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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:20221209T215924Z
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\n\n\nAbstract\
nThe notion of topological boundary actions has recently found striking ap
plications 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 boundary a
ction - the so-called Furstenberg boundary. We discuss applications in pro
blems of C*-simplicity and uniqueness of the Haar state of the dual.\n\nTh
is is joint work with Pawel Kasprzak\, Adam Skalski and Roland Vergnioux.\
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:20221209T215924Z
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\n\n\nAbstract\nWe give a decomposition
of the equivariant Kasparov category for a discrete quantum group with to
rsions. This formulates the Baum-Connes assembly map for general discrete
quantum groups possibly with torsion. As an application\, we show that the
group C*-algebra of a discrete quantum group in a certain class satisfies
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:20221209T215924Z
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\n\n\nAbstr
act\nSylvester's law of inertia states that two self-adjoint matrices A an
d B are related as $A = X^*BX$ for some invertible complex matrix $X$ if a
nd only if $A$ and $B$ have the same signature $(N_+\,N_-\,N_0)$\, i.e. th
e same number of positive\, negative and zero eigenvalues. In this talk\,
we will discuss a quantized version of this law: we consider the reflectio
n equation *-algebra (REA)\, which is a quantization of the *-algebra of p
olynomial functions on self-adjoint matrices\, together with a natural adj
oint action by quantum $GL(N\,\\mathbb{C})$. We then show that to each irr
educible bounded *-representation of the REA can be associated an extended
signature $(N_+\,N_-\,N_0\,[r])$ with $[r]$ in $\\mathbb{R}/\\mathbb{Z}$\
, and we will explain in what way this is a complete invariant of the orbi
ts under the action by quantum $GL(N\,\\mathbb{C})$. This is part of a wor
k 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:20221209T215924Z
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\n\n\nAbstract\nIn 2006\, Ralf Meyer and Ryszard Nest prov
ed that the G-equivariant Kasparov category of a locally compact group G c
arries the structure of a tensor-triangulated category. This structure con
veniently handles the usual homological algebra\, bootstrap constructions
and assembly maps involved in many KK-theoretical calculations\, e.g. in c
onnection with the Baum-Connes conjecture. As with any tensor triangulate
d category\, we can also associate to the G-equivariant Kasparov category
its spectrum in the sense of Paul Balmer. This is a topological space (sim
ilar to the Zariski spectrum of a commutative ring) which allows us\, as i
t were\, to re-inject some genuinely geometric ideas in non-commutative ge
ometry. It turns out that the spectrum contains enough information to prov
e the Baum-Connes conjecture for G\, hence we should expect the question o
f its computation to be very hard. In this talk\, after discussing such p
reliminaries and motivation\, I will present joint work with Ralf Meyer pr
oviding the state of the art on this subject. Although more general partia
l results are known\, a complete answer is only known so far for finite gr
oups 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:20221209T215924Z
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\n\n\nA
bstract\nThe Riesz transform is one of the most important and classical ex
amples of a Fourier multiplier on the real numbers. It may be described 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 conte
xt the Riesz transform may always be defined for any diffusion semigroup o
n the reals. In case the generator of this semi-group is the Laplace opera
tor the classical Riesz transform is retrieved. In quantum probability the
quantum Markov semi-groups play the role of the diffusion semi-groups and
again a suitable notion of Riesz transform can be described.\n\nWe show t
hat the Riesz transform may be used to prove rigidity properties of von Ne
umann algebras. We focus in particular on examples from compact quantum gr
oups. Using these tools we show that a class of quantum groups admits rigi
dity properties. The class has the following properties:\n\n(1) $\\text{SU
}_q(2)$ is contained in it.\n\n(2) The class is stable under monoidal equi
valence\, free products\, dual quantum subgroups and wreath products with
$S^+_N$.\n\nThe rigidity properties include the Akemann-Ostrand property a
nd strong solidity. Part of this talk is based on joint work with Mateusz
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:20221209T215924Z
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\n\n\nAbstract\
nThe classical Gelfand correspondence justifies the slogan that C*-algebr
as are to be thought of as "non-commutative Hausdorff spaces"\, and Rieff
el's theory of compact quantum metric spaces provides\, in the same vein\,
a non-commutative counterpart to the theory of compact metric spaces. The
aim of my talk is to introduce the basics of this theory\, and explain so
me new results on dynamical systems of compact quantum metric spaces. If
time permits\, I will also touch upon another recent result\, which show
s how quantized intervals approximate a classical interval in the quantum
version of the Gromov-Hausdorff distance. This is based on joint works wi
th 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:20221209T215924Z
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\n\n\nAbstract\nIn recent decades\, we have seen that quan
tum symmetries of quantum\nmathematical objects\, like non-commutative spa
ces and quantum field\ntheories\, are best described by quantum groups\, s
ubfactors\, and\nunitary tensor categories. Subfactor classification has l
ed to\ndiscovery of interesting "exotic" quantum symmetries and to importa
nt\nconstructions for unitary tensor categories. For example\, Q-systems\n
(special C* Frobnius algebra objects) were introduced by Longo to\ncharact
erize the canonical endomorphism for type III subfactors\, which\nis the a
nalog of Jones' basic construction for type $II_1$ and Kosaki's\nversion f
or type III. We will use this perspective to discuss some\nsubfactor resul
ts which go beyond small index classification\, making\nconnections to qua
ntum groups along the way. We'll then discuss a\nversion of a unitary high
er idempotent completion for C*/W*\n2-categories based on Gaiotto-Johnson-
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:20221209T215924Z
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\n\n\nAbstract\nI will discuss the question whether Hopf
algebras having monoidally equivalent category of comodules have the 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:20221209T215924Z
UID:QGS/9
DESCRIPTION:Title: Quan
tum Cuntz-Krieger algebras\nby Christian Voigt (University of Glasgow\
, UK) as part of Quantum Groups Seminar\n\n\nAbstract\nThe notion of a qua
ntum graph\, a concept going back to work of Erdos-Katavolos-Shulman and W
eaver\, provides a noncommutative generalisation of finite graphs. Quantum
graphs play an intriguing role in the analysis of quantum symmetries of g
raphs via monoidal equivalences\, and\nnaturally appear also in quantum in
formation theory.\n\nIn this talk\, I will discuss the construction of cer
tain C*-algebras associated with directed quantum graphs\, in analogy to t
he definition of Cuntz-Krieger algebras\, and illustrate this with some ex
amples. (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:20221209T215924Z
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\n\n\nAbstract\nCard s
huffles can be thought of as random walks on the symmetric group\, and the
study of these random walks has been a subject of interest to probabilist
s for more than forty years. Even for one of the simplest examples\, the r
andom transposition walk\, precise results concerning the convergence to e
quilibrium were only very recently obtained. After briefly describing that
setting\, I will report on a joint work with L. Teyssier and S. Wang wher
e we study an analogue of the random transposition walk on the quantum sym
metric group\, therefore a kind of "quantum card shuffle". In particular\,
we obtain a similar asymptotic description of the convergence to equilibr
ium\, called the "limit profile"\, involving the free Poisson distribution
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:20221209T215924Z
UID:QGS/11
DESCRIPTION:Title: Non
commutative Tensor Triangular Geometry\nby Daniel Nakano (University o
f Georgia\, USA) as part of Quantum Groups Seminar\n\n\nAbstract\nIn this
talk\, I will show how to develop a general noncommutative version of Balm
er's tensor triangular geometry that is applicable to arbitrary monoidal t
riangulated categories (M$\\Delta$C). Insights from noncommutative ring th
eory is used to obtain a framework for prime\, semiprime\, and completely
prime (thick) ideals of an M$\\Delta$C\, $\\mathbf K $\, and then to assoc
iate to $\\mathbf K$ a topological space --the Balmer spectrum $\\text{Spc
}{\\mathbf K}$.\n\nWe develop a general framework for (noncommutative) su
pport data\, coming in three different flavors\, and show that $\\text{Spc
}{\\mathbf K}$ is a universal terminal object for the first two notions (
support and weak support). The first two types of support data are then us
ed 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 t
hird type (quasi support) is used in another theorem that provides a metho
d for the explicit classification of the thick right ideals of $\\mathbf K
$\, which in turn can be applied to classify the thick two-sided ideals an
d $\\text{Spc }{\\mathbf K}$.\n\nIf time permits applications will be give
n for quantum groups and non-cocommutative finite-dimensional Hopf algebra
s studied by Benson and Witherspoon.\n\nThis is joint and ongoing work wit
h Milen Yakimov and Kent Vashaw\n
LOCATION:https://researchseminars.org/talk/QGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20210301T150000Z
DTEND;VALUE=DATE-TIME:20210301T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/12
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/12/
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:20221209T215924Z
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\
n\n\nAbstract\nIn his quest in constructing conformal field theories from
subfactors Vaughan Jones found an efficient machine to construct actions o
f groups like the Thompson groups. I will briefly explain the story of thi
s discovery. I will then present a general overview of those Jones actions
providing explicit examples. Some of the results presented come from join
t works with Vaughan Jones and with Valeriano Aiello and Roberto Conti.\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:20221209T215924Z
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\n\n\nAbstract\nIn the 2000s a s
eries of seminal papers by Heckenberger and Kolb introduced an essentially
unique covariant $q$-deformed de Rham complex for the irreducible quantum
flag manifolds. In the years since\, it has become increasingly clear tha
t these differential graded algebras have a central role to play in the no
ncommutative geometry of Drinfeld-Jimbo quantum groups. Until now\, howeve
r\, the question of how to extend Heckenberger and Kolb's construction bey
ond the irreducible case has not been examined. Here we address this quest
ion for the $A$-series Drinfeld-Jimbo quantum groups $U_q(\\frak{sl}_{n+1}
)$\, and show that for precisely two reduced decompositions of the longest
element of the Weyl group\, Lusztig's associated space of quantum root ve
ctors gives a quantum tangent space for the full quantum flag manifold $\\
mathcal{O}_q(F_{n+1})$ with associated differential graded algebra of clas
sical dimension. Moreover\, its restriction to the quantum Grassmannians r
ecovers the $q$-deformed complex of Heckenberger and Kolb\, giving a conce
ptual explanation for their origin. Time permitting\, we will discuss the
noncommutative Kähler geometry of thesespaces and the proposed extension
of the root space construction to the other series. (Joint work with P. So
mberg)\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:20221209T215924Z
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\n\n\nAbstract\nThe
Yang-Baxter equation (YBE) and the reflection equation (RE) are two funda
mental\nsymmetries in mathematics arising from particles moving along a li
ne or a half-line.\nThe quest for constant solutions of YBE (R-matrices) i
s at the very origin of the Drinfeld-Jimbo\nquantum groups and their unive
rsal R-matrix. Similarly\, constant solutions of RE (k-matrices)\nnaturall
y appear in the context of quantum symmetric pairs (QSP).\n\nIn joint work
with Bart Vlaar\, we construct a discrete family of universal k-matrices
associated to\nan arbitrary quantum symmetric Kac-Moody pair as operators
on category O integrable\nrepresentations. This generalises previous resul
ts by Balagovic-Kolb and Bao-Wang valid\nfor finite-type QSP. In this talk
\, I will explain how\, in affine type\, this construction gives rise to\n
parameter-dependent operators (spectral k-matrices) on finite-dimensional
representations of\nquantum loop algebras solving the same RE introduced b
y Cherednik and Sklyanin in the 1980s\nin the context of quantum integrabi
lity 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:20221209T215924Z
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\n\n\nAbstract\n(j
oint work with Suvrajit Bhattacharjee and Alex Chirvasitu) \n\nIn this tal
k\, I prove the existence of a universal (terminal) object in a number of
categories of Hopf algebras acting on a given subfactor $N \\subset M$ (fi
nite index\, type $\\text{II}_1$) such that $N$ is in the fixed point suba
lgebra of the action. These universal Hopf algebras can be interpreted as
a quantum group version of Galois group of the subfactor. We compute such
universal quantum groups for certain class of subfactors\, notably those c
oming 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:20221209T215924Z
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\n\n\nAbstract\nI will r
evisit and categorify concepts from the theory of fusion categories — in
cluding idempotent completeness and semi-simplicity\, ultimately leading t
o a notion of `fusion 2-category’. I will highlight structural similarit
ies and differences between fusion 1- and 2-categories and discuss several
concrete examples. If time permits\, I will discuss the role of fusion 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:20221209T215924Z
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\n\n\nAb
stract\nThe Toeplitz algebra attached to the unit disk is the universal C
∗-algebra generated by an\nisometry\, and is a non-commutative analogue
of the unit disk. Similarly\, one can attach algebras to non-commutative c
ounterparts of non-compact Hermitian symmetric spaces. I will discuss resu
lts to the effect that such quantum spaces cannot admit quantum group stru
ctures\, i.e. their attached non-commutative “function algebras” do no
t admit reasonable Hopf algebra structures.\n\n(joint w/ Jacek Krajczok an
d 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:20221209T215924Z
UID:QGS/19
DESCRIPTION:Title: Clu
ster realization of spherical DAHA\nby Alexander Schapiro (UC Berkeley
\, USA) as part of Quantum Groups Seminar\n\n\nAbstract\nSpherical subalge
bra of Cherednik's double affine Hecke algebra of type A admits a polynomi
al representation in which its generators act via elementary symmetric fun
ctions and Macdonald operators. Recognizing the elementary symmetric funct
ions as eigenfunctions of quantum Toda Hamiltonians\, and applying (the in
verse of) the Toda spectral transform\, one obtains a new representation o
f spherical DAHA. In this talk\, I will discuss how this new representatio
n gives rise to an injective homomorphism from the spherical DAHA into a q
uantum cluster algebra in such a way that the action of the modular group
on the former is realized via cluster transformations.\n\nThe talk is base
d on a joint work in progress with Philippe Di Francesco\, Rinat Kedem\, a
nd 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:20221209T215924Z
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\n\n\nA
bstract\nFusion categories are algebraic objects which generalize the repr
esentation 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 modul
e category structure on Hilb(X)\, the category of finite dimensional Hilbe
rt bundles over a compact Hausdorff space X. When X is connected\, we disc
uss obstructions to the existence of such actions and describe techniques
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:20221209T215924Z
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\n\n\nAbstract\nIn the late 90's\, Nevo and Zimmer wrote a seri
es of papers describing the general structure of stationnary actions of hi
gher rank semi-simple Lie groups G on probability spaces. With Cyril Houda
yer we extended this result in two ways: first we upgraded it to actions o
n non-commutative spaces (von Neumann algebras)\, and we also managed to s
tudy actions of lattices in G. I will explain this non-commutative ergodic
theorem and the main ingredients of proof\, and give striking consequence
s on the unitary representations of these lattices and their characters.\n
LOCATION:https://researchseminars.org/talk/QGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20210405T140000Z
DTEND;VALUE=DATE-TIME:20210405T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/22
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/22/
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:20221209T215924Z
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\n\n\nAbstract\nIn this
talk I will explain how quantum groups arise in quantum information theor
y via a class of graph based nonlocal games. Our point of departure will b
e an interactive protocol (nonlocal game) where two provers try to convinc
e a verifier that two graphs are isomorphic. Allowing provers to take adva
ntage of shared quantum mechanical resources will then allow us to define
quantum isomorphism of graphs as the ability of quantum players to win the
corresponding game with certainty. We will see that quantum isomorphism c
an be naturally reformulated in the language of quantum groups.\n
LOCATION:https://researchseminars.org/talk/QGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20210104T150000Z
DTEND;VALUE=DATE-TIME:20210104T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/24
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20210201T150000Z
DTEND;VALUE=DATE-TIME:20210201T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/25
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20210208T150000Z
DTEND;VALUE=DATE-TIME:20210208T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/26
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20210517T140000Z
DTEND;VALUE=DATE-TIME:20210517T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/27
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20201221T150000Z
DTEND;VALUE=DATE-TIME:20201221T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/28
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20201228T150000Z
DTEND;VALUE=DATE-TIME:20201228T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/29
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/29/
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:20221209T215924Z
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\n\n\nA
bstract\n(based on a joint work [2] with Joost Vercruysse)\n\nThe study of
partial symmetries (partial actions and coactions\, partial representatio
ns and corepresentations\, partial comodule algebras) is a relatively rece
nt field in continuous expansion and\, therein\, one of the relevant quest
ions is the existence and uniqueness of a so-called globalization (or enve
loping action). \nFor instance\, in the framework of partial actions of gr
oups any global action of a group $G$ on a set induces a partial action of
the group on any subset by restriction. The idea behind the concept of gl
obalization of a given partial action is to find a (universal) $G$-set suc
h that the initial partial action can be realized as the restriction of th
is global one.\n\nWe propose here a categorical approach to partial symmet
ries and the globalization question\, explaining several of the existing r
esults and\, at the same time\, providing a procedure to construct globali
zations in concrete contexts of interest. Our approach relies on the notio
n of geometric partial comodules\, recently introduced by Hu and Vercruyss
e [1] in order to describe partial actions of algebraic groups from a Hopf
-algebraic point of view.\n\nUnlike classical partial actions\, which exis
t only for (topological) groups and Hopf algebras\, geometric partial como
dules can be defined over any coalgebra in a monoidal category with pullba
cks and they allow to describe phenomena that are out of the reach of the
theory of partial (co)actions\, even in the Hopf algebra framework. At the
same time\, geometric partial comodules allow to approach in a unified wa
y partial actions of groups on sets\, partial coactions of Hopf algebras o
n algebras and partial (co)actions of Hopf algebras on vector spaces.\nThu
s\, the question of studying the existence (and uniqueness) of globalizati
on for geometric partial comodules naturally arises as a unifying way to a
ddress the issue.\n\nReferences:\n\n[1] J. Hu\, J.Vercruysse - Geometrical
ly partial actions. Trans. Amer. Math. Soc. 373 (2020)\, no. 6\, 4085-4143
.\n\n[2] P. Saracco\, J. Vercruysse - Globalization for geometric partial
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:20221209T215924Z
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\n\n\nAbstract\nSkew braces have recently attracted attention as a method
to study set-theoretical solutions of the Yang-Baxter equation. In this t
alk\, we will present a new approach for studying these solutions\, by loo
king at Hopf algebras in the category of complete lattices and join-preser
ving morphisms\, denoted by SupLat. Any Hopf algebra\, H in SupLat\, has a
corresponding group\, R(H)\, which we call its remnant and a co-quasitria
ngular structure on H induces a brading operator on R(H)\, which induces a
skew brace structure on R(H). From this correspondence\, we will recover
several aspects of the theory of skew braces. In particular\, we will cons
truct the universal skew brace of a set-theoretical YBE solution\, as 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:20221209T215924Z
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\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\, we disc
uss a complete list of inequivalent irreducible representations of $U_q(2)
$ and its Peter-Weyl decomposition. Then\, for $\\theta\\notin\\mathbb{Q}\
\setminus\\{0\,1\\}$\, we discuss the $K$-theory of the underlying $C^*$-a
lgebra $C(U_q(2))$\, and a spectral triple which is equivariant under its
own comultiplication action. The spectral triple obtained here is even\, $
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 associated Fre
dholm 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:20221209T215924Z
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\n\n\n
Abstract\nWe consider quantum subgroups of Wang’s free orthogonal quantu
m 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 are sel
fadjoint which is dropped in the latter case. We compare these two cases a
long the lines of so called "easy" quantum groups and we observe that the
step from the orthogonal to the unitary case is huge. This is a survey tal
k on the landscape of "easy" quantum groups with a particular emphasis 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:20221209T215924Z
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
\n\n\nAbstract\nLet X be a locally compact\, Hausdorff space. The represen
table localization algebra for X was introduced and studied by Willett and
Yu. The K-theory of the algebra serves as the representable K-homology of
the space X.\n\nNow let G be a second countable\, locally compact group a
nd suppose that X is a proper G-space. It turns out that the K-theory of t
he crossed product by G of the representable localization algebra for X se
rves as the representable G-equivariant K-homology of the proper G-space X
.\n\nThe goal of this talk is to describe these facts and roles of the rep
resentable localization algebras in the study of the Baum--Connes conjectu
re.\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:20221209T215924Z
UID:QGS/35
DESCRIPTION:Title: A c
ovariant Stinespring theorem\nby Dominic Verdon (University of Bristol
\, UK) as part of Quantum Groups Seminar\n\n\nAbstract\nWe will introduce
a finite-dimensional covariant Stinespring theorem for compact quantum gro
ups. Let G be a compact quantum group\, and let T:= Rep(G) be the rigid C*
-tensor category of finite-dimensional continuous unitary representations
of G. Let Mod(T) be the rigid C*-2-category of cofinite semisimple finitel
y decomposable T-module categories. We show that finite-dimensional G-C*-a
lgebras (a.k.a C*-dynamical systems) can be identified with equivalence cl
asses 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 correspond
ing G-C*-algebras can be 'dilated' to isometries t: X -> Y \\otimes E\, wh
ere E: M2 -> M1 is some 'environment' 1-morphism. Dilations are unique up
to partial isometry on the environment\; in particular\, the dilation mini
mising the quantum dimension of the environment is unique up to a unitary.
When G is a compact group this implies and generalises previous covariant
Stinespring-type theorems.\n\nWe will also discuss some results relating
to rigid C*-2-categories\, including that any connected semisimple rigid C
*-2-category is equivalent to Mod(T) for some rigid C*-tensor category T.
(Here semisimple means not just semisimplicity of Hom-categories but also
idempotent splitting for 1-morphisms\, direct sums for objects\, etc.)\n\n
This 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:20221209T215924Z
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\n\n\nAbstract\nI w
ill motivate and explain the notion of a Gaussian state on a compact quant
um group G\, as introduced by Michael Schürmann. This concept leads to th
e idea of the Gaussian part of G\, understood as the smallest quantum subg
roup of G which supports all the Gaussian states of G. I will discuss prop
erties of Gaussian states and compute Gaussian parts for several examples.
This turns out to be related to quantum connectedness and certain topolog
ical generation questions for quantum subgroups. The talk will be based 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:20221209T215924Z
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\n\n\nAb
stract\nA famous theorem of Hulanicki says that a locally compact group is
amenable if and only if its full and reduced C*-algebras coincide. For gr
oupoids\, the situation is more delicate: While amenability implies equati
lity of the full and reduced C*-algebra\, the converse fails according to
examples by Willett. The behavior of Willett's groupoids can be explained
by their non-exactness. We show that if an étale groupoid satisfies a cer
tain exactness condition\, then equality of its full and reduced C*-algebr
a is equivalent to amenability of the groupoid.\n
LOCATION:https://researchseminars.org/talk/QGS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20211018T140000Z
DTEND;VALUE=DATE-TIME:20211018T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/38
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/38/
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:20221209T215924Z
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\n\n\nAbstract\nIn
this talk\, I will introduce the notion of a diagram algebra and explain t
heir connection to the representation theory of compact quantum groups. I
will also describe the role that they play for loop models in statistical
physics as well as the correspondence between their traces and random walk
s 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:20221209T215924Z
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\n\n\nAbstract\nT
he character variety of a manifold is its moduli space of flat G-bundles.
These moduli spaces and their quantizations appear in a number of places i
n mathematics\, representation theory\, and quantum field theory. Famously
\, Fock and Goncharov showed that a certain "decorated" variant of charact
er varieties carries the structure of a cluster variety -- that is\, the m
oduli space contains a distinguished set of toric charts\, with combinator
ially defined transitions functions (called mutations). This led them to a
now-famous quantization of their decorated character varieties.\n\nIn thi
s talk I'll explain that the by-hands construction of these charts by Fock
and Goncharov can in fact be extracted from a more general framework call
ed stratified factorization homology\, and I'll outline how this allows 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:20221209T215924Z
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\n\n\nAbstract\nNon-stable K-theory is the study of the homotopy
groups of the group of (quasi-) unitaries of a $C^{*}$-algebra. We will g
ive an overview of the theory\, and discuss a special class of $C^{*}$-alg
ebras\, termed as K-stable $C^{*}$-algebras along with its rational analog
ue. We shall give a permanence property related to K-stability (rational K
-stability) concerning continuous $C(X)$-algebras. We will end with an app
lication of the aforementioned result to crossed product $C^{*}$-algebras.
\n
LOCATION:https://researchseminars.org/talk/QGS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20211115T150000Z
DTEND;VALUE=DATE-TIME:20211115T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/42
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/42/
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:20221209T215924Z
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\n\n\nAbstr
act\nStrong $1$-boundedness is a property for a tracial von Neumann algebr
a $M$ that was introduced by Jung that allows one to distinguish $M$ from
the (interpolated) free group factors. Many examples came from group von N
eumann algebras\, such as those from certain groups having property (T). F
or quantum group von Neumann algebras\, Brannan and Vergnioux showed in a
landmark paper that those coming from the orthogonal free quantum groups a
re strongly $1$-bounded\, despite sharing many structural properties with
the free group factors. We first review these developments\, and then repo
rt on recent progress concerning permanence of strong $1$-boundedness unde
r finite index subfactors and applications to quantum automorphism groups
such as the quantum permutation group $S_{N^2}^+$. This last part is based
on ongoing joint work with Brannan\, Harris\, and Yamashita.\n\nNote 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:20221209T215924Z
UID:QGS/44
DESCRIPTION:Title: Dyn
amical quantum graphical calculus\nby Hadewijch De Clercq (Ghent Unive
rsity\, Belgium) as part of Quantum Groups Seminar\n\n\nAbstract\nGraphica
l calculus provides a diagrammatic framework for performing topological co
mputations with morphisms in strict tensor categories. The key idea is to
identify such morphisms with oriented diagrams labeled by their in- and ou
tput objects. This was formalized by Reshetikhin and Turaev\, by construct
ing for every strict tensor category $C$ a strict tensor functor that assi
gns isotopy classes of $C$-colored ribbon graphs to morphisms in $C$. This
can be applied to the tensor category of finite-dimensional representatio
ns of a quantum group $U_q(g)$.\n\nIn this talk\, I will first outline the
fundamentals of this finite-dimensional quantum graphical calculus. Then
I will explain how it can be extended to a larger category of quantum grou
p representations\, encompassing the quantum group analog of the BGG categ
ory $O$. In particular\, this extended framework allows to visualize $U_q(
g)$-intertwiners on Verma modules\, as well as morphisms depending on a dy
namical parameter\, such as dynamical R-matrices. Finally\, I will describ
e how this dynamical quantum graphical calculus can be used to obtain q-di
fference equations for quantum spherical functions.\n\nThis talk is based
on joint work with Nicolai Reshetikhin (UC Berkeley) and Jasper Stokman (U
niversity of Amsterdam)\n
LOCATION:https://researchseminars.org/talk/QGS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20211206T150000Z
DTEND;VALUE=DATE-TIME:20211206T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/45
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/45/
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:20221209T215924Z
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\n\n\nAbstra
ct\nThe algebra of the quantum symplectic $(4n-1)$-sphere $\\mathcal{O}(S_
q^{4n-1})$ is defined as a subalgebra of the quantum symplectic group by F
addeev\, Reshetikhin and Takhtajan. Recently D'Andrea and Landi investigat
ed faithfull irreducible $*$-representations of $\\mathcal{O}(S_q^{4n-1})$
. They proved that the first $n-1$ generators of its enveloping $C^*$-alge
bra $C(S_q^{4n-1})$ are all zero. The result is a generalisation of the ca
se 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 graph $C^
*$-algebra\, from which it follows that $C(S_q^{4n-1})$ is isomorphic to t
he quantum $(2n+1)$-sphere by Vaksman and Soibelman. Then\, I present a ca
ndidate of a vector space basis for $\\mathcal{O}(S_q^{4n-1})$ which is co
nstructed by a nontrivial application of the Diamond lemma. The conjecture
is supported by computer experiments for $n=1\,...\,8$. By finding a vec
tor space basis we can moreover conclude that the $n-1$ generators are 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 Mc Carthy (Munster Technological University\, Ireland)
DTSTART;VALUE=DATE-TIME:20220124T150000Z
DTEND;VALUE=DATE-TIME:20220124T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/47
DESCRIPTION:Title: The
Frucht property in the quantum group setting\nby Jeremiah Mc Carthy (
Munster Technological University\, Ireland) as part of Quantum Groups Semi
nar\n\n\nAbstract\nA classical theorem of Frucht states that every finite
group is the automorphism group of a finite graph. Is every quantum permut
ation group the quantum automorphism group of a finite graph? In this talk
we will answer this question with the help of orbits and orbitals. This t
alk 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:20221209T215924Z
UID:QGS/48
DESCRIPTION:Title: A m
etric characterization of freeness\nby Benoît Collins (Kyoto Universi
ty\, Japan) as part of Quantum Groups Seminar\n\n\nAbstract\nFreeness of r
andom variables has many characterizations\, with free cumulants\, free en
tropy\, Schwinger-Dyson equations\, etc. Here\, we discuss a new metric ch
aracterization with the norm of the sum of generators tensored by their ad
joint\, and explain the relation and applications to other problems in ope
rator algebras and von Neumann algebras. Time permitting\, we will also di
scuss some ingredients of the proof. This is based on joint work with Leon
ard 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:20221209T215924Z
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\n\n\nAbstract\nThis talk concerns quantum automorphism groups of
graphs\, a generalization of automorphism groups of graphs in the framewo
rk of compact matrix quantum groups. We will focus on certain colored grap
hs constructed from linear constraint systems. In particular\, we will giv
e an explicit connection of the solution group of the linear constraint sy
stem and the quantum automorphism group of the corresponding colored graph
. Using this connection and a decoloring procedure\, we will present an ex
ample of a graph with quantum symmetry and finite quantum automorphism gro
up. 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:20221209T215924Z
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\n\n\nAbstract\nHörmander proved that the Fourier mult
iplier is Lp-Lq bounded if the symbol lies in the weak Lr space\, for cert
ain p\,q\,r. In recent years\, this result was generalized to more general
groups and quantum groups. Here we presented an extension to certain loca
lly compact quantum groups. It covers the known results and the proof is s
impler. It also yields a family of Lp-Fourier multipliers over compact qua
ntum 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:20221209T215924Z
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\n\n\nAbs
tract\nIn this talk\, I will present a new combinatorial approach to the s
tudy of ergodic actions of compact quantum groups. The connection between
compact quantum groups and the combinatorics of partitions goes back to Ba
nica's founding work on the representation theory of free orthogonal quant
um groups\, and was later formalized in the seminal paper of Banica and Sp
eicher under the theory of "easy quantum groups". Based on some new altern
ative version of the Tannaka-Krein reconstruction procedure for ergodic ac
tions\, we extend Banica and Speicher's combinatorial approach to the sett
ing of ergodic actions of compact quantum groups. Our examples in particul
ar recovers actions on finite spaces\, on embedded homogeneous spaces and
on quotient spaces. Moreover\, we use this categorical point of view to st
udy the quantum rigidity of ergodic actions on classical spaces\, and show
that the free quantum groups cannot act ergodically on a classical connec
ted compact space\, thereby answering a question of D. Goswami and H. Huan
g.\n\nThe talk is based on the recent preprint arXiv:2112.07506 jointly wi
th 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:20221209T215924Z
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\n\n\nAbstract\nThe quant
ization problem is the problem of associating non-commutative quantum alge
bras to a classical Poisson algebra in such a way that the commutator is r
elated to the Poisson bracket. In a formal setting\, this problem and its
equivariant counterpart are well-understood and can always be solved (unde
r a mild assumption in the equivariant case). However\, in a C*-algebraic
setting\, there exist obstructions to equivariant quantization\, for examp
le for the 2-sphere. In this talk\, we will give a brief introduction to t
he quantization problem\, and propose a way to obtain an equivariant quant
ization of the 2-sphere in a Fréchet algebraic setting.\n
LOCATION:https://researchseminars.org/talk/QGS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20220314T150000Z
DTEND;VALUE=DATE-TIME:20220314T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/53
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20220321T150000Z
DTEND;VALUE=DATE-TIME:20220321T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/54
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/54/
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:20221209T215924Z
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\
n\n\nAbstract\nA braided compact quantum group (over T) is\, roughly speak
ing\, a “compact quantum group” object in the category of T-C*-algebra
s equipped with a twisted monoidal structure. In this talk\, we shall expl
ain the existence of a universal braided compact quantum group acting on a
graph C*-algebra in the category mentioned above. Time permitting\, we sh
all sketch the proof\, constructing along the way a braided analogue of th
e free unitary quantum group. Finally\, as an example\, we shall compute t
his 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:20221209T215924Z
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\n\n\nAbstract\nWe give a su
rvey of some results on crossed products by discrete group actions and dis
cuss their basic properties. Further\, we restrict our attention to finite
group actions with the Rokhlin property\, approximate representability\,
and their weakened versions. Time permitting\, we outline some structure
results for the crossed products by these classes of group actions and th
eir 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:20221209T215924Z
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\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 constru
ct universal deformation formulae\nfor actions on topological algebras (C*
or Fréchet) of the Lie groups which carries a negatively curved left-inv
ariant Kähler structure.\n\n(2) A second one\, joint with V.Gayral\, S. N
eshveyev and L. Tuset\, where we construct locally compact quantum groups
from star products on a class of Lie groups.\n\nThe Lie groups on which th
ese deformations are performed (in both (1) and (2)) are of ``Frobenius ty
pe''. This means that their Lie algebras carry an exact non-degenerate two
-cocycle or\, equivalently\, that they admit an open co-adjoint orbit. In
both cases\, the star products\, say at the formal level\, are of Fedosov
type i.e. associated with a left-invariant symplectic torsion free affine
connection on the group manifold at hand. In particular\, they are obtaine
d from differential theoretical considerations.\n\nHowever\, there is a di
chotomy: 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 effec
t on the regularity of the categories those constructions live in: smooth
versus measurable or topological.\nMore precisely:\nIn (1)\, we definitely
deal with a ``smooth object''\, e.g. the universal deformation formula (i
.e. the twist) allows to deform smooth vectors of the group action\, e.g.
they are relevant in differential noncommutative geometry in the sense of
A. Connes. But\, no locally compact quantum group is present there. And un
til now\, I haven't be able to define a reasonable notion of ``smooth quan
tum group'' attached to the construction.\nIn (2)\, the quantum group is p
resent\, but the deformation procedure apparently breaks smoothness: smoot
h vectors of strongly continuous actions (i.e. smooth module-algebras) of
the group are not stable under twisting.\n\nIn the talk\, I will discuss
differential geometrical aspects of Frobenius Lie groups within this defor
mation quantization context. I will end with a suggestion based on the pos
sible use of a Lie group theoretical version of a\nmicrolocal analytical t
ool : Hörmander's smooth wave front set.\n
LOCATION:https://researchseminars.org/talk/QGS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20220228T150000Z
DTEND;VALUE=DATE-TIME:20220228T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/58
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/58/
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:20221209T215924Z
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\n\n
\nAbstract\nMany examples of quantum group actions carry a Yetter-Drinfeld
structure. Among them\, you find C*-algebras coming from the boundary the
ory of Drinfeld doubles\, which is closely related to the theory of ucp ma
ps and injective envelopes of Hamana. Exploring Tannaka-Krein duality for
quantum group actions\, it is possible to extend many concepts and results
of boundary theory to the categorical setting\, but the lack of a categor
ification of non-braided-commutative Yetter-Drinfeld algebras impose an ob
struction to a full analogy.\n\nIn this talk\, I will sketch how to perfor
m such a categorification and relate it to the study of injectivity for mo
dule categories. Based on joint works with E. Habbestad\, S. Neshveyev 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:20221209T215924Z
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\n\n\
nAbstract\nPairs in involution are an algebraic structure whose systematic
study\nis motivated by their applications in knot theory\, representation
theory and\ncyclic homology theories.\n\nIn this talk\, we will explore a
categorical view for these objects from the\nperspective of representatio
n theory of monoidal categories.\nA focus will lie on illustrating how the
ir existence is linked to a particular\nwell-behaved notion of duality cal
led pivotality.\nIn particular\, we will show how the language of monads a
llows us to combine\nthe algebraic with the categorical perspective of the
se 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:20221209T215924Z
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\n\n\nAbstract\nIn this talk\, we will define partial algebraic quantum
groups\, which are special cases of weak multiplier Hopf algebras\, as in
troduced by Van Daele and Wang. At the same time\, they provide a generali
zation to the notion of a partial compact quantum group\, as introduced by
De Commer and Timmermann. The main aim of the talk will be to realize the
Drinfeld double of a partial compact quantum group as a partial algebraic
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:20221209T215924Z
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\n\n\nAbstract\nIn recent joint work with Skalski and Voigt we
construct and study the Hecke algebra and Hecke operators associated with
an almost normal subgroup in a discrete quantum group. We also give in th
is framework a quantum version of the Schlichting completion\, which yield
s an algebraic quantum group with a compact-open subgroup. We describe a c
lass 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:20221209T215924Z
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\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 or a C*
2-category. By the work of Müger\, Q-systems give an axiomatization of t
he standard invariant of a finite index subfactor.\n\nFollowing work of Do
uglass-Reutter\, a Q-system is also a unitary version of a higher idempote
nt. In this talk\, we will describe a higher unitary idempotent completion
for C* 2-categories called Q-system completion.\n\nOur main goal is to sh
ow that C*Alg\, the C* 2-category of right correspondences of unital C*-al
gebras is Q-system complete. To do so\, we will use the graphical calculus
for C* 2-categories\, and adapt a subfactor reconstruction technique call
ed realization\, which is inverse to Q-system completion. This result allo
ws for the straightforward adaptation of subfactor results to C*-algebras\
, characterizing finite index extensions of unital C*-algebras equipped wi
th a faithful conditional expectation in terms of the Q-systems in C*Alg.
If time allows\, we will discuss an application to induce new symmetries o
f C*-algebras from old via Q-system completion.\n\nThis is joint work 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:20221209T215924Z
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\n\n\nAbstract\nWe de
velop filtered-graded techniques for algebras in monoidal\ncategories with
the goal of establishing a categorical version of Bongale's\n1967 result:
A filtered deformation of a Frobenius algebra over a field is\nFrobenius
as well. Towards the goal\, we construct a monoidal associated\ngraded fun
ctor\, building on prior works of Ardizzoni-Menini\, of Galatius et\nal.\,
and of Gwillian-Pavlov. We then produce equivalent conditions for an\nalg
ebra in a rigid monoidal category to be Frobenius in terms of the\nexisten
ce of categorical Frobenius form. These two results of independent\nintere
st are used to achieve our goal. As an application of our main\nresult\, w
e show that any exact module category over a symmetric finite\ntensor cate
gory is represented by a Frobenius algebra in it. This is joint\nwork 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:20221209T215924Z
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\n\n\nAbstract\nAmenability is a deeply studied property of
groups\, with many interesting reformulations and connections to the oper
ator algebraic aspects of groups. For example\, the reduced $C^*$-algebra
$C^*_r(G)$ of a discrete group has a unique tracial state if and only if t
here are no non-trivial amenable normal subgroups. This\, among other rela
ted results\, makes it apparent that the structure of the amenable subgrou
ps of $G$ contains important information about $C^*_r(G)$. For a quantum g
roup $\\mathbb{G}$\, an appropriate analogue of a subgroup is a coideal $N
\\subseteq L^\\infty(\\mathbb{G})$. We will present notions of relative am
enability\, amenability\, and coamenability for coideals of discrete and c
ompact quantum groups motivated by "relativizations" of amenability and co
amenability of a subgroup of a group. We will discuss the known relationsh
ips between these formally distinct notions and their relevance to certain
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:20221209T215924Z
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\n\n\nAbstract\nIf $G$ is a locally compact group\, w
e have the full group C*-algebra $C^*(G)$ and the reduced $C^*_r(G)$. We c
all a C*-algebra properly between $C^*(G)$ and $C^*_r(G)$ exotic.\n\nSimil
arly\, if $G$ acts on a C*-algebra $A$ we can form the full crossed produc
t $C^*(G\\ltimes A)$ and the reduced crossed product $C^*_r(G\\ltimes A)$.
An exotic crossed product is a C*-algebra properly between the two. Work
by Baum\, Guentner\, and Willett show that these algebras are relevant to
the Baum-Connes conjecture.\n\nWe think that the best way to study these a
lgebras is by also looking at the corresponding dual theory of coactions.
I will discuss some of these aspects\, but there will be more questions th
an answers.\n\nThis is joint work with Steve Kaliszewski and John Quigg.\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:20221209T215924Z
UID:QGS/67
DESCRIPTION:Title: Alg
ebraic quantum hypergroups and duality\nby Alfons Van Daele (KU Leuven
\, Belgium) as part of Quantum Groups Seminar\n\n\nAbstract\nLet $G$ be a
finite group and $H$ a subgroup. The set $\\mathcal{G}$ of double cosets $
HpH$\, with $p \\in G$ has the structure of an hypergroup. The product of
two elements $HpH$ and $HqH$ is the set of cosets $HrH$ where $r \\in pHq$
. The algebra $A$ of functions on $\\mathcal{G}$ is the space of functions
on $G$ that are constant on double cosets. It carries a natural coproduct
\, 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 dual al
gebra is known as the Hecke algebra associated with the pair $G\,H$.\nIn t
his talk I will discuss the notion of an algebraic quantum hypergroup\, it
s fundamental properties and duality for algebraic quantum hypergroups.\nI
will illustrate this with an example\, coming from bicrossproduct theory\
, 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 general
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:20221209T215924Z
UID:QGS/70
DESCRIPTION:Title: C*-
algebras associated to Temperley-Lieb polynomials\nby Erik Habbestad (
Universityof Oslo\, Norway) as part of Quantum Groups Seminar\n\n\nAbstrac
t\nWe define Temperley-Lieb polynomials and consider the (standard) subpro
duct systems they generate. This subproduct system turns out to be equivar
iant with respect to a compact quantum group G monoidally equivalent to $U
_q(2)$. Exploiting this we are able to describe the C*-algebras associated
to the subproduct system\, which turn out to be closesly related to the l
inking algebra $B(U_q(2)\,G)$. This is joint work with Sergey Neshveyev.\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:20221209T215924Z
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\n\n\nAbstract\nGiven a locally compact group G\, Leptin
's theorem states that G is amenable if and only if the Fourier algebra A(
G) admits a bounded approximate identity\, where the latter property is kn
own as co-amenability of the quantum dual of G. In the quantum setting\, t
his characterization is known as the duality between amenability and co-am
enability. It is proved that a discrete quantum group is amenable if and o
nly if its dual compact quantum group is co-amenable. The definition of co
-amenability for quantum homogeneous spaces is given by Kalantar-Kasprzak-
Skalski-Vergnioux. Furthermore\, they ask whether the co-amenability of a
quantum homogeneous space is equivalent to the (relative) amenability of i
ts co-dual. In this talk\, we will answer this question for quantum homoge
neous 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:No talk
DTSTART;VALUE=DATE-TIME:20221101T150000Z
DTEND;VALUE=DATE-TIME:20221101T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/73
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20221206T150000Z
DTEND;VALUE=DATE-TIME:20221206T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/74
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefaan Vaes (KU Leuven\, Belgium)
DTSTART;VALUE=DATE-TIME:20221122T160000Z
DTEND;VALUE=DATE-TIME:20221122T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
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\n\n\nAbstract\nI present a joint work
with Lukas Rollier. We construct the quantum automorphism group of any con
nected locally finite\, possibly infinite\, graph as a locally compact qua
ntum group that has the classical (locally compact) automorphism group as
a closed quantum subgroup. For finite graphs\, we get the quantum automorp
hism group of Banica and Bichon. One of the key tools is the construction
of a unitary tensor category associated with any connected locally finite
graph. When this graph is the Cayley graph of a finitely generated group\,
the associated unitary tensor category has a canonical fiber functor. We
thus also obtain a quantization procedure for arbitrary finitely generated
groups. In the particular example of groups defined by a triangle present
ation\, this construction gives the property (T) discrete quantum groups f
rom earlier joint work with Valvekens.\n
LOCATION:https://researchseminars.org/talk/QGS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20221025T140000Z
DTEND;VALUE=DATE-TIME:20221025T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T215924Z
UID:QGS/76
DESCRIPTION:Title: ---
---\nby No talk as part of Quantum Groups Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/QGS/76/
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:20221209T215924Z
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\n\n\nAbstract\nWe compare actions on C*-algebras of two construction
s of locally compact quantum groups\, the bicrossed product due to Vaes-Va
inerman and the double crossed product due to Baaj-Vaes. We give a one-to-
one correspondence between them up to Morita equivalence\, in the same spi
rit as Takesaki-Takai and Baaj-Skandalis dualities. This includes a dualit
y between a quantum double and the product of the original quantum group w
ith its opposite. We will explain its consequences for equivariant Kasparo
v theory in relation to the quantum analog of the Baum-Connes conjecture.\
n
LOCATION:https://researchseminars.org/talk/QGS/77/
END:VEVENT
END:VCALENDAR