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BEGIN:VEVENT
SUMMARY:Shahn Majid (Queen Mary University)
DTSTART;VALUE=DATE-TIME:20221010T140000Z
DTEND;VALUE=DATE-TIME:20221010T150000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/1
DESCRIPTION:Title: Qu
antum Riemannian Geometry of the A_n graph\nby Shahn Majid (Queen Mary
University) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbs
tract\nWe solve for quantum Riemannian geometries on the finite lattice in
terval • − • − · · · − • with $n$ nodes (the Dynkin graph o
f type $A_n$) and find that they are necessarily $q$-deformed with $q$ a r
oot of unity. This comes out of the intrinsic geometry and not by assuming
any quantum group in the picture. Specifically\, we discover a novel ‘b
oundary effect’ whereby\, in order to admit a quantum-Levi Civita connec
tion\, the ‘metric weight’ at any edge is forced to be greater pointin
g towards the bulk compared to towards the boundary\, with ratio given by
$(i + 1_)q/(i)_q$ at node $i$\, where $(i)_q$ is a $q$-integer. The Christ
offel symbols are also $q$-deformed. The limit $q \\to 1$ is the quantum R
iemannian geometry of the natural numbers $N$ with rational metric multipl
es $(i + 1)/i$ in the direction of increasing $i$. In both cases there is
a unique metric up to normalisation with zero Ricci scalar curvature. Elem
ents of QFT and quantum gravity are exhibited for $n = 3$ and for the cont
inuum limit of the geometry of $N$. The Laplacian for the scaler-flat metr
ic becomes the Airy equation operator $(1/ x) d^2/ dx^2$ in so far as a li
mit exists. The talk is based on joint work with J. Argota-Quiroz availabl
e on arXiv: 2204.12212 (math.QA).\n
LOCATION:https://researchseminars.org/talk/EQuAL/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorant Szegedy (University of Vienna)
DTSTART;VALUE=DATE-TIME:20221024T140000Z
DTEND;VALUE=DATE-TIME:20221024T150000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/2
DESCRIPTION:Title: Pa
rity and Spin conformal field theory with boundaries and defects\nby L
orant Szegedy (University of Vienna) as part of European Quantum Algebra L
ectures (EQuAL)\n\n\nAbstract\nRational conformal field theory (CFT) on or
iented surfaces is well understood in terms of 3-dimensional topological f
ield theory (TFT). We extend these notions to surfaces with spin structure
s using defects in oriented CFT and a modified TFT taking values in super
vector spaces.\n
LOCATION:https://researchseminars.org/talk/EQuAL/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Meusburger (University of Erlangen-Nuremberg)
DTSTART;VALUE=DATE-TIME:20221107T150000Z
DTEND;VALUE=DATE-TIME:20221107T160000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/3
DESCRIPTION:Title: Tu
raev-Viro-Barrett-Westbury invariants with defects\nby Catherine Meusb
urger (University of Erlangen-Nuremberg) as part of European Quantum Algeb
ra Lectures (EQuAL)\n\n\nAbstract\nTuraev-Viro-Barrett-Westbury state sum
models are concrete constructions\nof TQFTs based on triangulated 3-manifo
lds and spherical fusion\ncategories. Introducing defects in these models
is of interest for\ndefect TQFTs and for applications in condensed matter
physics.\n\nIn the talk we explain how to construct Turaev-Viro-Barrett-We
stbury\nstate sums with defects in terms of generalised 6j symbols. Defect
\nsurfaces are labeled with bimodule categories over spherical fusion\ncat
egories\, defect lines and points form graphs on these surfaces and\nare l
abeled with bimodule functors and bimodule natural transformations.\nWe sh
ow that the resulting state sums are triangulation independent\,\ncompute
examples and interpret them.\n\nBased on https://arxiv.org/abs/2205.06874\
n
LOCATION:https://researchseminars.org/talk/EQuAL/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Woike (University of Burgundy)
DTSTART;VALUE=DATE-TIME:20221121T150000Z
DTEND;VALUE=DATE-TIME:20221121T160000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/4
DESCRIPTION:Title: Qu
antum representations of mapping class groups and factorization homology\nby Lukas Woike (University of Burgundy) as part of European Quantum Al
gebra Lectures (EQuAL)\n\n\nAbstract\nQuantum representations of mapping c
lass groups are finite-dimensional representations of mapping class groups
that have their origin in quantum algebra (e.g. the representation theory
of Hopf algebras) and that often has strong ties to three-dimensional top
ological field theory. After explaining the interest in these representati
ons from the perspectives of algebra\, topology and mathematical physics a
nd how they can be formally described through modular functors\, I will gi
ve an idea of the classical construction procedures. I will then present a
new and more general construction procedure using cyclic and modular oper
ads\, as well as factorization homology. The main result of this approach
is a classification of modular functors. This is based on different joint
works with Lukas Müller and Adrien Brochier.\n
LOCATION:https://researchseminars.org/talk/EQuAL/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Müller (Max Planck Institute for Mathematics\, Bonn)
DTSTART;VALUE=DATE-TIME:20221205T150000Z
DTEND;VALUE=DATE-TIME:20221205T160000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/5
DESCRIPTION:Title: Re
flection Structures and Spin Statistics in Low Dimensions\nby Lukas M
üller (Max Planck Institute for Mathematics\, Bonn) as part of European Q
uantum Algebra Lectures (EQuAL)\n\n\nAbstract\nIn physics the spin of a pa
rticle determines its statistics.\n\nFurthermore\, physical systems (in Eu
clidean signature) usually have a reflection structure\, i.e. an identific
ation of orientation reversal with complex conjugation. Neither of these t
wo structures is part of Atiyah's original definition of topological quant
um field theories.\n\nThey can be formulated in the setting of functorial
field theories as equivariant symmetric monoidal functors from a bordism c
ategory to an appropriate target. Based on the cobordism hypothesis I will
present a complete classification of such functors in dimension one and t
wo. The answers can be formulated in terms of algebraic objects associated
to an internal fermionic symmetry (2-)group. The talk is based on joint w
ork in progress with Luuk Stehouwer.\n
LOCATION:https://researchseminars.org/talk/EQuAL/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vanessa Miemietz (University of East Anglia)
DTSTART;VALUE=DATE-TIME:20221219T150000Z
DTEND;VALUE=DATE-TIME:20221219T160000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/6
DESCRIPTION:Title: Sy
mmetric bimodules and Hopf algebras\nby Vanessa Miemietz (University o
f East Anglia) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nA
bstract\nI will explain the basics of finitary 2-representation theory and
explain a reduction theorem that motivates the study of certain types of
2-categories. I will then explain two examples of such\, associated to Hop
f algebras and symmetric bimodules\, and explain the connection between th
e two.\n
LOCATION:https://researchseminars.org/talk/EQuAL/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Tabiri (African Institute for Mathematical Sciences\, Ghana
)
DTSTART;VALUE=DATE-TIME:20230213T150000Z
DTEND;VALUE=DATE-TIME:20230213T160000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/7
DESCRIPTION:Title: Pl
ane Curves which are Quantum Homogeneous Spaces\nby Angela Tabiri (Afr
ican Institute for Mathematical Sciences\, Ghana) as part of European Quan
tum Algebra Lectures (EQuAL)\n\n\nAbstract\nPlane Curves which are Quantum
Homogeneous Spaces Abstract: In this talk\, we will discuss the construct
ion of examples of quantum homogeneous spaces using the equation of a plan
e curve. The Hopf algebras we construct are isomorphic to the quantum plan
e and down-up algebras when the degree of the equation is two or three res
pectively. Interesting properties and open problems about these Hopf algeb
ras will be discussed\n
LOCATION:https://researchseminars.org/talk/EQuAL/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Kontrec (RIMS\, Kyoto University)
DTSTART;VALUE=DATE-TIME:20230227T150000Z
DTEND;VALUE=DATE-TIME:20230227T160000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/8
DESCRIPTION:Title: Re
presentation theory and duality properties of some affine W-algebras\n
by Ana Kontrec (RIMS\, Kyoto University) as part of European Quantum Algeb
ra Lectures (EQuAL)\n\n\nAbstract\nOne of the most important families of v
ertex algebras are affine vertex algebras and their associated $\\mathcal{
W}$-algebras\, which are connected to various aspects of geometry and phys
ics. Among the simplest examples of $\\mathcal{W}$-algebras is the Bershad
sky-Polyakov vertex algebra $\\mathcal{W}^k(\\mathfrak{g}\, f_{min})$\, as
sociated to $\\mathfrak{g} = sl(3)$ and the minimal nilpotent element $f_
{min}$.\nIn this talk we are particularly interested in the Bershadsky-Pol
yakov algebra $\\mathcal W_k$ at positive integer levels\, for which we o
btain a complete classification of irreducible modules.\nIn the case $k=1
$\, we show that this vertex algebra has a Kazama-Suzuki-type dual isomorp
hic to the simple affine vertex superalgebra $L_{k'} (osp(1 \\vert 2))$ fo
r $k'=-5/4$. This is joint work with D. Adamovic.\n
LOCATION:https://researchseminars.org/talk/EQuAL/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco De Renzi (University of Zurich)
DTSTART;VALUE=DATE-TIME:20230313T150000Z
DTEND;VALUE=DATE-TIME:20230313T160000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/9
DESCRIPTION:Title: Al
gebraic presentation of cobordisms and quantum invariants in dimensions 3
and 4\nby Marco De Renzi (University of Zurich) as part of European Qu
antum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe category 2Cob of 2-dimen
sional cobordisms is freely generated by a commutative Frobenius algebra:
the circle. This yields a complete classification of 2-dimensional TQFTs (
Topological Quantum Field Theories). In this talk\, I will discuss some co
nsequences of analogous algebraic presentations in dimensions 3 and 4\, du
e to Bobtcheva and Piergallini. In both cases\, the fundamental algebraic
structures are provided by certain Hopf algebras called BPH algebras. In d
imension 3\, I will consider the category 3Cob of connected cobordisms bet
ween connected surfaces with connected boundary. I will explain that an al
gebraic presentation conjectured (or rather announced without proof) by Ha
biro is in fact equivalent to the one established by Bobtcheva and Piergal
lini. In dimension 4\, I will focus on a category denoted 4HB\, whose morp
hisms are 2-deformation classes of 4-dimensional 2-handlebodies. I will sh
ow that any unimodular ribbon category contains a BPH algebra\, which can
be characterized very explicitly. This result proves the existence of a ve
ry large family of TQFT functors on 4HB. Finally\, I will explain that a u
nimodular ribbon category has the potential to detect exotic phenomena in
dimension 4 only if it is neither semisimple nor factorizable. This is a j
oint work with A. Beliakova\, I. Bobtcheva\, and R. Piergallini.\n
LOCATION:https://researchseminars.org/talk/EQuAL/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojana Femic (Serbian Academy of Sciences and Arts)
DTSTART;VALUE=DATE-TIME:20230327T140000Z
DTEND;VALUE=DATE-TIME:20230327T150000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/10
DESCRIPTION:Title: C
ategorical centers and Yetter Drinfel`d-modules as 2-categorical (bi)lax
structures\nby Bojana Femic (Serbian Academy of Sciences and Arts) as
part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nJoint wor
k with Sebastian Halbig\n\nCenter categories of monoidal categories ${\\ma
thcal C}$ and of bimodule categories ${\\mathcal M}$ are very well known a
nd studied in the literature. \nWe consider the (weak) center category ${\
\mathcal Z}(F\,{\\mathcal M}\,G)$ of a ${\\mathcal C}\\text{-} {\\mathcal
D}$-bimodule category ${\\mathcal M}$ twisted by two lax monoidal functor
s \n$F:{\\mathcal E}\\to {\\mathcal D}$ and $G:{\\mathcal E}\\to {\\mathca
l C}$\, for another monoidal category ${\\mathcal E}$. (The weakness cor
responds to dealing with half-braidings\, while with strongness we allude
to (invertible) braidings.)\n\nWe show how the 2-categorical viewpoint pro
vides a deeper insight on such center categories. Namely\, for fixed bica
tegories ${\\mathcal B}$ and ${\\mathcal B}'$ there are bicategories $\\op
eratorname{Lax}_{lx}({\\mathcal B}\,{\\mathcal B}')$ and $\\operatorname{L
ax}_{clx}({\\mathcal B}\,{\\mathcal B}')$ of lax functors ${\\mathcal B} \
\to {\\mathcal B}'$\, lax (resp. colax) transformations and their modifica
tions. We reveal how in a specific case of ${\\mathcal B}$ and ${\\mathca
l B}'$ we can identify the hom-categories of these two bicategories with t
he weak left (resp. right) twisted centers\, so that the horizontal compos
ition in the bicategories corresponds to the composition of weak twisted
center categories between themselves. In this way we obtain a bicategory o
f weak left (resp. right) centers categories. We show how a full sub-bicat
egory of both of them recovers the bicategory $TF({\\mathcal C}\,{\\mathca
l D})$ from [Shim\, Section 3]. Moreover\, we prove a more general result
in bicategories by which the rigidity of $TF({\\mathcal C}\,{\\mathcal D
})$ is recovered. \n\nOn the other hand\, we introduce a 2-category ${\\r
m Bilax}({\\mathcal K}\,{\\mathcal K}')$ of bilax functors (among 2-categ
ories ${\\mathcal K}$ and ${\\mathcal K}'$)\, bilax natural transformation
s and bilax modifications. Its 0-cells are a 2-categorification of bilax f
unctors of [Agui] and of bimonoidal functors of [CS]. We show how bilax f
unctors generalize the notions of bialgebras in braided monoidal categorie
s\, $bimonads$ in 2-categories (with respect to Yang-Baxter operators\,
YBO's)\, and preserve bimonads (w.r.t. YBO's)\, $module$ $comonads$ and $c
omodule$ $monads$\, and $relative$ $bimonad$ $modules$. Moreover\, the com
ponent functors of a bilax functor on hom-categories factor through the ca
tegory of $Hopf$ $bimodules$ (w.r.t. YBO's). (The 2-categorical notions in
italic letters are introduced in our work.) \n\nWe finally show that th
ere is a 2-category equivalence ${\\rm Bilax} (1\, \\Sigma{\\mathcal C})\\
simeq{\\mathcal YD}(\\Sigma{\\mathcal C})$ and a faithful 2-functor ${\\r
m Bilax}(1\,{\\mathcal K})\\hookrightarrow\\operatorname{Dist}({\\mathcal
K})$. Here ${\\mathcal YD}(\\Sigma{\\mathcal C})$ is a 2-category of Yett
er-Drinfel`d modules in a braided monoidal category ${\\mathcal C}$ and $
\\operatorname{Dist}({\\mathcal K})$ is the 2-category of mixed distributi
ve laws of [PW].\n\n\n[Agui] M. Aguiar\, S. Mahajan\, Monoidal functors\,
species and Hopf algebras\, CRM Monograph Series 29 Amer. Math. Soc. (2010
).\n\n[CS] M. B. McCurdy\, R. Street\, What Separable Frobenius Monoidal F
unctors Preserve\,\nCahiers de Topologie et Geometrie Differentielle Categ
oriques 51/1 (2010).\n\n[Shim] K. Shimizu: Ribbon structures of the Drinfe
l`d center\, arXiv:1707.09691 (2017a)\n\n[PW] J. Power\, H. Watanabe\, Com
bining a monad and a comonad\, Theoretical Computer Science 280 (2002)\, 1
37--262.\n
LOCATION:https://researchseminars.org/talk/EQuAL/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Vrije Universiteit Brussel)
DTSTART;VALUE=DATE-TIME:20230424T140000Z
DTEND;VALUE=DATE-TIME:20230424T150000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/11
DESCRIPTION:Title: N
ichols algebras\nby Leandro Vendramin (Vrije Universiteit Brussel) as
part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nNichols a
lgebras appear in several branches of mathematics\, going from Hopf algebr
as and quantum groups\, to Schubert calculus and conformal field theories.
In this talk\, we review the main problems related to Nichols algebras an
d I discuss some classification theorems and some applications.\n
LOCATION:https://researchseminars.org/talk/EQuAL/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Saracco (Université Libre de Bruxelles)
DTSTART;VALUE=DATE-TIME:20230522T140000Z
DTEND;VALUE=DATE-TIME:20230522T150000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/12
DESCRIPTION:Title: C
losed categories\, modules and (one-sided) Hopf algebras\nby Paolo Sar
acco (Université Libre de Bruxelles) as part of European Quantum Algebra
Lectures (EQuAL)\n\n\nAbstract\nA well-known characterization of Hopf alge
bras\, that I always found fascinating and elegant\, states that an algebr
a A over a field k is a Hopf algebra if and only if its category of module
s is a closed monoidal category in such a way that the forgetful functor t
o vector spaces preserves the closed monoidal structure. We usually split
this result into two steps: the lifting of the monoidal structure correspo
nds to the bialgebra structure\, and then the further lifting of the close
d structure as adjoint to the monoidal one corresponds to the existence of
an antipode. However\, closed structures can be defined independently of
monoidal ones and have their own dignity and importance. Which new structu
re on our algebra A would correspond to lifting the closed structure of ve
ctor spaces alone? How would this relate with the familiar bialgebra and H
opf algebra structures coming from lifting the monoidal and closed monoida
l ones? It turns out that lifting the closed structure corresponds to the
existence of algebra maps 𝛿 : A -> A⊗A^op and ε : A -> k satisfying
appropriate conditions. Moreover\, a quite unexpected source of examples i
s provided by certain one-sided Hopf algebras\, i.e. bialgebras with a mor
phism which is just a one-sided convolution inverse of the identity. In th
is seminar\, based on an ongoing collaboration with Johannes Berger and Jo
ost Vercruysse which is continuing discussions with Gabriella Böhm\, I wi
ll present our progresses in the study of these new algebraic structures.\
n
LOCATION:https://researchseminars.org/talk/EQuAL/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoyuki Arakawa (RIMS\, Kyoto University)
DTSTART;VALUE=DATE-TIME:20231005T090000Z
DTEND;VALUE=DATE-TIME:20231005T100000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/13
DESCRIPTION:Title: H
ilbert Schemes of the points in the plane and quasi-lisse vertex superalge
bras\nby Tomoyuki Arakawa (RIMS\, Kyoto University) as part of Europea
n Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nFor each complex reflect
ion group $\\Gamma$ one can attach a canonical symplectic singularity $\\m
athcal{M}_{\\Gamma}$. Motivated by the 4D/2D duality discovered by Beem e
t at.\, Bonetti\, Menegheli and Rastelli conjectured the existence of a su
persymmetric vertex operator algebra $\\mathbf{W}_{\\Gamma}$ whose associa
ted variety is isomorphic to $\\mathcal{M}_{\\Gamma}$. We prove this conj
ecture when the complex reflection group $\\Gamma$ is the symmetric group
$S_N$\, by constructing a sheaf of $\\hbar$-adic vertex algebras on the Hi
lbert schemes of $N$-points in the plane. In physical terms\, the vertex
operator algebra $\\mathbf{W}_{S_N}$ corresponds\, by the 4D/2D duality
\, to the $4$-dimensional $\\mathcal{N}=4$ super Yang-Mills theory with ga
uge group $SL_N$.\nThis is a joint work with Toshiro Kuwabara and Sven Mol
ler.\n
LOCATION:https://researchseminars.org/talk/EQuAL/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joost Vercruysse (Université Libre de Bruxelles)
DTSTART;VALUE=DATE-TIME:20231019T090000Z
DTEND;VALUE=DATE-TIME:20231019T100000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/14
DESCRIPTION:Title: G
eneralizations of Yetter-Drinfel'd modules and the center construction of
monoidal categories\nby Joost Vercruysse (Université Libre de Bruxell
es) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nTh
is is joint work with Ryan Aziz. A Yetter-Drinfel'd module over a bialgebr
a $H$\, is at the same time a module and a comodule over $H$ satisfying a
particular compatibility condition. It is well-known that the category of
Yetter-Drinfel'd modules (say\, over a finite dimensional Hopf algebra $H$
) is equivalent to the center of the monoidal category of $H$-(co)modules
as well as to the category of modules over the Drinfel'd double of $H$. Ca
enepeel\, Militaru and Zhu introduced a generalized version of Yetter-Drin
feld modules. More precisely\, they consider two bialgebras $H$\, $K$\, to
gether with an bimodule coalgebra $C$ and a bicomodule algebra $A$ over th
em. A generalized Yetter-Drinfel'd module in their sense\, is an $A$-modul
e that is at the same time a $C$-comodule satisfying a certain compatibili
ty condition. Under finiteness conditions\, they showed that these modules
are exactly modules of a suitably constructed smash product build out of
$A$ and $C$. The aim of this talk is to show how the category of these gen
eralized Yetter-Drinfel'd can be obtained as a relative center of the cate
gory of $A$-modules\, viewed as a bi-actegory over the categories of $H$-m
odules and $K$-modules. Moreover\, we also show how other variations of Ye
tter-Drinfel'd modules\, such as anti-Yetter-Drinfel'd modules\, arise as
a particular case and we discuss the bicategorical structure that arises t
his way.\n
LOCATION:https://researchseminars.org/talk/EQuAL/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Norton (University of Kent)
DTSTART;VALUE=DATE-TIME:20231214T100000Z
DTEND;VALUE=DATE-TIME:20231214T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/15
DESCRIPTION:Title: D
ecomposition numbers for unipotent blocks with small sl_2-weight in finite
classical groups\nby Emily Norton (University of Kent) as part of Eur
opean Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhoff (University of Hamburg)
DTSTART;VALUE=DATE-TIME:20231102T100000Z
DTEND;VALUE=DATE-TIME:20231102T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/16
DESCRIPTION:Title: C
omplexes of stable $\\infty$-categories\nby Tobias Dyckerhoff (Univers
ity of Hamburg) as part of European Quantum Algebra Lectures (EQuAL)\n\n\n
Abstract\nDerived categories have come to play a decisive role in a wide r
ange of topics. Several recent developments\, in particular in the context
of topological Fukaya categories\, arouse the desire to study not just si
ngle categories\, but rather complexes of categories. In this talk\, we wi
ll discuss examples of such complexes in algebra\, topology\, algebraic ge
ometry\, and symplectic geometry\, along with some results and conjectures
involving them. Based on joint work with Merlin Christ and Tashi Walde.\n
LOCATION:https://researchseminars.org/talk/EQuAL/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Taipe (Université Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20231116T100000Z
DTEND;VALUE=DATE-TIME:20231116T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/17
DESCRIPTION:Title: Q
uantum Transformation Groupoids\nby Frank Taipe (Université Paris-Sac
lay) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nW
e define quantum transformation groupoids\, a class of multiplier Hopf alg
ebroids generalizing transformation groupoids and algebraic quantum groups
. An interesting characteristic of this algebraic class is that it admits
a Pontryagin-like duality. In the first part of the talk\, we will discuss
how the study of quantum transformation groupoids appears in a Galois-typ
e theory of inclusions of von Neumann algebras. Then in the second part\,
we will give the construction of a quantum transformation groupoid from a
braided commutative measured Yetter-Drinfeld *-algebra on an algebraic qua
ntum group in the sense of A. Van Daele.\n
LOCATION:https://researchseminars.org/talk/EQuAL/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azat Gainutdinov (Université de Tours\, CNRS)
DTSTART;VALUE=DATE-TIME:20231130T100000Z
DTEND;VALUE=DATE-TIME:20231130T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/18
DESCRIPTION:Title: N
on-semisimple link and manifold invariants for symplectic fermions\nby
Azat Gainutdinov (Université de Tours\, CNRS) as part of European Quantu
m Algebra Lectures (EQuAL)\n\n\nAbstract\nI will talk about link and three
-manifold invariants defined in terms of a non-semisimple finite ribbon ca
tegory C together with a choice of tensor ideal and modified trace. If the
ideal is all of C\, these invariants agree with those defined by Lyubashe
nko in the 90’s\, and as we show\, they only depend on the Grothendieck
class of the objects labelling the link. These invariants are therefore no
t able to determine non-split extensions. However\, we observed an interes
ting phenomenon: if one chooses an intermediate proper ideal between C and
the minimal ideal of projective objects\, the invariants do distinguish n
on-trivial extensions. This is demonstrated in the case of C being the rib
bon category of N pairs of symplectic fermions. This is a joint work with
J. Berger and I. Runkel.\n
LOCATION:https://researchseminars.org/talk/EQuAL/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bazlov (University of Manchester)
DTSTART;VALUE=DATE-TIME:20240118T100000Z
DTEND;VALUE=DATE-TIME:20240118T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/19
DESCRIPTION:Title: C
ocycle and Galois cocycle twists of algebras\, representations and orders<
/a>\nby Yuri Bazlov (University of Manchester) as part of European Quantum
Algebra Lectures (EQuAL)\n\n\nAbstract\nIn a construction known as Drinfe
ld twist\, a 2-cocycle on a Hopf algebra H is used to modify the coproduct
on H as well as the associative product in any H-module algebra A. I am i
nterested to know to what extent the representation theory of the twist of
A can be recovered from that of A\; the A#H-module category\, unchanged u
nder the twist\, plays a role here. I will talk about an application of th
is idea to rational Cherednik-type algebras\, which led\, in a joint work
with E. Jones-Healey\, to establishing nontrivial isomorphisms between bra
ided and classical versions of these algebras. Twists also help to approac
h representation theory of the so-called mystic reflection groups\, define
d by the Chevalley-Serre-Shephard-Todd property of their action on a quant
um polynomial ring. An important source of twists\, motivated by torsors i
n geometry\, should be cocycles arising from (Hopf-)Galois extensions of a
lgebras\, and I will discuss this in the context of constructing orders an
d normal integral bases in central simple algebras over a number field.\n
LOCATION:https://researchseminars.org/talk/EQuAL/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fiona Torzewska (University of Bristol)
DTSTART;VALUE=DATE-TIME:20240201T100000Z
DTEND;VALUE=DATE-TIME:20240201T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/20
DESCRIPTION:Title: T
opological quantum field theories and homotopy cobordisms\nby Fiona To
rzewska (University of Bristol) as part of European Quantum Algebra Lectur
es (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bridgeman (Ghent University)
DTSTART;VALUE=DATE-TIME:20240215T100000Z
DTEND;VALUE=DATE-TIME:20240215T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/21
DESCRIPTION:Title: I
nvertible Bimodule Categories and Generalized Schur Orthogonality\nby
Jacob Bridgeman (Ghent University) as part of European Quantum Algebra Lec
tures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Balagovic (University of Newcastle)
DTSTART;VALUE=DATE-TIME:20240229T100000Z
DTEND;VALUE=DATE-TIME:20240229T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/22
DESCRIPTION:Title: B
raided Module Categories\nby Martina Balagovic (University of Newcastl
e) as part of European Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20240314T100000Z
DTEND;VALUE=DATE-TIME:20240314T110000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/23
DESCRIPTION:Title: F
inding quantum groups in QFT\nby Tudor Dimofte (University of Edinburg
h) as part of European Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Langlois-Rémillard (Hausdorff Center for Mathematics\, Uni
versität Bonn)
DTSTART;VALUE=DATE-TIME:20240509T090000Z
DTEND;VALUE=DATE-TIME:20240509T100000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/24
DESCRIPTION:Title: Q
uotients of the affine Temperley-Lieb algebras with a view towards general
ised Deligne interpolation categories\nby Alexis Langlois-Rémillard (
Hausdorff Center for Mathematics\, Universität Bonn) as part of European
Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe affine (and periodic)
Temperley-Lieb algebras appeared in the study of conformal field theories
as useful tools to study the continuum scaling limits of critical statisti
cal models. The fusion of their modules is believed to be connected to the
fusion of bulk fields in CFT. However\, the connection is not obvious. In
part to seek the ideal structure to investigate the scaling limit\, we st
udy certain quotients of the affine Temperley-Lieb algebras\, which we nam
e uncoiled algebras\, and we study their Jones-Wenzl idempotents. In this
talk\, we will present the uncoiled algebras\, the construction of their J
ones-Wenzl idempotents and investigate the traces of these\, relating it t
o the extremal weight projectors of Queffelec and Wedrich. Time permitting
\, we will investigate a generalisation of these structures related to Del
igne interpolation categories. \n\nThis is based on joint work with Alexi
Morin-Duchesne\n
LOCATION:https://researchseminars.org/talk/EQuAL/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léo Schelstraete (Université catholique de Louvain)
DTSTART;VALUE=DATE-TIME:20240523T090000Z
DTEND;VALUE=DATE-TIME:20240523T100000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/25
DESCRIPTION:Title: O
dd Khovanov homology and higher representation theory\nby Léo Schelst
raete (Université catholique de Louvain) as part of European Quantum Alge
bra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agustina Czenky (University of Oregon)
DTSTART;VALUE=DATE-TIME:20240606T080000Z
DTEND;VALUE=DATE-TIME:20240606T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/26
DESCRIPTION:Title: U
noriented 2-dimensional TQFTs and the category Rep(S_t \\wr Z_2)\nby A
gustina Czenky (University of Oregon) as part of European Quantum Algebra
Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Calderón Mateus (Universidad de los Andes)
DTSTART;VALUE=DATE-TIME:20240620T130000Z
DTEND;VALUE=DATE-TIME:20240620T140000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/27
DESCRIPTION:Title: C
lassification of graded Hopf algebra quotients\nby Fabio Calderón Mat
eus (Universidad de los Andes) as part of European Quantum Algebra Lecture
s (EQuAL)\n\n\nAbstract\nLet $G$ be a group. A Hopf algebra $H$ is called
$G$-graded if $H$ is $G$-graded as an algebra\, and the grading is compati
ble with the comultiplication\, counit and antipode. Examples of such Hopf
algebras include cocentral extensions of Hopf algebras and the twisted Dr
infeld double of groups. In this talk\, we present a classification of Hop
f ideals for a $G$-graded (quasi-)Hopf algebra based on the following para
metrization: normal subgroups $N$ of $G$\, Hopf ideals in the homogeneous
component of the identity $H_e$ that are invariant under $N$\, and $G$-equ
ivariant trivializations of a specific quotient constructed with these par
ameters. This approach incorporates ideas from earlier work by César Gali
ndo and Corey Jones\, who parameterized all fusion subcategories arising f
rom equivariantization through a group action on a fusion category. Howeve
r\, in our results\, the Hopf algebras are not necessarily semisimple\, an
d $G$ is not necessarily finite. This talk is based on ongoing joint work
with César Galindo.\n
LOCATION:https://researchseminars.org/talk/EQuAL/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Barrett (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20241009T090000Z
DTEND;VALUE=DATE-TIME:20241009T100000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/28
DESCRIPTION:Title: G
ray categories with duals and their diagrams\nby John Barrett (Univers
ity of Nottingham) as part of European Quantum Algebra Lectures (EQuAL)\n\
nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Burciu (Institute of Mathematics of Romanian Academy)
DTSTART;VALUE=DATE-TIME:20241023T090000Z
DTEND;VALUE=DATE-TIME:20241023T100000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081258Z
UID:EQuAL/29
DESCRIPTION:Title: B
urnside vanishing type properties for fusion categories\nby Sebastian
Burciu (Institute of Mathematics of Romanian Academy) as part of European
Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EQuAL/29/
END:VEVENT
END:VCALENDAR