BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shahn Majid (Queen Mary University) DTSTART:20221010T140000Z DTEND:20221010T150000Z DTSTAMP:20260422T225656Z 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:20221024T140000Z DTEND:20221024T150000Z DTSTAMP:20260422T225656Z 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:20221107T150000Z DTEND:20221107T160000Z DTSTAMP:20260422T225656Z 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:20221121T150000Z DTEND:20221121T160000Z DTSTAMP:20260422T225656Z 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:20221205T150000Z DTEND:20221205T160000Z DTSTAMP:20260422T225656Z 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:20221219T150000Z DTEND:20221219T160000Z DTSTAMP:20260422T225656Z 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:20230213T150000Z DTEND:20230213T160000Z DTSTAMP:20260422T225656Z 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:20230227T150000Z DTEND:20230227T160000Z DTSTAMP:20260422T225656Z 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:20230313T150000Z DTEND:20230313T160000Z DTSTAMP:20260422T225656Z 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:20230327T140000Z DTEND:20230327T150000Z DTSTAMP:20260422T225656Z 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:20230424T140000Z DTEND:20230424T150000Z DTSTAMP:20260422T225656Z 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:20230522T140000Z DTEND:20230522T150000Z DTSTAMP:20260422T225656Z 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:20231005T090000Z DTEND:20231005T100000Z DTSTAMP:20260422T225656Z 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:20231019T090000Z DTEND:20231019T100000Z DTSTAMP:20260422T225656Z 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:20231214T100000Z DTEND:20231214T110000Z DTSTAMP:20260422T225656Z 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\n\nAbstract\nThere are many famil iar module categories admitting a categorical action of a Lie algebra. The combinatorial shadow of such an action often yields answers to module-the oretic questions\, for instance via crystals. In proving a conjecture of G erber\, Hiss\, and Jacon\, it was shown by Dudas\, Varagnolo\, and Vassero t that the category of unipotent representations of a finite classical gro up has such a categorical action. In this talk I will explain how we can u se the categorical action to deduce closed formulas for certain families o f decomposition numbers of these groups. This is joint work with Olivier D udas.\n LOCATION:https://researchseminars.org/talk/EQuAL/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Tobias Dyckerhoff (University of Hamburg) DTSTART:20231102T100000Z DTEND:20231102T110000Z DTSTAMP:20260422T225656Z 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:20231116T100000Z DTEND:20231116T110000Z DTSTAMP:20260422T225656Z 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:20231130T100000Z DTEND:20231130T110000Z DTSTAMP:20260422T225656Z 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:20240118T100000Z DTEND:20240118T110000Z DTSTAMP:20260422T225656Z 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:20240201T100000Z DTEND:20240201T110000Z DTSTAMP:20260422T225656Z 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\n\nAbstract\nI will begin by explaining the construction of a category CofCos\, whose objects are topological spaces and whose morphism s are cofibrant cospans. Here the identity cospan is chosen to be of the f orm $X\\to X\\times [0\,1]\\rightarrow X$\, in contrast with the usual ide ntity in the bicategory $Cosp(V)$ of cospans over a category $V$. The cate gory $CofCos$ has a subcategory $HomCob$ in which all spaces are homotopic ally 1-finitely generated. There exist functors into HomCob from a number of categorical constructions which are potentially of use for modelling pa rticle trajectories in topological phases of matter: embedded cobordism ca tegories and motion groupoids for example. Thus\, functors from HomCob int o Vect give representations of the aforementioned categories.\n\nI will al so construct a family of functors $Z_G\\colon HomCob\\to Vect$\, one for e ach finite group $G$\, and show that topological quantum field theories pr eviously constructed by Yetter\, and an untwisted version of Dijkgraaf-Wit ten\, generalise to functors from HomCob. I will construct this functor in such a way that it is clear the images are finite dimensional vector spac es\, and the functor is explicitly calculable. I will also give example ca lculations throughout.\n LOCATION:https://researchseminars.org/talk/EQuAL/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Bridgeman (Ghent University) DTSTART:20240215T100000Z DTEND:20240215T110000Z DTSTAMP:20260422T225656Z 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\n\nAbstract\nThe Schur orthogonality relations are a corne rstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new\, readily verifiable condition on the skeletal data for deciding whether a given bimodule category is invert ible and therefore defines a Morita equivalence. Ultimately\, the conditio n arises from Schur orthogonality relations on the characters of the annul ar algebra associated to a module category. As a first application\, we pr ovide an algorithm for the construction of the full skeletal data of the i nvertible bimodule category associated to a given module category\, which is obtained in a unitary gauge when the underlying categories are unitary. As a second application\, we show that our condition for invertibility is equivalent to the notion of MPO-injectivity\, thereby closing an open que stion concerning tensor network representations of string-net models exhib iting topological order. Work with Laurens Lootens and Frank Verstraete. B ased on arXiv: 2211.01947\n LOCATION:https://researchseminars.org/talk/EQuAL/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Martina Balagovic (University of Newcastle) DTSTART:20240229T100000Z DTEND:20240229T110000Z DTSTAMP:20260422T225656Z 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:20240314T100000Z DTEND:20240314T110000Z DTSTAMP:20260422T225656Z 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\n\nAbstract\nI w ill explain a construction leading to the structure of a braided module ca tegory over the braided category of finite dimensional representations of a quantum group\, and discuss what we can hope to say about such a categor y. Joint work with Stefan Kolb.\n LOCATION:https://researchseminars.org/talk/EQuAL/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexis Langlois-Rémillard (Hausdorff Center for Mathematics\, Uni versität Bonn) DTSTART:20240509T090000Z DTEND:20240509T100000Z DTSTAMP:20260422T225656Z 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:20240523T090000Z DTEND:20240523T100000Z DTSTAMP:20260422T225656Z 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\n\nAbstract\nKhovanov homology is a homological inv ariant of links categorifying the Jones polynomial. It is by now well-unde rstood through the lens of higher representation theory\, categorifying th e relationship between the Jones polynomial and the representation theory of Uq(sl2). Surprisingly\, there exists another categorification of the Jo nes polynomial\, called odd Khovanov homology. Subsequently\, higher odd ( or “super”) analogues were discovered in representation theoretic and geometric contexts. In this talk\, I will begin with a gentle introduction to the above\, and then explain how odd Khovanov homology can be understo od as stemming from a supercategorification of the representation theory o f Uq(gl2). This is joint work with Pedro Vaz.\n LOCATION:https://researchseminars.org/talk/EQuAL/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Agustina Czenky (University of Oregon) DTSTART:20240606T080000Z DTEND:20240606T090000Z DTSTAMP:20260422T225656Z 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\n\nAbstract\nLet k be an algebraically closed field of characteristic zero. The category of oriented 2-dimensional cobordisms can be understood in purely algebraic terms via a description by generators a nd relations\; moreover\, it is possible to recover from it the Deligne ca tegory Rep(S_t)\, which interpolates the category of finite-dimensional re presentations of the symmetric group S_n from n a positive integer to any parameter t in k. We show an analogous story happens in the unoriented cas e: via its description by generators and relations\, we recover the genera lized Deligne category Rep(S_t \\wr Z_2)\, which interpolates the category of finite-dimensional representations of the wreath product S_t \\wr Z_2. \n LOCATION:https://researchseminars.org/talk/EQuAL/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabio Calderón Mateus (Universidad de los Andes) DTSTART:20240620T130000Z DTEND:20240620T140000Z DTSTAMP:20260422T225656Z 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:20241009T090000Z DTEND:20241009T100000Z DTSTAMP:20260422T225656Z 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\ n\nAbstract\nGray categories with a coherent notion of duals are captured well by a calculus of three-dimensional diagrams\, generalising the famili ar string diagrams for braided categories. The talk will discuss what is i n the paper with this title (Advances in Mathematics\, Volume 450\, 2024\, 109740)\, what got left out\, and what is still missing.\n LOCATION:https://researchseminars.org/talk/EQuAL/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Burciu (Institute of Mathematics of Romanian Academy) DTSTART:20241023T090000Z DTEND:20241023T100000Z DTSTAMP:20260422T225656Z 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\n\nAbstract\nA classical result of Burn side in the character theory of finite groups states that any irreducible non-linear character of a finite group vanishes on at least one element of the group. In this talk\, we show that a similar vanishing property holds for weakly integral fusion categories. It is known that Harada’s ident ity\, related with the product of all conjugacy class sums of a finite gro up\, is a consequence of Burnside’s vanishing property of characters. We prove a similar formula for any weakly integral fusion category and discu ss some other new consequences of this result. This is partially joint wor k with S. Palcoux.\n LOCATION:https://researchseminars.org/talk/EQuAL/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Hankyung Ko (Uppsala University) DTSTART:20241106T100000Z DTEND:20241106T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/30 DESCRIPTION:Title: D iagrammatic singular Soergel bimodules\nby Hankyung Ko (Uppsala Univer sity) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\n In joint work with Ben Elias\, Nicolas Libedinsky\, Leonardo Patimo\, we c onstruct a diagrammatic basis of the morphism spaces of singular Soergel b imodules\, analogous to the diagrammatic basis for the regular Soergel bim odules given by Elias-Williamson (modelled on the algebraic `light leaves' basis due to Libedinsky). The talk is an introduction to this diagrammati cs and related combinatorics\, where we also aim to draw some singular lig ht leaves.\n LOCATION:https://researchseminars.org/talk/EQuAL/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Zahra Nazemian (Universitaet Graz) DTSTART:20241204T100000Z DTEND:20241204T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/32 DESCRIPTION:Title: P oisson Modules over Hopf Poisson Order Algebras\nby Zahra Nazemian (Un iversitaet Graz) as part of European Quantum Algebra Lectures (EQuAL)\n\n\ nAbstract\nHopf Poisson order (HPO) algebras were introduced and studied b y Brown\, Nazemian\, and Zhang (preprint\, 2024). We investigate the class of Poisson modules over HPO algebras and show that it forms a monoidal ca tegory.\n \nMoreover\, we prove that the left homological integral of an H PO algebra $H$\, denoted $ \\int_H^l$\, is a left Poisson module. It is al so a right Poisson module if and only if $\\int_H^l = \\int_H^r $. \n \nRe ferences:\n- Hopf Poisson Order Algebras\, K. Brown\, Z. Nazemian\, and J. J. Zhang\, (preprint\, 2024).\n- Homological Integrals of Hopf Algebras\, D.-M. Lu\, Q.-S. Wu\, and J.J. Zhang\, Trans. Amer. Math. Soc. 359 (2007)\ , 4945–4975.\n- Category of Poisson Modules over HPO Algebras\, Z. Nazem ian\, in progress.\n LOCATION:https://researchseminars.org/talk/EQuAL/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Mizuki Oikawa (University of Tokyo) DTSTART:20241218T100000Z DTEND:20241218T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/33 DESCRIPTION:Title: C enter construction for group-crossed tensor categories\nby Mizuki Oika wa (University of Tokyo) as part of European Quantum Algebra Lectures (EQu AL)\n\n\nAbstract\nIn this talk\, I will talk about my recent generalizati on of the Drinfeld center construction for group-crossed tensor categories . A group-crossed tensor category is a tensor category with compatible gro up action and grading\, which naturally appear in two-dimensional conforma l theory as categories of twisted modules. Indeed\, my construction for su ch categories yields categories "braided for a matched pair of groups"\, w hich is a notion introduced recently by Natale. I will also talk about my work in preparation: an equivariant version of Müger's factorization theo rem and a group-crossed version of Morita equivalence.\n LOCATION:https://researchseminars.org/talk/EQuAL/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Ramona Wolf (University of Siegen) DTSTART:20250122T100000Z DTEND:20250122T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/34 DESCRIPTION:Title: C omputing F-symbols for the center of a fusion category via tube algebras\nby Ramona Wolf (University of Siegen) as part of European Quantum Alge bra Lectures (EQuAL)\n\n\nAbstract\nApplications of fusion categories ofte n require the F-symbols to be known explicitly\, for example\, for constru cting lattice models in physics. Although\, in principle\, these matrices can always be determined by solving the pentagon equation\, this task is o ften difficult in practice since it corresponds to solving a vast system o f coupled polynomial equations in a large number of variables. This is esp ecially true if we are interested in the center of a fusion category\, whi ch typically has too many objects and multiplicities to allow for a direct calculation of the F-symbols. In this talk\, I will discuss how one can c onstruct the center (including the F-symbols) from a known fusion category using representation theory of the tube algebra of the category.\n LOCATION:https://researchseminars.org/talk/EQuAL/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Lachowska (École Polytechnique Fédérale de Lausanne) DTSTART:20250205T100000Z DTEND:20250205T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/35 DESCRIPTION:Title: C ombinatorics of the center of the small quantum group\nby Anna Lachows ka (École Polytechnique Fédérale de Lausanne) as part of European Quant um Algebra Lectures (EQuAL)\n\n\nAbstract\nThe small quantum group $u_q(g) $ associated to the Lie algebra $g$ and a root of unity $q$ was introduced by Lusztig in 1990 and plays an important role in quantum and modular rep resentation theory. Despite significant advances in the last two years\, t he dimension of the center of $u_q(g)$ is unknown in general. I will descr ibe the combinatorial aspects of the problem\, in particular the relation between the center of $u_q(g)$ and the space of the diagonal coinvariants \, the Harish-Chandra center and the Higman ideal.\nThis is a joint work w ith Qi You\, Nicolas Hemelsoet and Oscar Kivinen.\n LOCATION:https://researchseminars.org/talk/EQuAL/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Nivedita (University of Oxford) DTSTART:20250219T104500Z DTEND:20250219T114500Z DTSTAMP:20260422T225656Z UID:EQuAL/36 DESCRIPTION:Title: M odels for 2-Hilb and 3-Hilb as target categories for Functorial Field Theo ries\nby Nivedita (University of Oxford) as part of European Quantum A lgebra Lectures (EQuAL)\n\n\nAbstract\nWe introduce W*-Cat\, the bicategor y of complete W*‐categories\, functors and natural transformations and d iscuss its equivalence with the Morita category of von Neumann algebras (v N2). We highlight some analogies of W*‐categories with Hilbert spaces po inting towards W*-Cat being a model for 2-Hilb (based on https://arxiv.org /abs/2411.01678). We also introduce a categorified analogue of von Neumann algebras\, motivating definition of a Bicommutant Category such that the Morita category of bicommutant categories would model 3-Hilb. This is work in progress.\n LOCATION:https://researchseminars.org/talk/EQuAL/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Edmund Heng (IHES) DTSTART:20250305T100000Z DTEND:20250305T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/37 DESCRIPTION:Title: 1 -step beyond semisimple algebras: fusion quivers\nby Edmund Heng (IHES ) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe study of module categories over fusion categories have focussed mostly on the semisimple ones. In this talk I will introduce the notion of fusion qu ivers and their representations\, the categories of which form hereditary (global projective dimension 1) abelian module categories over fusion cate gories. This naive “one-step” generalisation from semisimple module ca tegories uncovers a wealth of interesting new connections to Coxeter theor y. In particular\, I will present a classification result in the spirit of Gabriel: the finite-representation-type fusion quivers are classified by the Coxeter—Dynkin diagrams\; the latter includes the (crystallographic) Dynkin diagram from Lie algebras ABCDEFG and\, perhaps surprisingly\, als o the non-crystallographic diagrams H and I\, which all together classify the finite Coxeter groups. This is based on joint work with Ben Elias.\n LOCATION:https://researchseminars.org/talk/EQuAL/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiaoting Zhang (China Normal University) DTSTART:20250319T100000Z DTEND:20250319T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/38 DESCRIPTION:Title: F usion-stable tilting/stability structures on triangulated categories\n by Xiaoting Zhang (China Normal University) as part of European Quantum Al gebra Lectures (EQuAL)\n\n\nAbstract\nWe study fusion-stable tilting/stabi lity structures on triangulated categories and show that the space of Fusi on-stable stability conditions form a complex manifold. As an application\ , we give a new proof of $K(\\pi\,1)$-conjecture for finite non-simply lac ed Coxeter-Dynkin type. This is a joint work with Qiu Yu.\n LOCATION:https://researchseminars.org/talk/EQuAL/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Isaac Oppong (University of Greenwich) DTSTART:20250507T090000Z DTEND:20250507T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/39 DESCRIPTION:Title: D erivations and Hochschild cohomology of quantum nilpotent algebras\nby Isaac Oppong (University of Greenwich) as part of European Quantum Algebr a Lectures (EQuAL)\n\n\nAbstract\nWe compute the derivations of Quantum Ni lpotent Algebras under a technical (but necessary) assumption on the cente r. As a consequence\, we give an explicit description of the first Hochsch ild cohomology group of $U_q^+(\\mathfrak{g})$\, the positive part of the quantized enveloping algebra of a finite-dimensional complex simple Lie al gebra $\\mathfrak{g}$. Our results are obtained leveraging an initial clus ter constructed by Goodearl and Yakimov.\n LOCATION:https://researchseminars.org/talk/EQuAL/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Cesar Galindo (Universidad de los Andes) DTSTART:20250521T120000Z DTEND:20250521T130000Z DTSTAMP:20260422T225656Z UID:EQuAL/40 DESCRIPTION:Title: Z estings for Hopf algebras\nby Cesar Galindo (Universidad de los Andes) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nIn th is talk\, I will present a framework for "zestings" of Hopf algebras\, a t echnique we hve extended from fusion categories to general tensor categori es. I will provide a detailed translation of the categorical zesting const ruction into explicit Hopf algebraic terms. We show how associative zestin g of a Hopf algebra's comodule category yields a coquasi-Hopf algebra\, wh ere the comodule category of this new structure is precisely the zested ca tegory.\n\nFurthermore\, we present concrete formulas for constructing zes tings of pointed Hopf algebras\, particularly for cyclic group gradings\, encompassing both diagonal and non-diagonal braided vector spaces. Finally \, I will illustrate this construction with new examples of coquasi-Hopf a lgebras\, including those derived from Nichols algebras of super type A(1| 2) and the Fomin-Kirillov algebra in three variables.\n\nThis is joint wor k with Ivan Angiono and Giovanny Mora.\n LOCATION:https://researchseminars.org/talk/EQuAL/40/ END:VEVENT BEGIN:VEVENT SUMMARY:James Macpherson (Instituto Superior Técnico Lisboa) DTSTART:20250604T090000Z DTEND:20250604T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/41 DESCRIPTION:Title: C onstructing a categorified evaluation 2-functor for affine sl(3)\nby J ames Macpherson (Instituto Superior Técnico Lisboa) as part of European Q uantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/EQuAL/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Lentner (Universität Hamburg) DTSTART:20250618T090000Z DTEND:20250618T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/42 DESCRIPTION:Title: P roving the Logarithmic Kazhdan-Lusztig Correspondence\nby Simon Lentne r (Universität Hamburg) as part of European Quantum Algebra Lectures (EQu AL)\n\n\nAbstract\nThe logarithmic Kazhdan-Lusztig correspondence by B. Fe igin and others is a conjectural equivalence between braided tensor catego ries of representations of quantum groups and of certain vertex algebras\, which are algebras with an analytic flavour that appear in quantum field theory. I will give a gentle introduction into the physics side and recall some previous result of mine that certain analytic operators called scree nings fulfill the relations of an associated Nichols algebra.\n\nIn arXiv: 2501.10735 I recently gave a proof of the conjectural category equivalence in quite general situations\, also including Nichols algebras beyond quan tum groups\, under the assumption that the vertex algebra side is analytic ally nice enough. The proof is based on joint work with T. Creutzig and M. Rupert\, in which we settled first small cases. The proof is almost compl etely algebraic and interesting in its own right\, the essential statement is: Every braided tensor category together with a big commutative algebra A\, such that the category of local A-modules is semisimple and the categ ory of A-modules contains no additional simple modules\, is equivalent to representations of a quantum group associated to a Nichols algebra\, which is determined by certain Ext1-groups. In a certain sense\, this is a cate gorical and braided version of the Andruskiewitsch-Schneider program\, and prominently uses important results in this area by I. Angiono and others. \n LOCATION:https://researchseminars.org/talk/EQuAL/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Kenichi Shimizu (Shibaura Institute of Technology) DTSTART:20250924T090000Z DTEND:20250924T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/43 DESCRIPTION:Title: S imple algebras in Rep(uq(sl2))\nby Kenichi Shimizu (Shibaura Institute of Technology) as part of European Quantum Algebra Lectures (EQuAL)\n\n\n Abstract\nThe notion of an algebra in a tensor category plays an important role in the theory of tensor categories and their applications. Simple al gebras in finite tensor categories\, much like in ordinary ring theory\, f orm one of the most fundamental classes of algebras. Although simple algeb ras are especially important in Morita theory of finite tensor categories\ , the basic theory of simple algebras is not yet fully developed. In this talk\, I will present some Morita theoretic results on module categories o ver finite tensor categories and explain how these results can be applied to construct simple algebras with additional properties\, such as being Fr obenius or symmetric Frobenius. I will also present examples in the catego ry Rep(uq(sl2)) of modules over the small quantum sl2 at a root of unity o f odd order. This talk is based on joint work with Daisuke Nakamura\, Hin Wan Ng and Taiki Shibata.\n LOCATION:https://researchseminars.org/talk/EQuAL/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Halbig (Universität Marburg) DTSTART:20251008T090000Z DTEND:20251008T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/44 DESCRIPTION:Title: A non-semisimple version of the Kitaev model\nby Sebastian Halbig (Univ ersität Marburg) as part of European Quantum Algebra Lectures (EQuAL)\n\n \nAbstract\nIn 1997\, Alexei Kitaev proposed a foundational model for faul t-tolerant quantum computation based on complex semisimple Hopf algebras. Its key feature is a topologically invariant code space which is construct ed using combinatorial data encoded by a graph embedded into a closed orie nted surface. This ensures robustness against a wide range of errors. Beyo nd applications in quantum computing\, the model has remarkable connection s with combinatorics\, Hopf algebra representation theory\, homological al gebra\, and topological quantum field theories. In this talk\, based on jo int work with U.\\ Krähmer\, we present a generalisation of the Kitaev mo del to arbitrary finite-dimensional Hopf algebras. Two challenges prevent a straightforward approach. First\, the extended Hilbert space\, a Yetter- -Drinfeld module whose invariant submodule is the code space\, relies on a n involutive antipode---a condition equivalent to the underlying Hopf alge bra being semisimple. Second\, topological invariance is proven using proj ectors assembled from (co)integrals. Since we do not have these tools at o ur disposal\, we follow a new approach\, inspired by homological considera tions. We introduce involutive Hopf bimodules\, which are related to coeff icients of Hopf cyclic cohomology and allow us to form appropriate\, Yette r–Drinfeld valued\, variants of extend Hilbert spaces. Instead of consid ering invariant submodules\, the analoga of the code spaces arise as biten sor products---combinations of cotensor and tensor products. Our proof of their topological invariance relies on a notion of excision and uses actio ns of a group related to mapping class groups. Towards computing bitensor products\, we discuss induction-restriction type identities\, which are pa rticularly useful for eg. small quantum groups.\n LOCATION:https://researchseminars.org/talk/EQuAL/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Rhiannon Savage (University College London) DTSTART:20251022T090000Z DTEND:20251022T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/45 DESCRIPTION:Title: S tacks in Derived Bornological Geometry\nby Rhiannon Savage (University College London) as part of European Quantum Algebra Lectures (EQuAL)\n\n\ nAbstract\nRecent foundational work by Ben-Bassat\, Kelly\, and Kremnizer describes a model for derived analytic geometry as homotopical geometry re lative to the infinity category of simplicial commutative complete bornolo gical rings. In this talk\, we will discuss a representability theorem for derived stacks in these contexts and we will set out some new foundations for derived smooth geometry. We will also briefly discuss the representab ility of the derived moduli stack of non-linear elliptic partial different ial equations by an object we call a derived C∞-bornological affine sche me.\n LOCATION:https://researchseminars.org/talk/EQuAL/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Sanford (University of Edinburgh) DTSTART:20251105T100000Z DTEND:20251105T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/46 DESCRIPTION:Title: A Curious Braided Category over R\nby Sean Sanford (University of Edinb urgh) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\n In quantum mechanics\, time reversal symmetry is generally understood in t erms of an antiunitary operator. When a fusion category over C has an ant iunitary symmetry\, the fixed points of such a symmetry form a fusion cate gory over the real numbers. Since fusion categories are meant to describe systems of particles\, the resulting real fusion category describes those particles that are time-reversal invariant.\n \nIn recent joint work with Thibault Décoppet (https://arxiv.org/abs/2412.15019)\, we discovered a c ertain braided fusion category over R that represents a higher dimensional analogue of the quaternions. Based on recent conjectures regarding the Wi tt group of nondegenerate braided fusion categories\, we expect that this category generates the kernel of the map Witt(Vec_R)->Witt(Vec_C)\, which is just Z/2.\n \nIn this talk\, I will describe this curious category: its fusion rules and braiding\, how it comes about\, and it's significance fr om the perspective of condensed matter.\n LOCATION:https://researchseminars.org/talk/EQuAL/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Melody Molander (The Ohio State University) DTSTART:20251119T100000Z DTEND:20251119T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/47 DESCRIPTION:Title: S kein Theory of Affine ADE Subfactor Planar Algebras\nby Melody Molande r (The Ohio State University) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe Kuperberg Program seeks to describe presentati ons of subfactor planar algebras in order to classify them and prove resul ts about their corresponding categories purely diagrammatically. This prog ram has been completed for index less than 4 and remains an area of ongoin g research for index greater than 4. This talk will discuss the program at index 4. At this index\, planar algebras other than Temperley-Lieb have a n affine $A$\, $D$\, or $E$ principal graph. Categories corresponding to s ome of the affine A planar algebras are monoidally equivalent to cyclic po inted fusion categories. For affine $E_7$\, to prove sufficiency of its pr esentation\, we define a jellyfish algorithm. I will describe the jellyfis h algorithm using a half braiding and discuss that it gives a well-defined surjective function onto $C$.\n LOCATION:https://researchseminars.org/talk/EQuAL/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Zetto (Universität Hamburg) DTSTART:20251203T100000Z DTEND:20251203T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/48 DESCRIPTION:Title: C auchy-completions and extended TFTs\nby Markus Zetto (Universität Ham burg) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\n An enriched category is said to be Cauchy-complete if it admits all absolu te colimits — those weighted colimits that commute with every enriched f unctor. For instance\, an ordinary (Set-enriched) category is Cauchy-compl ete precisely when it is idempotent complete\, while an Ab-enriched catego ry is so when it is both idempotent complete and additive.\n\nI will exten d this notion to enriched (∞\,n)-categories and explain how\, via the co bordism hypothesis\, it yields a flexible and general formalism for const ructing and classifying framed fully extended topological field theories. In particular\, it clarifies the role of higher idempotents\, also known a s condensations in the sense of Gaiotto and Johnson-Freyd. Joint work in p rogress with David Reutter.\n LOCATION:https://researchseminars.org/talk/EQuAL/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Iordanis Romaidis (University of Edinburgh) DTSTART:20251217T100000Z DTEND:20251217T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/49 DESCRIPTION:Title: H olonomic skein modules\nby Iordanis Romaidis (University of Edinburgh) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nFor a reductive group G and a quantum parameter q\, skein theory assigns skein algebras to surfaces and skein modules to 3-manifolds. Skein modules of cl osed 3-manifolds at generic q were conjectured by Witten to be finite-dime nsional—a statement later proved by Gunningham\, Jordan\, and Safronov. In this talk\, I will present joint work with David Jordan on a generaliza tion of this conjecture to 3-manifolds with boundary. In this setting\, th e finiteness property is replaced by the condition that the skein module i s holonomic over the boundary skein algebra. Roughly\, a module is holonom ic if it is finitely generated and has a Lagrangian support. We prove holo nomicity for skein modules of GL2 and SL2​ by constructing transfer bimo dules\, and proving holonomicity preservation theorems analogous to those in the classical theory of D-modules.\n LOCATION:https://researchseminars.org/talk/EQuAL/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrià Marin Salvador (University of Oxford) DTSTART:20260121T100000Z DTEND:20260121T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/50 DESCRIPTION:Title: C ontinuous Tensor Categories and Direct Integrals\nby Adrià Marin Salv ador (University of Oxford) as part of European Quantum Algebra Lectures ( EQuAL)\n\n\nAbstract\nFinitely semisimple tensor categories are ubiquitous in quantum algebra: they appear in the representation theory of Hopf alge bras\, quantum groups\, TQFTs\, CFTs\, and others. However\, one usually n eeds extra adjectives to ensure that the categories one comes across satis fy the necessary finite properties of finitely semisimple tensor categorie s. Without enough adjectives\, one sometimes encounters tensor categories which are still “semisimple”\, but have continuously many simple objec ts\, and a generic object is a direct integral of such simple objects\, as opposed to a direct sum. In this talk\, we will introduce a new model to treat these type of categories: continuous tensor categories\; and provide some basic examples. Time permitting\, we will explore how continuous ten sor categories allow us to compute certain categories appearing in the stu dy of non-rational 2d conformal field theories such as the non-compact bos on and related theories.\n LOCATION:https://researchseminars.org/talk/EQuAL/50/ END:VEVENT BEGIN:VEVENT SUMMARY:David Jordan (University of Edinburgh) DTSTART:20260204T100000Z DTEND:20260204T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/51 DESCRIPTION:Title: D efects in skein theory\nby David Jordan (University of Edinburgh) as p art of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nI will giv e an overview of some recent progress constructing skein module invariants of 3-manifolds with defects. The defects to be discussed come in three d ifferent classes detailed below. Warning: with all these examples to cove r\, there might be precious few proofs!\n\nI will explain how "electric-ma gnetic 1-form symmetry" arises in skein theory as invertible line defects\ , and how it enters into (conjectural) electric-magnetic/Langlands/S-duali ty\, following joint work with Gunningham and Safronov.\n\nI will then dis cuss a recent work of Jennifer Brown and myself\; independent works of Jua n Ramon Gomez\; separate independent works of Julia Bierent and Matthias V ancraeynest\, which ares all around constructing defects in skein theory m odelling parabolic induction and restriction (by non-invertible plane defe cts)\, as well as Weyl group twists (by invertible line defects)\, with ap plications to the quantum A-polynomial\, the irregular Deligne--Simpson pr oblem and the abelianisation program of Gaiotto--Moore-Neitzke.\n\nFinally \, I will touch on some nascent joint work with Eric Chen and Iordanis Rom aidis aimed at constructing and analysing line defects associated to quant um symmetric pairs\, with a view towards exploring the relative Langlands program of Ben-Zvi--Sakellaridis--Venkatesh.\n LOCATION:https://researchseminars.org/talk/EQuAL/51/ END:VEVENT BEGIN:VEVENT SUMMARY:David Jaklitsch (University of Oslo) DTSTART:20260218T100000Z DTEND:20260218T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/52 DESCRIPTION:Title: ⊗-Frobenius functors and exact module categories\nby David Jaklitsch (University of Oslo) as part of European Quantum Algebra Lectures (EQuAL) \n\n\nAbstract\nFrobenius algebras are structures relevant in multiple dis ciplines such as subfactor theory\, conformal field theory or topological field theory. The purpose of the talk is to present results based on arxiv :2501.16978 about preservation and construction of Frobenius algebras. We introduce the notion of ⊗-Frobenius functors and provide characterizatio ns relating them with the other Frobenius-type functors. These are used to twist module categories. Results on sufficient conditions for the preserv ation of certain properties under twisting and preservation of Frobenius a lgebras are summarized.\n LOCATION:https://researchseminars.org/talk/EQuAL/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Justine Fasquel (Université Bourgogne) DTSTART:20260304T100000Z DTEND:20260304T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/53 DESCRIPTION:Title: P artial VS Inverse quantum hamiltonian reductions\nby Justine Fasquel ( Université Bourgogne) as part of European Quantum Algebra Lectures (EQuAL )\n\n\nAbstract\nW-algebras form a rich family of vertex algebras\, arisin g from simple Lie algebras and their nilpotent orbits through a cohomologi cal procedure known as quantum hamiltonian reduction. As the nilpotent orb it grows\, the reduction becomes increasingly intricate\, while the repres entation theory of the corresponding W-algebra is simplified. In this talk \, I would like to discuss two additional concepts\, the partial and inver se quantum hamiltonian reductions\, that help understanding the quantum ha miltonian reduction and clarify how W‑algebras attached to different nil potent orbits are related.\n LOCATION:https://researchseminars.org/talk/EQuAL/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Huston (University of Leeds) DTSTART:20260318T100000Z DTEND:20260318T110000Z DTSTAMP:20260422T225656Z UID:EQuAL/54 DESCRIPTION:Title: A gentle introduction to fusion 2-categories\nby Peter Huston (Universi ty of Leeds) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbs tract\nFusion 2-categories are a generalization of fusion 1-categories\, c orresponding under the cobordism hypothesis to fully extended (3+1)D TQFTs . In this talk\, I will motivate the definition of fusion 2-category\, exp lore the classification of fusion 2-categories given in arxiv:2411.05907\, and sketch some applications of fusion 2-categories in studying non-inver tible symmetries.\n LOCATION:https://researchseminars.org/talk/EQuAL/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Kürsat Sözer (Université de Lille) DTSTART:20260422T090000Z DTEND:20260422T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/55 DESCRIPTION:Title: Q uantum invariants of maps from 3-manifolds to homotopy 2-types\nby Kü rsat Sözer (Université de Lille) as part of European Quantum Algebra Lec tures (EQuAL)\n\n\nAbstract\nTopological quantum field theories (TQFTs) pr ovide a powerful framework for constructing invariants of manifolds. Their extension to homotopy quantum field theories (HQFTs) refines these invari ants by incorporating maps to a target space. In this talk\, I recall Dijk graaf–Witten invariants and their state-sum description\, and explain th eir extension to HQFTs with target BG. I then discuss the passage from gro ups to crossed modules as algebraic models for homotopy 2-types\, and outl ine the associated tensor-categorical and Hopf-algebraic structures\, incl uding Hopf crossed module coalgebras. Finally\, I present joint work with Alexis Virelizier\, where we construct Kuperberg-type invariants for pairs (M\,g)\, with g∈[M\,B\\chi] where \\chi is a crossed module. The constr uction uses \\chi-labeled Heegaard diagrams and involutory Hopf \\chi-coal gebras\, extending the classical Kuperberg invariant and admitting an inte rpretation in terms of invariant of flat principal 2-bundles.\n LOCATION:https://researchseminars.org/talk/EQuAL/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Blas Torrecillas (Universidad de Almería) DTSTART:20260506T090000Z DTEND:20260506T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/56 DESCRIPTION:by Blas Torrecillas (Universidad de Almería) as part of Europ ean Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/EQuAL/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilaria Colazzo (University of Leeds) DTSTART:20260520T090000Z DTEND:20260520T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/57 DESCRIPTION:by Ilaria Colazzo (University of Leeds) as part of European Qu antum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/EQuAL/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristina Anghel (Université Clermont Auvergne) DTSTART:20260603T090000Z DTEND:20260603T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/58 DESCRIPTION:by Cristina Anghel (Université Clermont Auvergne) as part of European Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/EQuAL/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Tony Zorman (Universität Hamburg) DTSTART:20260617T090000Z DTEND:20260617T100000Z DTSTAMP:20260422T225656Z UID:EQuAL/59 DESCRIPTION:by Tony Zorman (Universität Hamburg) as part of European Quan tum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/EQuAL/59/ END:VEVENT END:VCALENDAR