Yamashita.\n\nNot
e the unusual day and time!\n
LOCATION:https://researchseminars.org/talk/QGS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hadewijch De Clercq (Ghent University\, Belgium)
DTSTART;VALUE=DATE-TIME:20211129T150000Z
DTEND;VALUE=DATE-TIME:20211129T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/44
DESCRIPTION:Title: Dyn
amical quantum graphical calculus\nby Hadewijch De Clercq (Ghent Unive
rsity\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nGr
aphical calculus provides a diagrammatic framework for performing topologi
cal computations with morphisms in strict tensor categories. The key idea
is to identify such morphisms with oriented diagrams labeled by their in-
and output objects. This was formalized by Reshetikhin and Turaev\, by con
structing for every strict tensor category $C$ a strict tensor functor tha
t assigns isotopy classes of $C$-colored ribbon graphs to morphisms in $C$
. This can be applied to the tensor category of finite-dimensional represe
ntations of a quantum group $U_q(g)$.\n\nIn this talk\, I will first outli
ne the fundamentals of this finite-dimensional quantum graphical calculus.
Then I will explain how it can be extended to a larger category of quantu
m group representations\, encompassing the quantum group analog of the BGG
category $O$. In particular\, this extended framework allows to visualize
$U_q(g)$-intertwiners on Verma modules\, as well as morphisms depending o
n a dynamical parameter\, such as dynamical R-matrices. Finally\, I will d
escribe how this dynamical quantum graphical calculus can be used to obtai
n q-difference equations for quantum spherical functions.\n\nThis talk is
based on joint work with Nicolai Reshetikhin (UC Berkeley) and Jasper Stok
man (University of Amsterdam)\n
LOCATION:https://researchseminars.org/talk/QGS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Emma Mikkelsen (University of Southern Denmark\, Denmark)
DTSTART;VALUE=DATE-TIME:20211213T150000Z
DTEND;VALUE=DATE-TIME:20211213T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/46
DESCRIPTION:Title: On
the quantum symplectic sphere\nby Sophie Emma Mikkelsen (University of
Southern Denmark\, Denmark) as part of Quantum Groups Seminar [QGS]\n\n\n
Abstract\nThe algebra of the quantum symplectic $(4n-1)$-sphere $\\mathcal
{O}(S_q^{4n-1})$ is defined as a subalgebra of the quantum symplectic grou
p by Faddeev\, Reshetikhin and Takhtajan. Recently D'Andrea and Landi inve
stigated faithfull irreducible $*$-representations of $\\mathcal{O}(S_q^{4
n-1})$. They proved that the first $n-1$ generators of its enveloping $C^*
$-algebra $C(S_q^{4n-1})$ are all zero. The result is a generalisation of
the case where $n=2$ which was shown by Mikkelsen and Szymański.\nIn this
talk\, I will first present how $C(S_q^{4n-1})$ can be described as a gra
ph $C^*$-algebra\, from which it follows that $C(S_q^{4n-1})$ is isomorphi
c to the quantum $(2n+1)$-sphere by Vaksman and Soibelman. Then\, I presen
t a candidate of a vector space basis for $\\mathcal{O}(S_q^{4n-1})$ which
is constructed by a nontrivial application of the Diamond lemma. The conj
ecture is supported by computer experiments for $n=1\,...\,8$. By finding
a vector space basis we can moreover conclude that the $n-1$ generators a
re non-zero inside the algebra $\\mathcal{O}(S_q^{4n-1})$.\n
LOCATION:https://researchseminars.org/talk/QGS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremiah McCarthy (Munster Technological University\, Ireland)
DTSTART;VALUE=DATE-TIME:20220124T150000Z
DTEND;VALUE=DATE-TIME:20220124T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/47
DESCRIPTION:Title: The
Frucht property in the quantum group setting\nby Jeremiah McCarthy (M
unster Technological University\, Ireland) as part of Quantum Groups Semin
ar [QGS]\n\n\nAbstract\nA classical theorem of Frucht states that every fi
nite group is the automorphism group of a finite graph. Is every quantum p
ermutation group the quantum automorphism group of a finite graph? In this
talk we will answer this question with the help of orbits and orbitals. T
his talk is based on joint work with Teo Banica.\n
LOCATION:https://researchseminars.org/talk/QGS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoît Collins (Kyoto University\, Japan)
DTSTART;VALUE=DATE-TIME:20220131T130000Z
DTEND;VALUE=DATE-TIME:20220131T140000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/48
DESCRIPTION:Title: A m
etric characterization of freeness\nby Benoît Collins (Kyoto Universi
ty\, Japan) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nFreenes
s of random variables has many characterizations\, with free cumulants\, f
ree entropy\, Schwinger-Dyson equations\, etc. Here\, we discuss a new met
ric characterization with the norm of the sum of generators tensored by th
eir adjoint\, and explain the relation and applications to other problems
in operator algebras and von Neumann algebras. Time permitting\, we will a
lso discuss some ingredients of the proof. This is based on joint work wit
h Leonard Cadilhac.\n
LOCATION:https://researchseminars.org/talk/QGS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Schmidt (University of Copenhagen\, Denmark)
DTSTART;VALUE=DATE-TIME:20220207T150000Z
DTEND;VALUE=DATE-TIME:20220207T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/49
DESCRIPTION:Title: A g
raph with quantum symmetry and finite quantum automorphism group\nby S
imon Schmidt (University of Copenhagen\, Denmark) as part of Quantum Group
s Seminar [QGS]\n\n\nAbstract\nThis talk concerns quantum automorphism gro
ups of graphs\, a generalization of automorphism groups of graphs in the f
ramework of compact matrix quantum groups. We will focus on certain colore
d graphs constructed from linear constraint systems. In particular\, we wi
ll give an explicit connection of the solution group of the linear constra
int system and the quantum automorphism group of the corresponding colored
graph. Using this connection and a decoloring procedure\, we will present
an example of a graph with quantum symmetry and finite quantum automorphi
sm group. This talk is based on joint work with David Roberson.\n
LOCATION:https://researchseminars.org/talk/QGS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haonan Zhang (Institute of Science and Technology Austria\, Austri
a)
DTSTART;VALUE=DATE-TIME:20220214T150000Z
DTEND;VALUE=DATE-TIME:20220214T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/50
DESCRIPTION:Title: Lp-
Lq Fourier multipliers on locally compact quantum groups\nby Haonan Zh
ang (Institute of Science and Technology Austria\, Austria) as part of Qua
ntum Groups Seminar [QGS]\n\n\nAbstract\nHörmander proved that the Fourie
r multiplier is Lp-Lq bounded if the symbol lies in the weak Lr space\, fo
r certain p\,q\,r. In recent years\, this result was generalized to more g
eneral groups and quantum groups. Here we presented an extension to certai
n locally compact quantum groups. It covers the known results and the proo
f is simpler. It also yields a family of Lp-Fourier multipliers over compa
ct quantum groups of Kac type. The talk is based on arXiv:2201.08346.\n
LOCATION:https://researchseminars.org/talk/QGS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simeng Wang (Harbin Institute of Technology\, China)
DTSTART;VALUE=DATE-TIME:20220221T140000Z
DTEND;VALUE=DATE-TIME:20220221T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/51
DESCRIPTION:Title: Par
titions\, quantum group actions and rigidity\nby Simeng Wang (Harbin I
nstitute of Technology\, China) as part of Quantum Groups Seminar [QGS]\n\
n\nAbstract\nIn this talk\, I will present a new combinatorial approach to
the study of ergodic actions of compact quantum groups. The connection be
tween compact quantum groups and the combinatorics of partitions goes back
to Banica's founding work on the representation theory of free orthogonal
quantum groups\, and was later formalized in the seminal paper of Banica
and Speicher under the theory of "easy quantum groups". Based on some new
alternative version of the Tannaka-Krein reconstruction procedure for ergo
dic actions\, we extend Banica and Speicher's combinatorial approach to th
e setting of ergodic actions of compact quantum groups. Our examples in pa
rticular recovers actions on finite spaces\, on embedded homogeneous space
s and on quotient spaces. Moreover\, we use this categorical point of view
to study the quantum rigidity of ergodic actions on classical spaces\, an
d show that the free quantum groups cannot act ergodically on a classical
connected compact space\, thereby answering a question of D. Goswami and H
. Huang.\n\nThe talk is based on the recent preprint arXiv:2112.07506 join
tly with Amaury Freslon and Frank Taipe.\n
LOCATION:https://researchseminars.org/talk/QGS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Schmitt (Leibniz University Hannover\, Germany)
DTSTART;VALUE=DATE-TIME:20220307T150000Z
DTEND;VALUE=DATE-TIME:20220307T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/52
DESCRIPTION:Title: Qua
ntization of the 2-sphere\nby Philipp Schmitt (Leibniz University Hann
over\, Germany) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nThe
quantization problem is the problem of associating non-commutative quantu
m algebras to a classical Poisson algebra in such a way that the commutato
r is related to the Poisson bracket. In a formal setting\, this problem an
d its equivariant counterpart are well-understood and can always be solved
(under a mild assumption in the equivariant case). However\, in a C*-alge
braic setting\, there exist obstructions to equivariant quantization\, for
example for the 2-sphere. In this talk\, we will give a brief introductio
n to the quantization problem\, and propose a way to obtain an equivariant
quantization of the 2-sphere in a Fréchet algebraic setting.\n
LOCATION:https://researchseminars.org/talk/QGS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suvrajit Bhattacharjee (Charles University\, Czech Republic)
DTSTART;VALUE=DATE-TIME:20220328T140000Z
DTEND;VALUE=DATE-TIME:20220328T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/55
DESCRIPTION:Title: Bra
ided quantum symmetries of graph C*-algebras\nby Suvrajit Bhattacharje
e (Charles University\, Czech Republic) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nA braided compact quantum group (over T) is\, roughly
speaking\, a “compact quantum group” object in the category of T-C*-a
lgebras equipped with a twisted monoidal structure. In this talk\, we shal
l explain the existence of a universal braided compact quantum group actin
g on a graph C*-algebra in the category mentioned above. Time permitting\,
we shall sketch the proof\, constructing along the way a braided analogue
of the free unitary quantum group. Finally\, as an example\, we shall com
pute this universal braided compact quantum group for the Cuntz algebra.\n
LOCATION:https://researchseminars.org/talk/QGS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Asadi-Vasfi (Institute of Mathematics\, Czech Academy of Scien
ces\, Czech Republic)
DTSTART;VALUE=DATE-TIME:20220404T140000Z
DTEND;VALUE=DATE-TIME:20220404T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/56
DESCRIPTION:Title: An
introduction to crossed products by group actions on C*-algebras\nby A
li Asadi-Vasfi (Institute of Mathematics\, Czech Academy of Sciences\, Cze
ch Republic) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe giv
e a survey of some results on crossed products by discrete group actions a
nd discuss their basic properties. Further\, we restrict our attention to
finite group actions with the Rokhlin property\, approximate representabi
lity\, and their weakened versions. Time permitting\, we outline some str
ucture results for the crossed products by these classes of group actions
and their contributions to finite-dimensional quantum groups.\n
LOCATION:https://researchseminars.org/talk/QGS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Bieliavsky (Université Catholique de Louvain\, Belgium)
DTSTART;VALUE=DATE-TIME:20220411T140000Z
DTEND;VALUE=DATE-TIME:20220411T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/57
DESCRIPTION:Title: On
the differential geometry of Lie groups of Fröbenius type\nby Pierre
Bieliavsky (Université Catholique de Louvain\, Belgium) as part of Quantu
m Groups Seminar [QGS]\n\n\nAbstract\nThe talk will be based on the papers
.\n\n(1) In the first one\, joint with V. Gayral (Memoirs AMS 2015)\, we c
onstruct universal deformation formulae\nfor actions on topological algebr
as (C* or Fréchet) of the Lie groups which carries a negatively curved le
ft-invariant Kähler structure.\n\n(2) A second one\, joint with V.Gayral\
, S. Neshveyev and L. Tuset\, where we construct locally compact quantum g
roups from star products on a class of Lie groups.\n\nThe Lie groups on wh
ich these deformations are performed (in both (1) and (2)) are of ``Froben
ius type''. This means that their Lie algebras carry an exact non-degenera
te two-cocycle or\, equivalently\, that they admit an open co-adjoint orbi
t. In both cases\, the star products\, say at the formal level\, are of Fe
dosov type i.e. associated with a left-invariant symplectic torsion free a
ffine connection on the group manifold at hand. In particular\, they are o
btained from differential theoretical considerations.\n\nHowever\, there i
s a dichotomy: the orderings of the star products considered in (1) and (2
) are different. In (1)\, we deal with Weyl ordered star products\, while
in (2) with normal (or anti-normal) ones. This has\, apparently\, a strong
effect on the regularity of the categories those constructions live in: s
mooth versus measurable or topological.\nMore precisely:\nIn (1)\, we defi
nitely deal with a ``smooth object''\, e.g. the universal deformation form
ula (i.e. the twist) allows to deform smooth vectors of the group action\,
e.g. they are relevant in differential noncommutative geometry in the sen
se of A. Connes. But\, no locally compact quantum group is present there.
And until now\, I haven't be able to define a reasonable notion of ``smoot
h quantum group'' attached to the construction.\nIn (2)\, the quantum grou
p is present\, but the deformation procedure apparently breaks smoothness:
smooth vectors of strongly continuous actions (i.e. smooth module-algebra
s) of the group are not stable under twisting.\n\nIn the talk\, I will dis
cuss differential geometrical aspects of Frobenius Lie groups within this
deformation quantization context. I will end with a suggestion based on t
he possible use of a Lie group theoretical version of a\nmicrolocal analyt
ical tool : Hörmander's smooth wave front set.\n
LOCATION:https://researchseminars.org/talk/QGS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Hataishi (University of Oslo\, Norway)
DTSTART;VALUE=DATE-TIME:20220516T140000Z
DTEND;VALUE=DATE-TIME:20220516T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/59
DESCRIPTION:Title: Yet
ter-Drinfeld algebras\, module categories and injectivity\nby Lucas Ha
taishi (University of Oslo\, Norway) as part of Quantum Groups Seminar [QG
S]\n\n\nAbstract\nMany examples of quantum group actions carry a Yetter-Dr
infeld structure. Among them\, you find C*-algebras coming from the bounda
ry theory of Drinfeld doubles\, which is closely related to the theory of
ucp maps and injective envelopes of Hamana. Exploring Tannaka-Krein dualit
y for quantum group actions\, it is possible to extend many concepts and r
esults of boundary theory to the categorical setting\, but the lack of a c
ategorification of non-braided-commutative Yetter-Drinfeld algebras impose
an obstruction to a full analogy.\n\nIn this talk\, I will sketch how to
perform such a categorification and relate it to the study of injectivity
for module categories. Based on joint works with E. Habbestad\, S. Neshvey
ev and M. Yamashita.\n
LOCATION:https://researchseminars.org/talk/QGS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Halbig (TU Dresden\, Germany)
DTSTART;VALUE=DATE-TIME:20220530T140000Z
DTEND;VALUE=DATE-TIME:20220530T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/60
DESCRIPTION:Title: Piv
otality\, twisted centres and the anti-double of a Hopf monad\nby Seba
stian Halbig (TU Dresden\, Germany) as part of Quantum Groups Seminar [QGS
]\n\n\nAbstract\nPairs in involution are an algebraic structure whose syst
ematic study\nis motivated by their applications in knot theory\, represen
tation theory and\ncyclic homology theories.\n\nIn this talk\, we will exp
lore a categorical view for these objects from the\nperspective of represe
ntation theory of monoidal categories.\nA focus will lie on illustrating h
ow their existence is linked to a particular\nwell-behaved notion of duali
ty called pivotality.\nIn particular\, we will show how the language of mo
nads allows us to combine\nthe algebraic with the categorical perspective
of these pairs.\n\nThis talk is based on the article arXiv:2201.05361.\n
LOCATION:https://researchseminars.org/talk/QGS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan Konings (Vrije Universiteit Brussel\, Belgium)
DTSTART;VALUE=DATE-TIME:20220606T140000Z
DTEND;VALUE=DATE-TIME:20220606T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/61
DESCRIPTION:Title: Par
tial algebraic quantum groups and their Drinfeld doubles\nby Johan Kon
ings (Vrije Universiteit Brussel\, Belgium) as part of Quantum Groups Semi
nar [QGS]\n\n\nAbstract\nIn this talk\, we will define partial algebraic q
uantum groups\, which are special cases of weak multiplier Hopf algebras\,
as introduced by Van Daele and Wang. At the same time\, they provide a ge
neralization to the notion of a partial compact quantum group\, as introdu
ced by De Commer and Timmermann. The main aim of the talk will be to reali
ze the Drinfeld double of a partial compact quantum group as a partial alg
ebraic quantum group. This talk is based on joint work with K. De Commer.\
n
LOCATION:https://researchseminars.org/talk/QGS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roland Vergnioux (Université de Caen\, France)
DTSTART;VALUE=DATE-TIME:20220620T140000Z
DTEND;VALUE=DATE-TIME:20220620T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/62
DESCRIPTION:Title: Hec
ke algebras and the Schlichting completion for discrete quantum groups
\nby Roland Vergnioux (Université de Caen\, France) as part of Quantum Gr
oups Seminar [QGS]\n\n\nAbstract\nIn recent joint work with Skalski and Vo
igt we construct and study the Hecke algebra and Hecke operators associate
d with an almost normal subgroup in a discrete quantum group. We also give
in this framework a quantum version of the Schlichting completion\, which
yields an algebraic quantum group with a compact-open subgroup. We descri
be a class of examples arising from HNN extensions.\n
LOCATION:https://researchseminars.org/talk/QGS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Hernández Palomares (Texas A&M University\, USA)
DTSTART;VALUE=DATE-TIME:20220627T140000Z
DTEND;VALUE=DATE-TIME:20220627T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/63
DESCRIPTION:Title: Q-s
ystems and higher unitary idempotent completion for C*-algebras\nby Ro
berto Hernández Palomares (Texas A&M University\, USA) as part of Quantum
Groups Seminar [QGS]\n\n\nAbstract\nQ-systems were introduced by Longo to
study finite index inclusions of infinite von Neumann factors. A Q-system
is a unitary version of a Frobenius algebra object in a tensor category o
r a C* 2-category. By the work of Müger\, Q-systems give an axiomatizatio
n of the standard invariant of a finite index subfactor.\n\nFollowing work
of Douglass-Reutter\, a Q-system is also a unitary version of a higher id
empotent. In this talk\, we will describe a higher unitary idempotent comp
letion for C* 2-categories called Q-system completion.\n\nOur main goal is
to show that C*Alg\, the C* 2-category of right correspondences of unital
C*-algebras is Q-system complete. To do so\, we will use the graphical ca
lculus for C* 2-categories\, and adapt a subfactor reconstruction techniqu
e called realization\, which is inverse to Q-system completion. This resul
t allows for the straightforward adaptation of subfactor results to C*-alg
ebras\, characterizing finite index extensions of unital C*-algebras equip
ped with a faithful conditional expectation in terms of the Q-systems in C
*Alg. If time allows\, we will discuss an application to induce new symmet
ries of C*-algebras from old via Q-system completion.\n\nThis is joint wor
k with Q. Chen\, C. Jones and D. Penneys (arXiv: 2105.12010).\n
LOCATION:https://researchseminars.org/talk/QGS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harshit Yadav (Rice University\, USA)
DTSTART;VALUE=DATE-TIME:20220704T140000Z
DTEND;VALUE=DATE-TIME:20220704T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/64
DESCRIPTION:Title: Fil
tered Frobenius algebras in monoidal categories\nby Harshit Yadav (Ric
e University\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\
nWe develop filtered-graded techniques for algebras in monoidal\ncategorie
s with the goal of establishing a categorical version of Bongale's\n1967 r
esult: A filtered deformation of a Frobenius algebra over a field is\nFrob
enius as well. Towards the goal\, we construct a monoidal associated\ngrad
ed functor\, building on prior works of Ardizzoni-Menini\, of Galatius et\
nal.\, and of Gwillian-Pavlov. We then produce equivalent conditions for a
n\nalgebra in a rigid monoidal category to be Frobenius in terms of the\ne
xistence of categorical Frobenius form. These two results of independent\n
interest are used to achieve our goal. As an application of our main\nresu
lt\, we show that any exact module category over a symmetric finite\ntenso
r category is represented by a Frobenius algebra in it. This is joint\nwor
k with Dr. Chelsea Walton (Rice University)\n
LOCATION:https://researchseminars.org/talk/QGS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Anderson-Sackaney (Université de Caen\, France)
DTSTART;VALUE=DATE-TIME:20221018T140000Z
DTEND;VALUE=DATE-TIME:20221018T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/65
DESCRIPTION:Title: Rel
ative Amenability\, Amenability\, and Coamenability of Coideals\nby Be
njamin Anderson-Sackaney (Université de Caen\, France) as part of Quantum
Groups Seminar [QGS]\n\n\nAbstract\nAmenability is a deeply studied prope
rty of groups\, with many interesting reformulations and connections to th
e operator algebraic aspects of groups. For example\, the reduced $C^*$-al
gebra $C^*_r(G)$ of a discrete group has a unique tracial state if and onl
y if there are no non-trivial amenable normal subgroups. This\, among othe
r related results\, makes it apparent that the structure of the amenable s
ubgroups of $G$ contains important information about $C^*_r(G)$. For a qua
ntum group $\\mathbb{G}$\, an appropriate analogue of a subgroup is a coid
eal $N\\subseteq L^\\infty(\\mathbb{G})$. We will present notions of relat
ive amenability\, amenability\, and coamenability for coideals of discrete
and compact quantum groups motivated by "relativizations" of amenability
and coamenability of a subgroup of a group. We will discuss the known rela
tionships between these formally distinct notions and their relevance to c
ertain properties of the reduced $C^*$-algebras of discrete quantum groups
.\n
LOCATION:https://researchseminars.org/talk/QGS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magnus Landstad (Norwegian University of Science and Technology\,
Norway)
DTSTART;VALUE=DATE-TIME:20221108T150000Z
DTEND;VALUE=DATE-TIME:20221108T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/66
DESCRIPTION:Title: Exo
tic group algebras\, crossed products\, and coactions\nby Magnus Lands
tad (Norwegian University of Science and Technology\, Norway) as part of Q
uantum Groups Seminar [QGS]\n\n\nAbstract\nIf $G$ is a locally compact gro
up\, we have the full group C*-algebra $C^*(G)$ and the reduced $C^*_r(G)$
. We call a C*-algebra properly between $C^*(G)$ and $C^*_r(G)$ exotic.\n\
nSimilarly\, if $G$ acts on a C*-algebra $A$ we can form the full crossed
product $C^*(G\\ltimes A)$ and the reduced crossed product $C^*_r(G\\ltime
s A)$. An exotic crossed product is a C*-algebra properly between the two.
Work by Baum\, Guentner\, and Willett show that these algebras are releva
nt to the Baum-Connes conjecture.\n\nWe think that the best way to study t
hese algebras is by also looking at the corresponding dual theory of coact
ions. I will discuss some of these aspects\, but there will be more questi
ons than answers.\n\nThis is joint work with Steve Kaliszewski and John Qu
igg.\n
LOCATION:https://researchseminars.org/talk/QGS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfons Van Daele (KU Leuven\, Belgium)
DTSTART;VALUE=DATE-TIME:20221115T150000Z
DTEND;VALUE=DATE-TIME:20221115T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/67
DESCRIPTION:Title: Alg
ebraic quantum hypergroups and duality\nby Alfons Van Daele (KU Leuven
\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nLet $G$
be a finite group and $H$ a subgroup. The set $\\mathcal{G}$ of double co
sets $HpH$\, with $p \\in G$ has the structure of an hypergroup. The produ
ct of two elements $HpH$ and $HqH$ is the set of cosets $HrH$ where $r \\i
n pHq$. The algebra $A$ of functions on $\\mathcal{G}$ is the space of fun
ctions on $G$ that are constant on double cosets. It carries a natural cop
roduct\, dual to the product\, and given by\n$$∆(p\,q) = \\frac{1}{n} \\
sum_{h \\in H} f(phq)$$\nwhere $n$ is the number of elements in $H$. The d
ual algebra is known as the Hecke algebra associated with the pair $G\,H$.
\nIn this talk I will discuss the notion of an algebraic quantum hypergrou
p\, its fundamental properties and duality for algebraic quantum hypergrou
ps.\nI will illustrate this with an example\, coming from bicrossproduct t
heory\, constructed from a pair of closed subgroups $H$ and $K$ of a group
$G$\, with the assumption that $H \\cap K = {e}$.\nThis is part of more g
eneral work in progress with M. Landstad (NTNU\, Trondheim)\n
LOCATION:https://researchseminars.org/talk/QGS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Habbestad (Universityof Oslo\, Norway)
DTSTART;VALUE=DATE-TIME:20221213T150000Z
DTEND;VALUE=DATE-TIME:20221213T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/70
DESCRIPTION:Title: C*-
algebras associated to Temperley-Lieb polynomials\nby Erik Habbestad (
Universityof Oslo\, Norway) as part of Quantum Groups Seminar [QGS]\n\n\nA
bstract\nWe define Temperley-Lieb polynomials and consider the (standard)
subproduct systems they generate. This subproduct system turns out to be e
quivariant with respect to a compact quantum group G monoidally equivalent
to $U_q(2)$. Exploiting this we are able to describe the C*-algebras asso
ciated to the subproduct system\, which turn out to be closesly related to
the linking algebra $B(U_q(2)\,G)$. This is joint work with Sergey Neshve
yev.\n
LOCATION:https://researchseminars.org/talk/QGS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Khosravi (Seoul National University\, South Korea)
DTSTART;VALUE=DATE-TIME:20221129T100000Z
DTEND;VALUE=DATE-TIME:20221129T110000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/72
DESCRIPTION:Title: Co-
amenable quantum homogeneous spaces of compact Kac quantum groups\nby
Fatemeh Khosravi (Seoul National University\, South Korea) as part of Quan
tum Groups Seminar [QGS]\n\n\nAbstract\nGiven a locally compact group G\,
Leptin's theorem states that G is amenable if and only if the Fourier alge
bra A(G) admits a bounded approximate identity\, where the latter property
is known as co-amenability of the quantum dual of G. In the quantum setti
ng\, this characterization is known as the duality between amenability and
co-amenability. It is proved that a discrete quantum group is amenable if
and only if its dual compact quantum group is co-amenable. The definition
of co-amenability for quantum homogeneous spaces is given by Kalantar-Kas
przak-Skalski-Vergnioux. Furthermore\, they ask whether the co-amenability
of a quantum homogeneous space is equivalent to the (relative) amenabilit
y of its co-dual. In this talk\, we will answer this question for quantum
homogeneous spaces of compact Kac quantum groups under a mild assumption.
Based on joint work with Mehrdad Kalantar.\n
LOCATION:https://researchseminars.org/talk/QGS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefaan Vaes (KU Leuven\, Belgium)
DTSTART;VALUE=DATE-TIME:20221122T160000Z
DTEND;VALUE=DATE-TIME:20221122T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/75
DESCRIPTION:Title: Qua
ntum automorphism groups of connected locally finite graphs and quantizati
ons of finitely generated groups\nby Stefaan Vaes (KU Leuven\, Belgium
) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nI present a joint
work with Lukas Rollier. We construct the quantum automorphism group of a
ny connected locally finite\, possibly infinite\, graph as a locally compa
ct quantum group that has the classical (locally compact) automorphism gro
up as a closed quantum subgroup. For finite graphs\, we get the quantum au
tomorphism group of Banica and Bichon. One of the key tools is the constru
ction of a unitary tensor category associated with any connected locally f
inite graph. When this graph is the Cayley graph of a finitely generated g
roup\, the associated unitary tensor category has a canonical fiber functo
r. We thus also obtain a quantization procedure for arbitrary finitely gen
erated groups. In the particular example of groups defined by a triangle p
resentation\, this construction gives the property (T) discrete quantum gr
oups from earlier joint work with Valvekens.\n
LOCATION:https://researchseminars.org/talk/QGS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kan Kitamura (University of Tokyo\, Japan)
DTSTART;VALUE=DATE-TIME:20221220T150000Z
DTEND;VALUE=DATE-TIME:20221220T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/77
DESCRIPTION:Title: Par
tial Pontryagin duality for actions of quantum groups on C*-algebras\n
by Kan Kitamura (University of Tokyo\, Japan) as part of Quantum Groups Se
minar [QGS]\n\n\nAbstract\nWe compare actions on C*-algebras of two constr
uctions of locally compact quantum groups\, the bicrossed product due to V
aes-Vainerman and the double crossed product due to Baaj-Vaes. We give a o
ne-to-one correspondence between them up to Morita equivalence\, in the sa
me spirit as Takesaki-Takai and Baaj-Skandalis dualities. This includes a
duality between a quantum double and the product of the original quantum g
roup with its opposite. We will explain its consequences for equivariant K
asparov theory in relation to the quantum analog of the Baum-Connes conjec
ture.\n
LOCATION:https://researchseminars.org/talk/QGS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Plavnik (Indiana University Bloomington\, USA)
DTSTART;VALUE=DATE-TIME:20230124T150000Z
DTEND;VALUE=DATE-TIME:20230124T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/78
DESCRIPTION:Title: Com
paring different constructions of modular categories\nby Julia Plavnik
(Indiana University Bloomington\, USA) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nModular categories arise naturally in many areas of m
athematics\, such as conformal field theory\, representations of braid gro
ups\, quantum groups\, and Hopf algebras\, and low dimensional topology\,
and they have important applications in condensed matter physics.\n\nDespi
te recent progress in the classification of modular categories\, we are st
ill in the early stages of this theory and the general landscape remains l
argely unexplored. One important step towards deepening our understanding
of modular categories is to have well-studied constructions. In this talk\
, we will present an overview of various of these constructions and compar
e their properties. We will focus on ribbon zesting and symmetry gauging\,
and we will comment on some constructions in the G-crossed setting.\n
LOCATION:https://researchseminars.org/talk/QGS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Daws (University of Central Lancashire\, UK)
DTSTART;VALUE=DATE-TIME:20230131T150000Z
DTEND;VALUE=DATE-TIME:20230131T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/79
DESCRIPTION:Title: Aro
und the Approximation Property for Quantum Groups\nby Matthew Daws (Un
iversity of Central Lancashire\, UK) as part of Quantum Groups Seminar [QG
S]\n\n\nAbstract\nI will introduce what the "approximation property" (AP)
is for (locally compact) groups\, and provide a few applications. I will
then talk about how one might give an analogous definition for (locally co
mpact) quantum groups\, explaining some of the need technology along the w
ay. Time allowing\, I will discuss how the AP interacts with various comm
on constructions\, and also about "central" versions and links with tensor
categories.\n
LOCATION:https://researchseminars.org/talk/QGS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Aristov
DTSTART;VALUE=DATE-TIME:20230207T150000Z
DTEND;VALUE=DATE-TIME:20230207T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/80
DESCRIPTION:Title: Com
plex-analytic approach to quantum groups\nby Oleg Aristov as part of Q
uantum Groups Seminar [QGS]\n\n\nAbstract\nWe discuss quantum analogues of
complex Lie groups. Our approach is closer to classical quantum group the
ory than to C*-algebraic one (no multipliers and no invariant weights). I
propose to consider a topological Hopf algebra with a finiteness condition
(holomorphically ﬁnitely generated or HFG for short). This topic seems
to offer a wide range of research opportunities.\n\nOur focus is on exampl
es\, such as analytic forms of some classical quantum groups (a deformatio
n of a solvable Lie group and Drinfeld-Jimbo algebras). I also present som
e general results: (1) the category of Stein groups is anti-equivalent to
the category of commutative Hopf HFG algebras\; (2) If G is a compactly ge
nerated Lie group\, the associated convolution cocommutative topological H
opf algebra (introduced by Akbarov) is HFG. When\, in addition\, G is conn
ected and linear\, the structure of this cocommutative algebra can be desc
ribed explicitly. I also plan to discuss briefly holomorphic duality (whic
h is parallel to Pontryagin duality).\n
LOCATION:https://researchseminars.org/talk/QGS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Devarshi Mukherjee (University of Buenos Aires\, Argentina)
DTSTART;VALUE=DATE-TIME:20230221T150000Z
DTEND;VALUE=DATE-TIME:20230221T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/81
DESCRIPTION:Title: Non
commutative geometry in mixed characteristic\nby Devarshi Mukherjee (U
niversity of Buenos Aires\, Argentina) as part of Quantum Groups Seminar [
QGS]\n\n\nAbstract\nI will give an overview of noncommutative topological
algebras and their cohomology theories in the setting of the p-adic intege
rs.\n\nThis will entail constructions that are familiar from the complex c
ase\, such as the formation of a smooth subalgebra of a C*-algebra. The e
xamples I will specialise these constructions to are group algebras of dis
crete and p-adic Lie groups. It turns out that these are also examples of
bornological quantum groups (in the sense of Voigt). Finally\, if time per
mits\, I will also discuss the computations of the Hochschild homology of
the completions of such algebras.\n
LOCATION:https://researchseminars.org/talk/QGS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mao Hoshino (University of Tokyo\, Japan)
DTSTART;VALUE=DATE-TIME:20230307T150000Z
DTEND;VALUE=DATE-TIME:20230307T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/82
DESCRIPTION:Title: Equ
ivariant covering spaces of quantum homogeneous spaces\nby Mao Hoshino
(University of Tokyo\, Japan) as part of Quantum Groups Seminar [QGS]\n\n
\nAbstract\nIn this talk I will explain the imprimitivity theorems for equ
ivariant correspondences in two cases: for a general compact quantum group
under a finiteness condition\, and for the Drinfeld-Jimbo deformation of
a semisimple compact Lie group. These results involve the representation\n
theories of function algebras and the Tannaka-Krein duality for equivarian
t correspondences. I also would like to give some applications if time all
ows.\n
LOCATION:https://researchseminars.org/talk/QGS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Molander (University of California\, Santa Barbara\, USA)
DTSTART;VALUE=DATE-TIME:20230314T150000Z
DTEND;VALUE=DATE-TIME:20230314T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/83
DESCRIPTION:Title: Ske
in Theory for Affine ADE Subfactor Planar Algebras\nby Melody Molander
(University of California\, Santa Barbara\, USA) as part of Quantum Group
s Seminar [QGS]\n\n\nAbstract\nSubfactor planar algebras first were constr
ucted by Vaughan Jones as a diagrammatic axiomatization of the standard in
variant of a subfactor. These planar algebras also encode two other invari
ants of the subfactors: the index and the principal graph. The Kuperberg P
rogram asks to find all diagrammatic presentations of subfactor planar alg
ebras. This program has been completed for index less than 4. In this talk
\, I will introduce subfactor planar algebras and give some presentations
of subfactor planar algebras of index 4 which have affine ADE Dynkin diagr
ams as their principal graphs.\n
LOCATION:https://researchseminars.org/talk/QGS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Troupel (Université Paris Cité\, France)
DTSTART;VALUE=DATE-TIME:20230214T150000Z
DTEND;VALUE=DATE-TIME:20230214T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/84
DESCRIPTION:Title: Fre
e wreath products as fundamental graph C*-algebras\nby Arthur Troupel
(Université Paris Cité\, France) as part of Quantum Groups Seminar [QGS]
\n\n\nAbstract\nThe free wreath product of a compact quantum group by the
quantum permutation group $S_N^+$ has been introduced by Bichon in order t
o give a quantum counterpart of the classical wreath product. The represen
tation theory of such groups is well-known\, but some results about their
operator algebras were still open\, for example Haagerup property\, K-amen
ability or factoriality of the von Neumann algebra. I will present a joint
work with Pierre Fima in which we identify these algebras with the fundam
ental C*-algebras of certain graphs of C*-algebras\, and we deduce these p
roperties from these constructions.\n
LOCATION:https://researchseminars.org/talk/QGS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuyuki Kawahigashi (University of Tokyo\, Japan)
DTSTART;VALUE=DATE-TIME:20230328T110000Z
DTEND;VALUE=DATE-TIME:20230328T120000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/85
DESCRIPTION:Title: Top
ological order\, tensor networks and subfactors\nby Yasuyuki Kawahigas
hi (University of Tokyo\, Japan) as part of Quantum Groups Seminar [QGS]\n
\n\nAbstract\nI will explain interactions between two-dimensional topologi
cal order and subfactors from a viewpoint of tensor networks. The range o
f a certain finite dimensional projection appearing in statistical physics
is identified with the higher relative commutant of the subfactor arising
from such a tensor network. We then work out the machinery of alpha-indu
ction\nfor braided fusion categories in the setting of certain 4-tensors\,
called bi-unitary connections\, appearing in subfactor theory.\n
LOCATION:https://researchseminars.org/talk/QGS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Brannan (University of Waterloo\, Canada)
DTSTART;VALUE=DATE-TIME:20230425T140000Z
DTEND;VALUE=DATE-TIME:20230425T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/92
DESCRIPTION:Title: No-
signalling bicorrelations and generalized quantum automorphisms of graphs<
/a>\nby Michael Brannan (University of Waterloo\, Canada) as part of Quant
um Groups Seminar [QGS]\n\n\nAbstract\nI'll report on some recent joint wo
rk with Sam Harris\,\nLyudmila Turowska and Ivan Todorov (arXiv:2302.04268
)\, where we\nintroduce an analogue of bisynchronous correlations in the c
ontext of\nquantum input-quantum output non-local games. One of the main\
nmotivations of this work was to find a non-local game interpretation of\n
the quantum automorphisms and isomorphisms of quantum graphs that have\nap
peared recently in the literature. I'll explain how these\nconsiderations
are related to tracial representations of quantum\nautomorphism groups of
matrix algebras\, and in the case of ordinary\ngraphs\, lead us to a soft
er (and possibly more general) notion of\nquantum symmetry for graphs.\n
LOCATION:https://researchseminars.org/talk/QGS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mainak Ghosh (Indian Statistical Institute\, India)
DTSTART;VALUE=DATE-TIME:20230620T090000Z
DTEND;VALUE=DATE-TIME:20230620T100000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/98
DESCRIPTION:Title: Uni
tary connections and Q-systems\nby Mainak Ghosh (Indian Statistical In
stitute\, India) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nTh
e standard invariant plays a major role in subfactor theory. In this talk\
, I will discuss a 2-categorical generalization of an axiomatization of th
e standard invariant and further discuss some algebraic structures associa
ted to it. This is based on joint work with P. Das\, S. Ghosh and C. Jones
(arXiv:2211.03822) and on arxiv : 2302.04921.\n
LOCATION:https://researchseminars.org/talk/QGS/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joeri De Ro (Vrije Universiteit Brussel\, Belgium)
DTSTART;VALUE=DATE-TIME:20230606T140000Z
DTEND;VALUE=DATE-TIME:20230606T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/100
DESCRIPTION:Title: Ac
tions of compact and discrete quantum groups on operator systems\nby J
oeri De Ro (Vrije Universiteit Brussel\, Belgium) as part of Quantum Group
s Seminar [QGS]\n\n\nAbstract\nWe introduce the notion of an action of a d
iscrete or compact quantum group on an operator system\, and study equivar
iant operator system injectivity. Given an action of a discrete quantum gr
oup on an operator system X\, we introduce associated crossed products\, a
nd we prove that equivariant injectivity of the operator system X is equiv
alent with dual equivariant injectivity of the associated crossed products
. As an application of this result\, we prove a duality result for equivar
iant injective envelopes. This is joint work with Lucas Hataishi.\n
LOCATION:https://researchseminars.org/talk/QGS/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mateusz Wasilewski (IMPAM\, Poland)
DTSTART;VALUE=DATE-TIME:20231016T140000Z
DTEND;VALUE=DATE-TIME:20231016T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/101
DESCRIPTION:Title: Qu
antum Cayley graphs\nby Mateusz Wasilewski (IMPAM\, Poland) as part of
Quantum Groups Seminar [QGS]\n\n\nAbstract\nI will talk about a method of
associating a quantum graph to a discrete quantum group together with a p
rojection in its function algebra. These quantum graphs are analogues of C
ayley graphs and they do not depend on the choice of a generating projecti
on in the sense of metric geometry. Later I will show how they can help in
finding examples of finite quantum groups having Frucht property\, i.e. a
rising as quantum automorphism groups of quantum graphs.\n\nPart of the ta
lk will be based on an on-going joint work with Michael Brannan and Adam S
kalski.\n
LOCATION:https://researchseminars.org/talk/QGS/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amaury Freslon (Université Paris-Saclay\, France)
DTSTART;VALUE=DATE-TIME:20231023T140000Z
DTEND;VALUE=DATE-TIME:20231023T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/102
DESCRIPTION:Title: Cl
assical actions of quantum permutations\nby Amaury Freslon (Universit
é Paris-Saclay\, France) as part of Quantum Groups Seminar [QGS]\n\n\nAbs
tract\nQuantum permutation groups can act non-trivially\, and even ergodic
ally\, on finite spaces. This is\, in view of many quantum rigidity result
s\, an exception and it is natural to wonder whether there are other class
ical spaces on which quantum permutations can act. H. Huang constructed a
family of such spaces\, and we will show that these are the only possibili
ties. This is a joint work with F. Taipe and S. Wang.\n
LOCATION:https://researchseminars.org/talk/QGS/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siegfried Echterhoff (WWU Münster\, Germany)
DTSTART;VALUE=DATE-TIME:20231204T150000Z
DTEND;VALUE=DATE-TIME:20231204T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/103
DESCRIPTION:Title: Pr
oper actions\, fixed-point algebras\, and deformation via coactions\nb
y Siegfried Echterhoff (WWU Münster\, Germany) as part of Quantum Groups
Seminar [QGS]\n\n\nAbstract\nThe notion of proper actions of groups on spa
ces has various generalizations for group actions of noncommutative $C^*$-
algebras $A$\, which all allow the construction of generalized fixed-point
algebras $A^G$ which are Morita equivalent to ideals in the reduced cross
ed products $A\\rtimes_rG$. The weakest version was introduced by Rieffel
in 1990 and it played an important role in his theory of deformations vi
a actions of $\\mathbb R^d$. In this talk we want to report on some joint
work with Alcides Buss on a version of proper actions which allows the con
struction of maximal (or exotic) generalized fixed-point algebras which ar
e Morita equivalent to ideals in the maximal (resp. exotic) crossed produc
ts. We will report on several applications including Landstad duality for
coactions and deformation of C*-algebras via coactions in the sense of Kas
przak and Bowmick\, Neshveyev\, and Sangha.\n
LOCATION:https://researchseminars.org/talk/QGS/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Anderson-Sackaney (Université de Caen\, France)
DTSTART;VALUE=DATE-TIME:20231113T150000Z
DTEND;VALUE=DATE-TIME:20231113T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/104
DESCRIPTION:Title: To
pological Boundaries of Representations and Coideals\nby Benjamin Ande
rson-Sackaney (Université de Caen\, France) as part of Quantum Groups Sem
inar [QGS]\n\n\nAbstract\nWe will introduce and study quantum analogues of
Furstenberg-Hamana boundaries of representations of discrete quantum grou
ps\, where the Furstenberg boundary is the Furstenberg-Hamana boundary of
the left regular representation. Our focus is on the GNS representations o
f idempotent states\, or to put it differently\, the quasi-regular represe
ntations coming from coideals associated to compact quasi-subgroups. We us
e their Furstenberg-Hamana boundaries to study (co)amenability properties
of such coideals. Then\, we combine our work with recent work of Hataishi
and De Ro to settle open problems of Kalantar\, Kasprzak\, Skalski\, and V
ergnioux for wide classes of quantum groups\, including unimodular discret
e quantum groups and C*-exact discrete quantum groups. For example\, we pr
ove that a unimodular discrete quantum group has the unique trace property
iff it acts faithfully on its Furstenberg boundary.\n\nThis is joint work
with Fatemeh Khosravi.\n
LOCATION:https://researchseminars.org/talk/QGS/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Yuncken (Université de Lorraine\, France)
DTSTART;VALUE=DATE-TIME:20231120T150000Z
DTEND;VALUE=DATE-TIME:20231120T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/105
DESCRIPTION:Title: Cr
ystallizing compact semisimple Lie groups\nby Robert Yuncken (Universi
té de Lorraine\, France) as part of Quantum Groups Seminar [QGS]\n\n\nAbs
tract\nThe theory of crystal bases is a means of simplifying the represent
ation theory of semisimple Lie algebras by passing through quantum groups.
Varying the parameter q of the quantized enveloping algebras\, we pass f
rom the classical theory at $q=1$ through the Drinfeld-Jimbo algebras a
t $q\\in]0\,1[$ to the crystal limit at $q = 0$. At this point\, the main
features of the representation theory crystallize into purely combinatoria
l data described by crystal graphs. In this talk\, we will describe what
happens to the C*-algebra of functions on a compact semisimple Lie group u
nder the crystallization process\, yielding higher-rank graph algebras. Th
is is joint work with Marco Matassa.\n
LOCATION:https://researchseminars.org/talk/QGS/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malte Gerhold (Saarland University\, Germany)
DTSTART;VALUE=DATE-TIME:20231127T150000Z
DTEND;VALUE=DATE-TIME:20231127T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/106
DESCRIPTION:Title: Co
homology of free unitary quantum groups\nby Malte Gerhold (Saarland Un
iversity\, Germany) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\
nIn the talk\, we will discuss the free unitary quantum groups\n(or "unive
rsal quantum groups") of Wang and van Daele from a\n(co)homological perspe
ctive. We find a free resolution of the\ncounit\, a versatile tool which h
elps to compute cohomological data such\nas Hochschild cohomology or bialg
ebra cohomology of the associated Hopf\nalgebras. For free orthogonal quan
tum groups\, such resolutions have been\nfound by Collins\, Härtel\, and
Thom (in the Kac-case) and Bichon (in the\ngeneral case)\, and they will s
erve as our starting point for finding\nresolutions for free unitary quant
um groups.\n\nBased on joint work with I. Baraquin\, U. Franz\, A. Kula an
d M. Tobolski\n[arXiv:2309.07767]\n
LOCATION:https://researchseminars.org/talk/QGS/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uwe Franz (Université de Franche-Comté\, France)
DTSTART;VALUE=DATE-TIME:20240122T150000Z
DTEND;VALUE=DATE-TIME:20240122T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/107
DESCRIPTION:Title: Ga
ussian Parts of Compact Quantum Groups\nby Uwe Franz (Université de F
ranche-Comté\, France) as part of Quantum Groups Seminar [QGS]\n\n\nAbstr
act\nWe introduce the Gaussian part of a compact quantum group G\, namely
the largest quantum subgroup of G supporting all the Gaussian functionals
of G. We prove that the Gaussian part is always contained in the Kac part\
, and characterise Gaussian parts of classical compact groups\, duals of c
lassical discrete groups and q-deformations of compact Lie groups. The not
ion turns out to be related to a new concept of "strong connectedness" and
we exhibit several examples of both strongly connected and totally strong
ly disconnected compact quantum groups. Joint work with Amaury Freslon and
Adam Skalski.\n
LOCATION:https://researchseminars.org/talk/QGS/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joeri De Ro (Vrije Universiteit Brussel\, Belgium)
DTSTART;VALUE=DATE-TIME:20240129T150000Z
DTEND;VALUE=DATE-TIME:20240129T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/108
DESCRIPTION:Title: Eq
uivariant injectivity of crossed products\nby Joeri De Ro (Vrije Unive
rsiteit Brussel\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAb
stract\nWe introduce the notion of a G-operator space\, which consists of
an action of a locally compact quantum group G on an operator space X\, an
d we study the notion of G-equivariant injectivity for such an operator sp
ace. We define a natural associated crossed product operator space X ⋊ G
\, on which both the locally compact quantum group G and its dual act. We
completely characterise when these crossed products are equivariantly inje
ctive with respect to these actions. We discuss how these results generali
se and unify several recent results from the literature and we give some n
ew applications.\n
LOCATION:https://researchseminars.org/talk/QGS/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Girón Pacheco (KU Leuven\, Belgium)
DTSTART;VALUE=DATE-TIME:20240205T150000Z
DTEND;VALUE=DATE-TIME:20240205T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/109
DESCRIPTION:Title: In
tertwining techniques for actions of C*-tensor categories\nby Sergio G
irón Pacheco (KU Leuven\, Belgium) as part of Quantum Groups Seminar [QGS
]\n\n\nAbstract\nIntertwining techniques\, first used in the realm of C*-a
lgebras in Elliott’s classification of AF-algebras\, have been essential
in the classification theory of C*-algebras and their group actions. In t
his talk I will discuss intertwining and how it appears in C*-classificati
on\, I will then outline an adaptation of these techniques to the tensor c
ategory equivariant setting. Time permitting I will discuss an application
of these techniques to the study of tensor category equivariant Jiang-Su
stability.\n
LOCATION:https://researchseminars.org/talk/QGS/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kent Vashaw (Massachusetts Institute of Technology\, USA)
DTSTART;VALUE=DATE-TIME:20240212T150000Z
DTEND;VALUE=DATE-TIME:20240212T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/110
DESCRIPTION:Title: Qu
antum-symmetric equivalence via Manin's universal quantum groups\nby K
ent Vashaw (Massachusetts Institute of Technology\, USA) as part of Quantu
m Groups Seminar [QGS]\n\n\nAbstract\nWe study 2-cocycle (and more general
ly quantum-symmetric equivalences between) twists of graded algebras via t
heir associated universal quantum groups\, in the sense of Manin. We prove
that Zhang twists arise as a special case of 2-cocycle twist\, and that 2
-cocyle twisting preserves many fundamental homological invariants of grad
ed algebras. As a consequence\, we give a characterization of Artin--Schel
ter regular algebras using the language of 2-cocycle twists.\n
LOCATION:https://researchseminars.org/talk/QGS/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lyudmila Turowska (Chalmers University of Technology and Universit
y of Gothenburg\, Sweden)
DTSTART;VALUE=DATE-TIME:20240304T150000Z
DTEND;VALUE=DATE-TIME:20240304T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/111
DESCRIPTION:Title: No
-signalling values of cooperative quantum games\nby Lyudmila Turowska
(Chalmers University of Technology and University of Gothenburg\, Sweden)
as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nFinding values\, th
e optimal winning probability\, of various non-local games over different
strategies has been an important task in Quantum Information Theory and al
so for resolving the Connes Embedding Problem. In this talk I will discuss
values of quantum games (games with quantum inputs and outputs)\, arising
from the type hierarchy of quantum no-signalling correlations\, establish
ing operator space tensor norm expressions for each of the correlation typ
es. This is a joint work with Jason Crann\, Rupert Levene and Ivan Todorov
.\n
LOCATION:https://researchseminars.org/talk/QGS/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Laugwitz (University of Nottingham\, UK)
DTSTART;VALUE=DATE-TIME:20240219T150000Z
DTEND;VALUE=DATE-TIME:20240219T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/112
DESCRIPTION:Title: In
duced functors on Drinfeld centers\nby Robert Laugwitz (University of
Nottingham\, UK) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nI
will explain how the right/left adjoint of a monoidal functor induced a br
aided lax/oplax monoidal functors between the corresponding Drinfeld cente
rs. This requires some mild technical assumptions\, namely that the projec
tion formulas hold for the adjoint functor. This holds\, for example\, whe
n the monoidal categories are rigid. As the induced functors on the Drinfe
ld centers are (op)lax and compatible with braiding\, they preserve commut
ative (co)algebra objects. As classes of examples\, we consider monoidal r
estriction functors along extensions of Hopf algebras leading to (co)induc
tion functors on Yetter-Drinfeld module categories. This is joint work in
progress with Johannes Flake (Bonn) and Sebastian Posur (Münster).\n
LOCATION:https://researchseminars.org/talk/QGS/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon\, USA)
DTSTART;VALUE=DATE-TIME:20240311T170000Z
DTEND;VALUE=DATE-TIME:20240311T180000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/113
DESCRIPTION:Title: Gr
owth in tensor powers\nby Victor Ostrik (University of Oregon\, USA) a
s part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nThis talk is based o
n joint work with K. Coulembier\, P. Etingof\, D. Tubbenhauer. Let $G$ be
any group and let $V$ be a finite dimensional representation of $G$ over s
ome field. We consider tensor powers of $V$ and their decompositions into
indecomposable summands. The main question which will be addressed in this
talk: what can we say about count (e.g. total number) of these indecompos
able summands? It turns out that there are reasonable partial answers to t
his question asymptotically\, i.e. when the tensor power is large.\n\nPlea
se note the unusual time\n
LOCATION:https://researchseminars.org/talk/QGS/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Esposito (University of Salerno\, Italy)
DTSTART;VALUE=DATE-TIME:20240513T140000Z
DTEND;VALUE=DATE-TIME:20240513T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/114
DESCRIPTION:Title: Eq
uivariant formality and reduction\nby Chiara Esposito (University of S
alerno\, Italy) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn
this talk\, we discuss the reduction-quantization diagram in terms of form
ality. First\, we propose a reduction scheme for multivector fields and mu
ltidifferential operators\, phrased in terms of L-infinity morphisms. This
requires the introduction of equivariant multivector fields and equivaria
nt multidifferential operator complexes\, which encode the information of
the Hamiltonian action\, i.e.\, a G-invariant Poisson structure allowing f
or a momentum map. As a second step\, we discuss an equivariant version of
the formality theorem\, conjectured by Tsygan and recently solved in a jo
int work with Nest\, Schnitzer\, and Tsygan. This result has immediate con
sequences in deformation quantization\, since it allows for obtaining a qu
antum moment map from a classical momentum map with respect to a G-invaria
nt Poisson structure.\n
LOCATION:https://researchseminars.org/talk/QGS/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Pearce-Crump (Imperial College London\, UK)
DTSTART;VALUE=DATE-TIME:20240520T140000Z
DTEND;VALUE=DATE-TIME:20240520T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/115
DESCRIPTION:Title: Co
mpact Matrix Quantum Group Equivariant Neural Networks\nby Edward Pear
ce-Crump (Imperial College London\, UK) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nIn deep learning\, we would like to develop principle
d approaches for constructing neural networks. One important approach invo
lves identifying symmetries that are inherent in data and then encoding th
em into neural network architectures using representations of groups. Howe
ver\, there exist so-called “quantum symmetries” that cannot be unders
tood formally by groups. In this talk\, we show how to construct neural ne
tworks that are equivariant to compact matrix quantum groups using Woronow
icz’s version of Tannaka-Krein duality. We go on to characterise the lin
ear weight matrices that appear in these neural networks for a class of co
mpact matrix quantum groups known as “easy”. In particular\, we show
that every compact matrix group equivariant neural network is a compact ma
trix quantum group equivariant neural network.\n
LOCATION:https://researchseminars.org/talk/QGS/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Krajczok (Vrije Universiteit Brussel\, Belgium)
DTSTART;VALUE=DATE-TIME:20240527T140000Z
DTEND;VALUE=DATE-TIME:20240527T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/116
DESCRIPTION:Title: Mo
dular invariants of quantum groups\nby Jacek Krajczok (Vrije Universit
eit Brussel\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAbstra
ct\nA very interesting feature of compact quantum groups is that their Haa
r integral\, which is a normal state on $L^{\\infty}(G)$\, can be non-trac
ial. Via Tomita-Takesaki theory\, this gives rise to two groups of automor
phisms: modular automorphisms and scaling automorphisms. One can use them
to define a number of invariants\, related to whether these automorphisms
are trivial\, inner or approximately inner. During the talk I'll introduce
such invariants (also in the general locally compact case)\, discuss a co
njecture related to one of them\, and present their calculation in the cas
e of q-deformed compact\, simply connected\, semisimple Lie group $G_q$. T
he talk is based on a joint work with Piotr Sołtan.\n
LOCATION:https://researchseminars.org/talk/QGS/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Goodearl (Universite of California Santa Barbara\, USA)
DTSTART;VALUE=DATE-TIME:20240624T070000Z
DTEND;VALUE=DATE-TIME:20240624T080000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/117
DESCRIPTION:Title: Sp
ectra of quantum algebras\nby Ken Goodearl (Universite of California S
anta Barbara\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\
nThe talk will survey what is known and/or conjectured about the prime and
primitive spectra of quantum algebras\, particularly quantized coordinate
rings and related algebras such as quantized Weyl algebras. The topologic
al structure of these spectra\, their relations with classical algebraic v
arieties\, and their relations with each other will be discussed.\n
LOCATION:https://researchseminars.org/talk/QGS/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roland Vergnioux (Université de Caen\, France)
DTSTART;VALUE=DATE-TIME:20240603T140000Z
DTEND;VALUE=DATE-TIME:20240603T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/118
DESCRIPTION:Title: Ma
ximal amenability of the radial subalgebra in free quantum groups factors<
/a>\nby Roland Vergnioux (Université de Caen\, France) as part of Quantum
Groups Seminar [QGS]\n\n\nAbstract\nThe free orthogonal quantum groups $O
^+(N)$\, introduced by Shuzhou Wang\, are monoidally equivalent to the $SU
_q(2)$ compact quantum groups\, but on an analytical level they behave muc
h like the quantum duals of the classical free groups\, when $N > 2$. I wi
ll review their definition and main properties\, and present a new result
about the maximal amenability of the associated radial MASA\, obtained in
recent joint work with Xumin Wang.\n
LOCATION:https://researchseminars.org/talk/QGS/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Gromada (Czech Technical University\, Czechia)
DTSTART;VALUE=DATE-TIME:20240617T140000Z
DTEND;VALUE=DATE-TIME:20240617T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/119
DESCRIPTION:Title: Sy
mmetries\, quantizations\, and duality\nby Daniel Gromada (Czech Techn
ical University\, Czechia) as part of Quantum Groups Seminar [QGS]\n\n\nAb
stract\nIn the talk\, we are going to quantize several aspects of Cayley g
raphs. First\, we are going to study quantum symmetries of Cayley graphs o
f abelian groups. From the classical theory\, it is known that the Fourier
transform diagonalizes the adjacency matrix of any such Cayley graph.\nTh
is can be used to determine the graph's quantum automorphism group. Second
ly\, we are going to show\, how to quantize Cayley graphs of abelian group
s. We obtain a quantum graph by twisting the function algebra of the class
ical one. Finally\, we recall a classical\nconstruction that takes a dista
nce regular Cayley graph of an abelian group or\, more generally\, a trans
lation association scheme and constructs its dual by applying the Fourier
transform. We generalize this construction replacing abelian groups by arb
itrary finite quantum groups.\n
LOCATION:https://researchseminars.org/talk/QGS/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Matassa (Oslo Metropolitan University\, Norway)
DTSTART;VALUE=DATE-TIME:20240701T140000Z
DTEND;VALUE=DATE-TIME:20240701T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/120
DESCRIPTION:Title: Eq
uivariant quantizations of the positive nilradical and covariant different
ial calculi\nby Marco Matassa (Oslo Metropolitan University\, Norway)
as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe consider the pro
blem of quantizing the positive nilradical of a complex semisimple Lie alg
ebra of finite rank\, together with a certain fixed direct sum decompositi
on. The decompositions we consider are in one-to-one correspondence with t
otal orders on the simple roots\, and exhibit the nilradical as a direct s
um of graded modules for appropriate Levi factors. We show that this situa
tion can be quantized equivariantly as a finite-dimensional subspace withi
n the positive part of the corresponding quantized enveloping algebra. Fur
thermore\, we show that such subspaces give rise to left coideals\, with t
he possible exception of components corresponding to some exceptional Lie
algebras\, and this property singles them out uniquely. Finally\, we discu
ss how to use these quantizations to construct covariant first-order diffe
rential calculi on quantum flag manifolds\, which coincide with those intr
oduced by Heckenberger-Kolb in the irreducible case.\n
LOCATION:https://researchseminars.org/talk/QGS/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Rollier (Katholieke Universiteit Leuven\, Belgium)
DTSTART;VALUE=DATE-TIME:20240610T140000Z
DTEND;VALUE=DATE-TIME:20240610T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T170322Z
UID:QGS/121
DESCRIPTION:Title: Qu
antum automorphism groups of discrete structures\nby Lukas Rollier (Ka
tholieke Universiteit Leuven\, Belgium) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nGiven any mathematical structure\, it is a natural qu
estion to ask which quantum symmetries it admits. One can in general not h
ope to find a quantum automorphism group for any structure in the framewor
k of Kustermans-Vaes\, as a necessary condition for its existence is local
compactness of the classical automorphism group. In recent work\, a wide
range of discrete structures\, those which are connected and locally finit
e in a suitable sense\, were shown to admit an algebraic quantum automorph
ism group. The main tool for their construction is a generalization of the
Tannaka-Krein-Woronowicz reconstruction theorem. In particular\, this all
ows to construct quantum automorphism groups of connected locally finite q
uantum graphs\, such as Wasilewski's quantum Cayley graphs\, generalizing
joint results with Stefaan Vaes.\n
LOCATION:https://researchseminars.org/talk/QGS/121/
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