BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sergei Gukov (California Institute of Technology) DTSTART:20200522T160000Z DTEND:20200522T170000Z DTSTAMP:20260424T221532Z UID:TQFT/1 DESCRIPTION:Title: Hidden algebraic structures in topology\nby Sergei Gukov (Californ ia Institute of Technology) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\nWhich 4-manifold invariants can detect th e Gluck twist? And\, which 3-manifold invariants can detect the difference between surgeries on mutant knots? What is the most powerful topological quantum field theory (TQFT)? Guided by questions like these\, we will look for new invariants of 3-manifolds and smooth 4-manifolds. Traditionally\, a construction of many such invariants and TQFTs involves a choice of cer tain algebraic structure\, so that one can talk about "invariants for SU(2 )" or a "TQFT defined by a given Frobenius algebra." Surprisingly\, recent developments lead to an opposite phenomenon\, where algebraic structures are labeled by 3-manifolds and 4-manifolds\, so that one can speak of VOA- valued invariants of 4-manifolds or MTC-valued invariants of 3-manifolds. Explaining these intriguing connections between topology and algebra will be the main goal of this talk.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Danica Kosanović (Max-Planck Institut für Mathematik) DTSTART:20200529T160000Z DTEND:20200529T170000Z DTSTAMP:20260424T221532Z UID:TQFT/2 DESCRIPTION:Title: Knot invariants from homotopy theory\nby Danica Kosanović (Max-Pl anck Institut für Mathematik) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe embedding calculus of Goodwillie a nd Weiss is a certain homotopy theoretic technique for studying spaces of embeddings. When applied to the space of knots this method gives a sequenc e of knot invariants which are conjectured to be universal Vassiliev invar iants. This is remarkable since such invariants have been constructed only rationally so far and many questions about possible torsion remain open. In this talk I will present a geometric viewpoint on the embedding calculu s\, which enables explicit computations. In particular\, we prove that the se knot invariants are surjective maps\, confirming a part of the universa lity conjecture\, and we also confirm the full conjecture rationally\, usi ng some recent results in the field. Hence\, these invariants are at least as good as configuration space integrals.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Khovanov (Columbia University) DTSTART:20200619T160000Z DTEND:20200619T170000Z DTSTAMP:20260424T221532Z UID:TQFT/3 DESCRIPTION:Title: Introduction to foam evaluation\nby Mikhail Khovanov (Columbia Uni versity) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n \n\nAbstract\nFoam evaluation was discovered by Louis-Hardrien Robert and Emmanuel Wagner slightly over three years ago. It's a remarkable formula a ssigning a symmetric function to a foam\, that is\, to a decorated 2-dimen sional CW-complex embedded in three-space. We'll explain their formula in the 3-color case in the context of unoriented foams and discuss its relati on to Kronheimer-Mrowka homology of graphs and the four-color theorem.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:John Huerta (IST and CAMGSD) DTSTART:20200605T160000Z DTEND:20200605T170000Z DTSTAMP:20260424T221532Z UID:TQFT/4 DESCRIPTION:Title: Bundle Gerbes on Supermanifolds\nby John Huerta (IST and CAMGSD) a s part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstra ct\nBundle gerbes are a generalization of line bundles that play an import ant role in constructing WZW models with boundary. With an eye to applicat ions for WZW models with superspace target\, we describe the classificatio n of bundle gerbes on supermanifolds\, and sketch a proof of their existen ce for large families of super Lie groups.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Marko Stošić (Instituto Superior Técnico and CAMGSD) DTSTART:20200626T160000Z DTEND:20200626T170000Z DTSTAMP:20260424T221532Z UID:TQFT/5 DESCRIPTION:Title: Rational and algebraic links and knots-quivers correspondence\nby Marko Stošić (Instituto Superior Técnico and CAMGSD) as part of Topolog ical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will start with a brief overview of knots-quivers correspondence\, where colored HOMF LY-PT\n(or BPS) invariants of the knot are expressed as motivic Donaldson- Thomas invariants of a corresponding quiver.\nThis deep conjectural relati onship already had some surprising applications.\nIn this talk I will focu s on showing that the knots-quivers correspondence holds for rational link s\, as well as much larger class of arborescent links (algebraic links in the sense of Conway). This is done by extending the correspondence to tang les\, and showing that the set of tangles satisfying tangles-quivers corre spondence is closed under the tangle addition operation.\n\nThis talk is b ased on joint work with Paul Wedrich.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Antti Kupiainen (University of Helsinki) DTSTART:20200612T160000Z DTEND:20200612T170000Z DTSTAMP:20260424T221532Z UID:TQFT/6 DESCRIPTION:Title: Integrability of Liouville Conformal Field Theory\nby Antti Kupiai nen (University of Helsinki) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nA. Polyakov introduced Liouville Conform al Field theory (LCFT) in 1981 as a way to put a natural measure on the se t of Riemannian metrics over a two dimensional manifold. Ever since\, the work of Polyakov has echoed in various branches of physics and mathematics \, ranging from string theory to probability theory and geometry.\nIn the context of 2D quantum gravity models\, Polyakov’s approach is conjectura lly equivalent to the scaling limit of Random Planar Maps and through the Alday-Gaiotto-Tachikava correspondence LCFT is conjecturally related to ce rtain 4D Yang-Mills theories. Through the work of Dorn\,Otto\, Zamolodchik ov and Zamolodchikov and Teschner LCFT is believed to be to a certain exte nt integrable.\n\nI will review a probabilistic construction of LCFT devel oped together with David\, Rhodes and Vargas and recent proofs of the inte grability of LCFT:\n\n-The proof in a joint work with Rhodes and Vargas of the DOZZ formula\n(Annals of Mathematics\, 81-166\,191 (2020))\n\n-The pr oof in a joint work with Guillarmou\, Rhodes and Vargas of the\nbootstrap conjecture for LCFT (arXiv:2005.11530).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ezra Getzler (Northwestern University) DTSTART:20200724T160000Z DTEND:20200724T170000Z DTSTAMP:20260424T221532Z UID:TQFT/7 DESCRIPTION:Title: Gluing local gauge conditions in BV quantum field theory\nby Ezra Getzler (Northwestern University) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nIn supersymmetric sigma models\, th ere is frequently no global choice of Lagrangian submanifold for BV quanti zation. I will take the superparticle\, a toy version of the Green Schwarz superstring\, as my example\, and show how to extend the light-cone gauge to the physically relevant part of phase space. This involves extending a formula of Mikhalkov and A. Schwarz that generalizes the prescription of Batalin and Vilkovisky for the construction of the functional integral.\n\ nThis is joint work with S. Pohorence.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexis Virelizier (Université de Lille) DTSTART:20200911T160000Z DTEND:20200911T170000Z DTSTAMP:20260424T221532Z UID:TQFT/8 DESCRIPTION:Title: Homotopy Quantum Field Theories\nby Alexis Virelizier (Université de Lille) as part of Topological Quantum Field Theory Club (IST\, Lisbon) \n\n\nAbstract\nHomotopy quantum field theories (HQFTs) generalize topolog ical quantum field theories (TQFTs) by replacing manifolds by maps from ma nifolds to a fixed target space $X$. For example\, any cohomology class in $H^3(X)$ defines a 3-dimensional HQFT with target $X$. If $X$ is aspheric al\, that is $X = K(G\, 1)$ for some group $G$\, then this cohomological H QFT is related to the Dijkgraaf-Witten invariant and is computed as a Tura ev-Viro state sum via the category of $G$-graded vector spaces. More gener ally\, the state sum Turaev-Viro TQFT and the surgery Reshetikhin-Turaev T QFT extend to HQFTs (using graded fusion categories) which are related via the graded categorical center.
This is joint work with V. Turaev.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Ricardo Campos (CNRS - University of Montpellier) DTSTART:20200710T160000Z DTEND:20200710T170000Z DTSTAMP:20260424T221532Z UID:TQFT/9 DESCRIPTION:Title: The homotopy type of associative and commutative algebras\nby Rica rdo Campos (CNRS - University of Montpellier) as part of Topological Quant um Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nGiven a topological spa ce\, how much of its homotopy type is captured by its algebra of singular cochains? The experienced rational homotopy theorist will argue that one s hould consider instead a commutative algebra of forms. This raises the mor e algebraic question "Given a dg commutative algebra\, how much of its hom otopy type (quasi-isomorphism type) is contained in its associative part?" Despite its elementary formulation\, this question turns out to be surpri singly subtle and has important consequences.\nIn this talk\, I will show how one can use operadic deformation theory to give an affirmative answer in characteristic zero.\nWe will also see how the Koszul duality between L ie algebras and commutative algebras allows us to use similar arguments to deduce that under good conditions Lie algebras are determined by the (ass ociative algebra structure of) their universal enveloping algebras.\n\n\n( Joint with Dan Petersen\, Daniel Robert-Nicoud and Felix Wierstra and base d on arXiv:1904.03585)\n LOCATION:https://stable.researchseminars.org/talk/TQFT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Boavida de Brito (Instituto Superior Técnico and CAMGSD) DTSTART:20200717T160000Z DTEND:20200717T170000Z DTSTAMP:20260424T221532Z UID:TQFT/10 DESCRIPTION:Title: Galois symmetries of knot spaces\nby Pedro Boavida de Brito (Inst ituto Superior Técnico and CAMGSD) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nI’ll describe how the absolute Galois group of the rationals acts on a space which is closely related to the space of all knots. The path components of this space form a finitely generated abelian group which is\, conjecturally\, a universal receptacle for integral finite-type knot invariants. The added Galois symmetry allows us to extract new information about its homotopy and homology beyond char acteristic zero. I will then discuss some work in progress concerning high er-dimensional variants.\n\nThis is joint work with Geoffroy Horel.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:André Henriques (University of Oxford) DTSTART:20200925T160000Z DTEND:20200925T170000Z DTSTAMP:20260424T221532Z UID:TQFT/11 DESCRIPTION:Title: Reps of relative mapping class groups via conformal nets\nby Andr é Henriques (University of Oxford) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nGiven a surface with boundary Σ\ , its relative mapping class group is the quotient of Diff(Σ) by the subg roup of maps which are isotopic to the identity via an isotopy that fixes the boundary pointwise. (If Σ has no boundary\, then that's the usual map ping class group\; if Σ is a disc\, then that's the group Diff(S¹) of di ffeomorphisms of S¹.)\n\nConformal nets are one of the existing axiomatiz ations of chiral conformal field theory (vertex operator algebras being an other one). We will show that\, given an arbitrary conformal net and a sur face with boundary Σ\, we get a continuous projective unitary representat ion of the relative mapping class group (orientation reversing elements ac t by anti-unitaries). When the conformal net is rational and Σ is a close d surface (i.e. ∂Σ = ∅)\, then these representations are finite dimen sional and well known. When the conformal net is not rational\, then we mu st require ∂Σ ≠ ∅ for these representations to be defined. We will try to explain what goes wrong when Σ is a closed surface and the conform al net is not rational.
\n\nThe material presented in this talk is par tially based on my paper arXiv:1409.8672 with Arthur Bartels and Chris Dou glas.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Masoero (Group of Mathematical Physics\, University of Lisb on) DTSTART:20201002T160000Z DTEND:20201002T170000Z DTSTAMP:20260424T221532Z UID:TQFT/13 DESCRIPTION:Title: Counting Monster Potentials\nby Davide Masoero (Group of Mathemat ical Physics\, University of Lisbon) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe monster potentials were intr oduced by  Bazhanov-Lukyanov-Zamolodchikov in the framework of the ODE/IM correspondence. They should in fact be in 1:1 correspondence with excited states of the Quantum KdV model (an Integrable Conformal Field Theory) si nce they are the most general potentials whose spectral determinant solves the Bethe Ansatz equations of such a theory. By studying the large moment um limit of the monster potentials\, I retrieve that:\n\n1) The poles of t he monster potentials asymptotically condensate about the complex equilibr ia of the ground state potential.\n\n2) The leading correction to such asy mptotics is described by the roots of Wronskians of Hermite polynomials.\n \nThis allows me  to associate to each partition of N a unique monster po tential with N roots\, of which I compute the spectrum. As a consequence\, I prove up to a few mathematical technicalities that\, fixed an integer N \, the number of monster potentials with N roots coincide with the number of integer partitions of N\, which is the dimension of the level N subspac e of the quantum KdV model. In striking accordance with the ODE/IM corresp ondence.\n\nThe talk is based on the preprint https://arxiv.org/abs/2009. 14638 \, written in collaboration with Riccardo Conti (Group of Mathematic al Physics of Lisbon University).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Sutherland (Group of Mathematical Physics\, University of Lisb on) DTSTART:20200703T160000Z DTEND:20200703T170000Z DTSTAMP:20260424T221532Z UID:TQFT/14 DESCRIPTION:Title: Mirror symmetry for Painlevé surfaces\nby Tom Sutherland (Group of Mathematical Physics\, University of Lisbon) as part of Topological Qua ntum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThis talk will survey aspects of mirror symmetry for ten families of non-compact hyperkähler m anifolds on which the dynamics of one of the Painlevé equations is natura lly defined. They each have a pair of natural realisations: one as the com plement of a singular fibre of a rational elliptic surface and another as the complement of a triangle of lines in a (singular) cubic surface. The t wo realisations relate closely to a space of stability conditions and a cl uster variety of a quiver respectively\, providing a perspective on SYZ mi rror symmetry for these manifolds. I will discuss joint work in progress w ith Helge Ruddat studying the canonical basis of theta functions on these cubic surfaces.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Shapiro (University of Notre Dame) DTSTART:20201009T160000Z DTEND:20201009T170000Z DTSTAMP:20260424T221532Z UID:TQFT/15 DESCRIPTION:Title: Cluster realization of quantum groups and higher Teichmüller theory< /a>\nby Alexander Shapiro (University of Notre Dame) as part of Topologica l Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nQuantum higher T eichmüller theory\, as described by Fock and Goncharov\, endows a quantum character variety on a surface $S$ with a cluster structure. The latter a llows one to construct a canonical representation of the character variety \, which happens to be equivariant with respect to an action of the mappin g class group of $S$. It was conjectured by the authors that these represe ntations behave well with respect to cutting and gluing of surfaces\, whic h in turn yields an analogue of a modular functor. In this talk\, I will s how how the quantum group and its positive representations arise in this c ontext. I will also explain how the modular functor conjecture is related to the closedness of positive representations under tensor products as wel l as to the non-compact analogue of the Peter-Weyl theorem. If time permit s\, I will say a few words about the proof of the conjecture.\n\nThis talk is based on joint works with Gus Schrader.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Miranda Cheng (University of Amsterdam) DTSTART:20201016T160000Z DTEND:20201016T170000Z DTSTAMP:20260424T221532Z UID:TQFT/16 DESCRIPTION:Title: Quantum modular forms and $3$-manifolds\nby Miranda Cheng (Univer sity of Amsterdam) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nQuantum modular forms are functions on rational nu mbers that have rather mysterious weak modular properties. Mock modular fo rms and false theta functions are examples of holomorphic functions on the upper-half plane which lead to quantum modular forms. Inspired by the $3d -3d$ correspondence in string theory\, new topological invariants named ho mological blocks for (in particular plumbed) three-manifolds have been pro posed a few years ago. My talk aims to explain the recent observations on the quantum modular properties of the homological blocks\, as well as the relation to logarithmic vertex algebras.\n\nThe talk will be based on a se ries of work in collaboration with Sungbong Chun\, Boris Feigin\, Francesc a Ferrari\, Sergei Gukov\, Sarah Harrison\, and Gabriele Sgroi.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Mackaay (University of Algarve) DTSTART:20201106T170000Z DTEND:20201106T180000Z DTSTAMP:20260424T221532Z UID:TQFT/17 DESCRIPTION:Title: The double-centralizer theorem in 2-representation theory and its app lications\nby Marco Mackaay (University of Algarve) as part of Topolog ical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nFinitary bire presentation theory of finitary bicategories is a categorical analog of fi nite-dimensional representation theory of finite-dimensional algebras. The role of the simples is played by the so-called simple transitive birepres entations and the classification of the latter\, for any given finitary bi category\, is a fundamental problem in finitary birepresentation theory (t he classification problem). \nAfter briefly reviewing the basics of birepr esentation theory\, I will explain an analog of the double centralizer the orem for finitary bicategories\, which was inspired by Etingof and Ostrik' s double centralizer theorem for tensor categories. As an application\, I will show how it can be used to (almost completely) solve the classificati on problem for Soergel bimodules in any finite Coxeter type.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:João Faria Martins (University of Leeds) DTSTART:20201030T170000Z DTEND:20201030T180000Z DTSTAMP:20260424T221532Z UID:TQFT/18 DESCRIPTION:Title: Crossed modules\, homotopy 2-types\, knotted surfaces and welded knot s\nby João Faria Martins (University of Leeds) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will review the construction of invariants of knots\, loop braids and knotted surfaces de rived from finite crossed modules. I will also show a method to calculate the algebraic homotopy 2-type of the complement of a knotted surface $\\Si gma$ embedded in the 4-sphere from a movie presentation of $\\Sigma$. This will entail a categorified form of the Wirtinger relations for a knot gro up. Along the way I will also show applications to welded knots in terms o f a biquandle related to the homotopy 2-type of the complement of the tube of a welded knots.\n\nThe last stages of this talk are part of the framew ork of the Leverhulme Trust research project grant: RPG-2018-029: “Emer gent Physics From Lattice Models of Higher Gauge Theory.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Tudor Dimofte (University of California\, Davis) DTSTART:20201120T170000Z DTEND:20201120T180000Z DTSTAMP:20260424T221532Z UID:TQFT/19 DESCRIPTION:Title: $3d$ A and B models and link homology\nby Tudor Dimofte (Universi ty of California\, Davis) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will discuss some current work (with Garn er\, Hilburn\, Oblomkov\, and Rozansky) on new and old constructions of HO MFLY-PT link homology in physics and mathematics\, and new connections amo ng them. In particular\, we relate the classic proposal of Gukov-Schwarz-V afa\, involving M-theory on a resolved conifold\, to constructions in $3d$ TQFT's. In the talk\, I will focus mainly on the $3d$ part of the story. I'll review general aspects of $3d$ TQFT's\, in particular the "$3d$ A and B models" that play a role here\, and how link homology appears in them.\ n LOCATION:https://stable.researchseminars.org/talk/TQFT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Ostrik (University of Oregon) DTSTART:20201204T170000Z DTEND:20201204T180000Z DTSTAMP:20260424T221532Z UID:TQFT/20 DESCRIPTION:Title: Two dimensional topological field theories and partial fractions\ nby Victor Ostrik (University of Oregon) as part of Topological Quantum Fi eld Theory Club (IST\, Lisbon)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/TQFT/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Penka Georgieva (Sorbonne Université) DTSTART:20201218T170000Z DTEND:20201218T180000Z DTSTAMP:20260424T221532Z UID:TQFT/21 DESCRIPTION:Title: Klein TQFT and real Gromov-Witten invariants\nby Penka Georgieva (Sorbonne Université) as part of Topological Quantum Field Theory Club (I ST\, Lisbon)\n\n\nAbstract\nIn this talk I will explain how the Real Gromo v-Witten theory of local 3-folds with base a Real curve gives rise to an e xtension of a 2d Klein TQFT. The latter theory is furthermore semisimple w hich allows for complete computation from the knowledge of a few basic ele ments which can be computed explicitly. As a consequence of the explicit e xpressions we find in the Calabi-Yau case\, we obtain the expected Gopukum ar-Vafa formula and relation to SO/Sp Chern-Simons theory.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Dragović (Univ. Texas at Dallas) DTSTART:20201113T170000Z DTEND:20201113T180000Z DTSTAMP:20260424T221532Z UID:TQFT/22 DESCRIPTION:Title: Ellipsoidal billiards\, extremal polynomials\, and partitions\nby Vladimir Dragović (Univ. Texas at Dallas) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\n

A comprehensive study of periodic trajectories of the billiards within ellipsoids in the d-dimen sional Euclidean space is presented. The novelty of the approach is based on a relationship established between the periodic billiard trajectories a nd the extremal polynomials of the Chebyshev type on the systems of d inte rvals on the real line. Classification of periodic trajectories is based on a new combinatorial object: billiard partitions.

\n

The case study of trajectories of small periods T\, d ≤ T ≤ 2d is given. In particul ar\, it is proven that all d-periodic trajectories are contained in a coor dinate-hyperplane and that for a given ellipsoid\, there is a unique set o f caustics which generates d + 1-periodic trajectories. A complete catalog of billiard trajectories with small periods is provided for d = 3.

\n

The talk is based on the following papers:

\n

V. Dragović\, M. Ra dnović\, Periodic ellipsoidal billiard trajectories and extremal polynom ials\, Communications Mathematical Physics\, 2019\, Vol. 372\, p. 183-211.

\n

G. Andrews\, V. Dragović\, M. Radnović\, Combinatorics of the p eriodic billiards within quadrics\, \narXiv: 1908.01026\, The Ramanujan Jo urnal\, DOI: 10.1007/s11139-020-00346-y.

\n LOCATION:https://stable.researchseminars.org/talk/TQFT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Brent Pym (McGill University) DTSTART:20210115T170000Z DTEND:20210115T180000Z DTSTAMP:20260424T221532Z UID:TQFT/23 DESCRIPTION:Title: Multiple zeta values in deformation quantization\nby Brent Pym (M cGill University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn 1997\, Kontsevich gave a universal solution to t he deformation quantization problem in mathematical physics: starting from any Poisson manifold (the classical phase space)\, it produces a noncommu tative algebra of quantum observables by deforming the ordinary\nmultiplic ation of functions. His formula is a Feynman expansion whose Feynman integ rals give periods of the moduli space of marked holomorphic disks. I will describe joint work with Peter Banks and Erik Panzer\, in which we prove t hat Kontsevich's integrals evaluate to integer-linear\ncombinations of mul tiple zeta values\, building on Francis Brown's theory of polylogarithms o n the moduli space of genus zero curves.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Beliakova (University of Zürich) DTSTART:20201211T170000Z DTEND:20201211T180000Z DTSTAMP:20260424T221532Z UID:TQFT/24 DESCRIPTION:Title: Cyclotomic expansions of the $gl_N$ knot invariants\nby Anna Beli akova (University of Zürich) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nNewton’s interpolation is a method to reconstruct a function from its values at different points. In the talk I will explain how one can use this method to construct an explicit basis f or the center of quantum $gl_N$ and to show that the universal $gl_N$ knot invariant expands in this basis. This will lead us to an explicit constru ction of the so-called unified invariants for integral homology 3-spheres\ , that dominate all Witten-Reshetikhin-Turaev invariants. This is a joint work with Eugene Gorsky\, that generalizes famous results of Habiro for $s l_2$.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Severin Bunk (Univ. Hamburg) DTSTART:20210129T170000Z DTEND:20210129T180000Z DTSTAMP:20260424T221532Z UID:TQFT/25 DESCRIPTION:Title: Universal Symmetries of Gerbes and Smooth Higher Group Extensions \nby Severin Bunk (Univ. Hamburg) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nGerbes are geometric objects descri bing the third integer cohomology group of a manifold and the B-field in s tring theory\; they can essentially be understood as bundles of categories whose fibre is equivalent to the category of vector spaces. Starting from a hands-on example\, I will explain gerbes and their categorical features . The main topic of this talk will then be the study of symmetries of gerb es in a universal manner. We will see that these symmetries are completely encoded in an extension of smooth 2-groups. In the last part\, I will sur vey how this construction can be used to provide a new smooth model for th e string group\, via a theory of group extensions in $\\infty$-topoi.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Renee Hoekzema (Univ. Oxford) DTSTART:20210122T170000Z DTEND:20210122T180000Z DTSTAMP:20260424T221532Z UID:TQFT/26 DESCRIPTION:Title: Manifolds with odd Euler characteristic and higher orientability\ nby Renee Hoekzema (Univ. Oxford) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nOrientable manifolds have even Eule r characteristic unless the dimension is a multiple of 4. I give a general isation of this theorem: $k$-orientable manifolds have even Euler characte ristic (and in fact vanishing top Wu class)\, unless their dimension is $2 ^{k+1}m$ for some integer $m$. Here we call a manifold $k$-orientable if t he $i^{\\rm th}$ Stiefel-Whitney class vanishes for all $0 < i < 2^k$. Thi s theorem is strict for $k=0\,1\,2\,3$\, but whether there exist 4-orienta ble manifolds with an odd Euler characteristic is a new open question. Suc h manifolds would have dimensions that are a multiple of 32. I discuss man ifolds of dimension high powers of 2 and present the results of calculatio ns on the cohomology of the second Rosenfeld plane\, a special 64-dimensio nal manifold with odd Euler characteristic.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Elias (Univ. Oregon) DTSTART:20210226T170000Z DTEND:20210226T180000Z DTSTAMP:20260424T221532Z UID:TQFT/27 DESCRIPTION:Title: Introduction to the Hecke category and the diagonalization of the ful l twist\nby Ben Elias (Univ. Oregon) as part of Topological Quantum Fi eld Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe group algebra of the sym metric group has a large commutative subalgebra generated by Young-Jucys-M urphy elements\, which acts diagonalizably on any irreducible representati on. The goal of this talk is to give an accessible introduction to the cat egorification of this story. The main players are: Soergel bimodules\, whi ch categorify the Hecke algebra of the symmetric group\; Rouquier complexe s\, which categorify the braid group where Young-Jucys-Murphy elements liv e\; and the Elias-Hogancamp theory of categorical diagonalization\, which allows one to construct projections to "eigencategories."\n LOCATION:https://stable.researchseminars.org/talk/TQFT/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Vaz (Université Catholique de Louvain\, Belgium) DTSTART:20210108T170000Z DTEND:20210108T180000Z DTSTAMP:20260424T221532Z UID:TQFT/28 DESCRIPTION:Title: Categorification of Verma Modules in low-dimensional topology\nby Pedro Vaz (Université Catholique de Louvain\, Belgium) as part of Topolo gical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn this talk I will review the program of categorification of Verma modules and explai n their applications to low-dimensional topology\, namely to the construct ion of Khovanov invariants for links in the solid torus via a categorifica tion of the blob algebra.\n\nThe material presented spreads along several collaborations with Abel Lacabanne\, and Grégoire Naisse.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Florio Ciaglia (MPI Leipzig) DTSTART:20210212T170000Z DTEND:20210212T180000Z DTSTAMP:20260424T221532Z UID:TQFT/29 DESCRIPTION:Title: A groupoid-based perspective on quantum mechanics\nby Florio Ciag lia (MPI Leipzig) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\n

In this talk\, I will expound a point of view on the theoretical investigation of the foundations and mathematical formali sm of quantum mechanics which is based on Schwinger’s “Symbolism of at omic measurement” [8] on the physical side\, and on the notion of groupo id on the mathematical side. I will start by reviewing the “development ” of quantum mechanics and its formalism starting from Schrödinger’s wave mechanics\, passing through the Hilbert space quantum mechanics\, and arriving at the $C^∗$-algebraic formulation of quantum mechanics in ord er to give an intuitive idea of what is the “place” of the groupoid-ba sed approach to quantum theories presented here. Then\, after (what I hope will be) a highly digestible introduction to the notion of groupoid\, I w ill review two historic experimental instances in which the shadow of the structure of groupoid may be glimpsed\, namely\, the Ritz-Rydberg combinat ion principle\, and the Stern-Gerlach experiment. The last part of the tal k will be devoted to building a bridge between the groupoid-based approach to quantum mechanics and the more familiar $C^∗$-algebraic one by analy sing how to obtain a (possibly) non-commutative algebra out of a given gro upoid. Two relevant examples will be discussed\, and some comment on futur e directions (e.g.\, the composition of systems) will close the talk. The material presented is part of an ongoing project developed together with D r. F. Di Cosmo\, Prof. A. Ibort\, and Prof. G. Marmo. In particular\, the discrete-countable theory has already appeared in [1\, 2\, 3\, 4\, 5\, 6\, 7].

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References

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[1] F. M. Ciaglia\, F. Di Cosmo\, A. Ibort \, and G. Marmo. Evolution of Classical and Quantum States in the Groupoi d Picture of Quantum Mechanics. Entropy\, 11(22):1292 – 18\, 2020.

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[2] F. M. Ciaglia\, F. Di Cosmo\, A. Ibort\, and G. Marmo. Schwinger ’s Picture of Quantum Mechanics. International Journal of Geometric Meth ods in Modern Physics\, 17(04):2050054 (14)\, 2020.

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[3] F. M. Ci aglia\, F. Di Cosmo\, A. Ibort\, and G. Marmo. Schwinger’s Picture of Qu antum Mechanics IV: Composition and independence. International Journal of Geometric Methods in Modern Physics\, 17(04):2050058 (34)\, 2020.

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[4] F. M. Ciaglia\, A. Ibort\, and G. Marmo. A gentle introduction to S chwinger’s formulation of quantum mechanics: the groupoid picture. Mode rn Physics Letters A\, 33(20):1850122–8\, 2018.

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[5] F. M. Ciag lia\, A. Ibort\, and G. Marmo. Schwinger’s Picture of Quantum Mechanics I: Groupoids. International Journal of Geometric Methods in Modern Physics \, 16(08):1950119 (31)\, 2019.

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[6] F. M. Ciaglia\, A. Ibort\, an d G. Marmo. Schwinger’s Picture of Quantum Mechanics II: Algebras and Ob servables. International Journal of Geometric Methods in Modern Physics\, 16(09):1950136 (32)\, 2019.

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[7] F. M. Ciaglia\, A. Ibort\, and G . Marmo. Schwinger’s Picture of Quantum Mechanics III: The Statistical I nterpretation. International Journal of Geometric Methods in Modern Physic s\, 16(11):1950165 (37)\, 2019.

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[8] J. Schwinger. Quantum Mechani cs\, Symbolism of Atomic Measurements. Springer-Verlag\, Berlin\, 2001. \n LOCATION:https://stable.researchseminars.org/talk/TQFT/29/ END:VEVENT BEGIN:VEVENT SUMMARY:David Reutter (MPI Bonn) DTSTART:20210219T170000Z DTEND:20210219T180000Z DTSTAMP:20260424T221532Z UID:TQFT/30 DESCRIPTION:Title: Semisimple topological field theories in even dimensions\nby Davi d Reutter (MPI Bonn) as part of Topological Quantum Field Theory Club (IST \, Lisbon)\n\n\nAbstract\nA major open problem in quantum topology is the construction of an oriented 4-dimensional topological quantum field theory (TQFT) in the sense of Atiyah-Segal which is sensitive to exotic smooth s tructure. More generally\, how much manifold topology can a TQFT see? \n\n In this talk\, I will answer this question for semisimple field theories i n even dimensions — I will sketch a proof that such field theories can a t most see the stable diffeomorphism type of a manifold and conversely\, t hat if two sufficiently finite manifolds are not stably diffeomorphic then they can be distinguished by semisimple field theories. In this context\, `semisimplicity' is a certain algebraic condition applying to all current ly known examples of vector-space-valued TQFTs\, including `unitary field theories’\, and `once-extended field theories' which assign algebras or linear categories to codimension 2 manifolds. I will discuss implications in dimension 4\, such as the fact that oriented semisimple field theories cannot see smooth structure\, while unoriented ones can. \n\nThroughout\, I will use the Crane-Yetter field theory associated to a ribbon fusion cat egory\, as a guiding example.\n\nThis is based on arXiv:2001.02288 and joi nt work in progress with Chris Schommer-Pries.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Ikshu Neithalath (UCLA\, California) DTSTART:20210312T170000Z DTEND:20210312T180000Z DTSTAMP:20260424T221532Z UID:TQFT/31 DESCRIPTION:Title: Skein Lasagna modules of 2-handlebodies\nby Ikshu Neithalath (UCL A\, California) as part of Topological Quantum Field Theory Club (IST\, Li sbon)\n\n\nAbstract\nMorrison\, Walker and Wedrich recently defined a gene ralization of Khovanov-Rozansky homology to links in the boundary of a 4-m anifold. \nWe will discuss recent joint work with Ciprian Manolescu on com puting the "skein lasagna module\," a basic part of MWW's invariant\, for a certain class of 4-manifolds.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Owen Gwilliam (Univ. Massachusetts\, Amherst) DTSTART:20210305T140000Z DTEND:20210305T150000Z DTSTAMP:20260424T221532Z UID:TQFT/32 DESCRIPTION:Title: Bulk-boundary correspondences with factorization algebras\nby Owe n Gwilliam (Univ. Massachusetts\, Amherst) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nFactorization algebras pro vide a flexible language for describing the observables of a perturbative QFT\, as shown in joint work with Kevin Costello. Those constructions exte nd to a manifold with boundary for a special class of theories. I will dis cuss work with Eugene Rabinovich and Brian Williams that includes\, as an example\, a perturbative version of the correspondence between chiral ${\\ rm U}(1)$ currents on a Riemann surface and abelian Chern-Simons theory on a bulk 3-manifold\, but also includes a systematic higher dimensional ver sion for higher abelian CS theory on an oriented smooth manifold of dimens ion $4n+3$ with boundary a complex manifold of complex dimension $2n+1$. G iven time\, I will discuss how this framework leads to a concrete construc tion of the center of higher enveloping algebras of Lie algebras\, in work with Greg Ginot and Brian Williams.\n\nPLEASE NOTE THE UNUSUAL TIME!\n LOCATION:https://stable.researchseminars.org/talk/TQFT/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabio di Cosmo (Instituto de Ciencias Matemáticas\, Madrid) DTSTART:20210319T170000Z DTEND:20210319T174000Z DTSTAMP:20260424T221532Z UID:TQFT/33 DESCRIPTION:Title: Statistical Interpretation in the Schwinger’s picture of Quantum Me chanics\nby Fabio di Cosmo (Instituto de Ciencias Matemáticas\, Madri d) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAb stract\nIn this talk I will illustrate some ideas about the statistical in terpretation in the Schwinger’s picture of Quantum Mechanics. After a br ief introduction on the postulates assumed in this framework\, I will reca ll the basic ingredients of Connes’ non commutative integration theory. This language allows me to define\, on one hand quantum measures on the gr oupoid associated with the quantum systems\, and on the other weights on t he corresponding groupoid von-Neumann algebra. In particular\, quantum mea sures are a generalization of measures on sigma-algebras which is suited f or the description of interference phenomena. Then\, the final part of the talk will be devoted to the statistical interpretation associated with bo th situations.\n\nFirst part of a double session\, followed by a 20 minute break for coffee and discussion\, before the second speaker\, Pedro Resen de.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Resende (Instituto Superior Técnico\, Lisbon) DTSTART:20210319T180000Z DTEND:20210319T184000Z DTSTAMP:20260424T221532Z UID:TQFT/34 DESCRIPTION:Title: An abstract theory of physical measurements\nby Pedro Resende (In stituto Superior Técnico\, Lisbon) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nSince its early days\, quantum me chanics has forced physicists to consider the interaction between quantum systems and classically described experimental devices — a fundamental t enet for Bohr was that the results of measurements need to be communicated using the language of classical physics.\n\nSeveral decades of progress h ave led to improved understanding\, but the tension between “quantum” and “classical” persists. Ultimately\, how is classical information ex tracted from a measurement? Is classical information fundamental\, as in W heeler’s “it from bit”? In this talk\, which is based on ongoing wor k [1]\, I approach the problem mathematically by considering spaces whose points are measurements\, abstractly conceived in terms of the classical i nformation they produce. Concretely\, measurement spaces are stably Gelfan d quantales [2] equipped with a compatible sober topology\, but essentiall y their definition hinges on just two binary operations\, called compositi on and disjunction\, whose intuitive meanings are fairly clear. Despite th eir simplicity\, these spaces have interesting mathematical properties. C* -algebras yield measurement spaces of “quantum type\,” and Lie groupoi ds give us spaces of “classical type\,” such as those which are associ ated with a specific experimental apparatus. The latter also yield a conne ction to Schwinger’s selective measurements\, which have been recast in groupoid language by Ciaglia et al.\nAn interaction between the two types\ , providing a mathematical approach to Bohr’s quantum/classical split\, can be described in terms of groupoid (or Fell bundle) C*-algebras as in [ 3]. I will illustrate the basic ideas with simple examples\, such as spin measurements performed with a Stern–Gerlach apparatus.\n\nReferences\n\n [1] P. Resende\, An abstract theory of physical measurements (2021)\, avai lable at \nhttps://arxiv.org/abs/2102.01712.\n\n[2] P. Resende\, The many groupoids of a stably Gelfand quantale\, J. Algebra 498 (2018)\, 197–210 \, \nDOI 10.1016/j.jalgebra.2017.11.042.\n\n[3] P. Resende\, Quantales and Fell bundles\, Adv. Math. 325 (2018)\, 312–374\, \nDOI 10.1016/j.aim.20 17.12.001. MR3742593\n\nSecond part of a double session\, followed by a 20 minute discussion period.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Roger Picken (Instituto Superior Técnico\, Lisbon) DTSTART:20210409T160000Z DTEND:20210409T170000Z DTSTAMP:20260424T221532Z UID:TQFT/35 DESCRIPTION:Title: Link invariants from finite crossed modules and a lifting of the Eise rmann invariant\nby Roger Picken (Instituto Superior Técnico\, Lisbon ) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbs tract\nThis talk is based on work with João Faria Martins (Univ. Leeds) [ 1] and several projects with students. I will describe the construction of an invariant of tangles and framed tangles which takes values in an arbit rary crossed module of finite groups. This involves the fundamental crosse d module associated to a natural topological pair coming from a knot diagr am\, and a suitable class of morphisms from this fundamental crossed modul e to the chosen finite crossed module. Our construction includes all rack and quandle cohomology (framed) link invariants\, as well as the Eisermann invariant of knots [2-3]\, for which we also find a lifting. The Eiserman n invariant detects information about a suitable choice of meridian and lo ngitude in the knot complement boundary.\n\n

[1] João Faria Martins and Roger Picken: Link invariants from finite categorical groups\, Homology\, Homotopy and Applications\, 17(2) (2015)\, 205–233\; arXiv:1301.3803v2 [math.GT]\, arXiv:1612.03501v1 [math.GT]
\n[2] M. Eisermann: Knot colouring polynomials\, Pacific J. Math. 231 (2007)\, no. 2\, 305–336.
\n[3] M. Eisermann: Homological characterization of th e unknot\, J. Pure Appl. Algebra 177 (2003)\, no. 2\, 131–157.

\n LOCATION:https://stable.researchseminars.org/talk/TQFT/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (Grupo de Física Matemática\, Universidade de Lis boa) DTSTART:20210416T160000Z DTEND:20210416T170000Z DTSTAMP:20260424T221532Z UID:TQFT/36 DESCRIPTION:Title: Quantum differential equations\, qKZ difference equations\, and helic es\nby Giordano Cotti (Grupo de Física Matemática\, Universidade de Lisboa) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\ n\nAbstract\nQuantum differential equations (qDEs) are a rich object attac hed to complex smooth projective varieties. They encode information on the ir enumerative geometry\, topology and (conjecturally) on their algebraic geometry. In occasion of the 1998 ICM in Berlin\, B.Dubrovin conjectured a n intriguing connection between the enumerative geometry of a Fano manifol d $X$ with algebro-geometric properties of exceptional collections in the derived category $D_b(X)$. Under the assumption of semisimplicity of the q uantum cohomology of $X$\, the conjecture prescribes an explicit form for local invariants of $QH^*(X)$\, the so-called “monodromy data”\, in te rms of Gram matrices and characteristic classes of objects of exceptional collections. In this talk I will discuss an equivariant analog of these re lations\, focusing on the example of projective spaces. The study of the e quivariant quantum differential equations for partial flag varieties has b een initiated by V.Tarasov and A.Varchenko in 2017. They discovered the ex istence of a system of compatible qKZ difference equations\, which have ma de the study of the quantum differential equations easier than in the non- equivariant case. I will establish relations between the monodromy data of the joint system of the equivariant qDE and qKZ equations for $\\mathbb{P }^n$ and characteristic classes of objects of the derived category of T-eq uivariant coherent sheaves on $\\mathbb{P}^n$.\n\nBased on joint works wit h B.Dubrovin\, D.Guzzetti and A.Varchenko.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Si Li (Tsinghua University) DTSTART:20210514T080000Z DTEND:20210514T090000Z DTSTAMP:20260424T221532Z UID:TQFT/37 DESCRIPTION:Title: Geometry of Localized Effective Theories and Algebraic Index\nby Si Li (Tsinghua University) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\nWe describe a general framework to study the quantum geometry of -models when they are effectively localized to sma ll quantum fluctuations around constant maps. Such effective theories have exact descriptions at all loops in terms of target geometry and can be ri gorously formulated. We illustrate this idea by the example of topological quantum mechanics which will lead to an explicit construction of the univ ersal trace map on periodic cyclic chains of matrix Weyl algebras. As an a pplication\, we explain how to implement the idea of exact semi-classical approximation into a proof of the algebraic index theorem using Gauss Mani n connection.\n\nThis is joint work with Zhengping Gui and Kai Xu.\nZhengp ing Gui\, Si Li\, Kai Xu\,\nGeometry of Localized Effective Theories\, Exa ct Semi-classical Approximation and the Algebraic Index\nhttps://arxiv.org /pdf/1911.11173\n LOCATION:https://stable.researchseminars.org/talk/TQFT/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabian Haiden (Mathematical Institute\, University of Oxford) DTSTART:20210625T160000Z DTEND:20210625T170000Z DTSTAMP:20260424T221532Z UID:TQFT/38 DESCRIPTION:Title: Categorical Kähler Geometry\nby Fabian Haiden (Mathematical Inst itute\, University of Oxford) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThis is a report on joint work in progr ess with L. Katzarkov\, M. Kontsevich\, and P. Pandit. The Homological Mir ror Symmetry conjecture is stated as an equivalence of triangulated catego ries\, one coming from algebraic geometry and the other from symplectic to pology. An enhancement of the conjecture also identifies stability conditi ons (in the sense of Bridgeland) on these categories. We adopt the point o f view that triangulated (DG/A-infinity) categories are non-commutative sp aces of an algebraic nature. A stability condition can then be thought of as the analog of a Kähler class or polarization. Many\, often still conje ctural\, constructions of stability conditions hint at a richer structure which we think of as analogous to a Kähler metric. For instance\, a type of Donaldson and Uhlenbeck-Yau theorem is expected to hold. I will discuss these examples and common features among them\, leading to a tentative de finition.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruce Bartlett (Stellenbosch University) DTSTART:20210521T160000Z DTEND:20210521T170000Z DTSTAMP:20260424T221532Z UID:TQFT/39 DESCRIPTION:Title: Asymptotics of the classical and quantum $6j$ symbols\nby Bruce Bartlett (Stellenbosch University) as part of Topological Quantum Field Th eory Club (IST\, Lisbon)\n\n\nAbstract\nThe classical (resp. quantum) 6j s ymbols are real numbers which encode the associator information for the te nsor category of representations of SU(2) (resp. the quantum group of SU(2 ) at level k). They form the building blocks for the Turaev-Viro 3-dimensi onal TQFT. I will review the intriguing asymptotic formula for these symb ols in terms of the geometry of a Euclidean tetrahedron (in the classical case) or a spherical tetrahedron (in the quantum case)\, due to Ponzano-Re gge and Taylor-Woodward respectively. There is a wonderful integral formul a for the square of the classical 6j symbols as a group integral over SU(2 )\, and I will report on investigations into a similar conjectural integra l formula for the quantum 6j symbols. In the course of these investigation s\, we observed and proved a certain reciprocity formula for the Wigner de rivative for spherical tetrahedra. Joint with Hosana Ranaivomanana.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Melnikov (International Institute of Physics) DTSTART:20210528T160000Z DTEND:20210528T170000Z DTSTAMP:20260424T221532Z UID:TQFT/40 DESCRIPTION:Title: Entanglement and complexity from TQFT\nby Dmitry Melnikov (Intern ational Institute of Physics) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn the 1990s Aravind proposed that topo logical links can be used to classify different patterns of quantum entang lement. One way this connection can be investigated is through an appropri ate quantum mechanical definition of knots. I will start from the category theory definition of a TQFT and derive a relation between measures of qua ntum entanglement and topological invariants of links. We will see how pat terns of quantum entanglement emerge in the TQFT picture. Meanwhile\, comp lexity is a complementary measure of quantum correlations. In the TQFT cas e\, it can also be related to topological invariants. I will discuss a few definitions of complexity for several families of knots and links.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Saemann (Heriot-Watt University) DTSTART:20210507T160000Z DTEND:20210507T170000Z DTSTAMP:20260424T221532Z UID:TQFT/41 DESCRIPTION:Title: Adjusted Higher Gauge Theory: Connections and Parallel Transport\ nby Christian Saemann (Heriot-Watt University) as part of Topological Quan tum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nOrdinary higher gauge theory suffers from the problem that all the curvature forms but the top d egree one\, which are called fake curvatures\, have to vanish. If this con dition was omitted\, the gauge structure\, the underlying higher principal bundle and the corresponding parallel transport would be inconsistent. Fo r vanishing fake curvatures\, however\, one can locally gauge away the non -abelian parts of the higher connection\, ending up with a connection on a n abelian gerbe. This is clearly unsatisfactory for non-topological higher gauge theories. A solution to this problem is what we call "adjusted high er gauge theory"\, in which the usual definition of the curvatures is adju sted by additional data. This lifts the requirement for vanishing fake cur vatures. Moreover\, it matches constructions of theoretical physicists in the context of supergravity. In this talk\, I will review the above points and say a few words about my motivation for studying adjusted higher gaug e theories.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Ingmar Saberi (University of Heidelberg) DTSTART:20210604T160000Z DTEND:20210604T170000Z DTSTAMP:20260424T221532Z UID:TQFT/42 DESCRIPTION:Title: Twists of supergravity theories via algebraic geometry\nby Ingmar Saberi (University of Heidelberg) as part of Topological Quantum Field Th eory Club (IST\, Lisbon)\n\n\nAbstract\nTwists of supersymmetric field the ories have been the source of an enormous amount of new mathematics\, incl uding (just for example) Seiberg-Witten theory and mirror symmetry. It is reasonable to expect that twists of supergravity theories will exhibit eve n richer structure\, but they remain comparatively unexplored\, largely du e to their intricacy. For example\, a holomorphically twisted version of t he AdS/CFT correspondence was proposed by Kevin Costello and Si Li\, motiv ated by constructions in topological string theory and the work of Bershad sky-Cecotti-Ooguri-Vafa\; Costello and Li conjectured a connection between their version of BCOV theory and the type IIB supergravity theory\, but d id not verify this connection directly. I will show that the pure spinor s uperfield technique\, which has been known for some time in the physics li terature\, can be used to elegantly and economically construct supersymmet ric theories\, as well as to swiftly compute their twists. In each case\, the resulting structures are governed by the classical algebraic geometry of certain affine varieties. If time permits\, I'll discuss the examples o f type IIB supergravity and eleven-dimensional supergravity in some detail .\n LOCATION:https://stable.researchseminars.org/talk/TQFT/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Theo Johnson-Freyd (Dalhousie University and Perimeter Institute) DTSTART:20210618T160000Z DTEND:20210618T170000Z DTSTAMP:20260424T221532Z UID:TQFT/43 DESCRIPTION:Title: Higher S-matrices\nby Theo Johnson-Freyd (Dalhousie University an d Perimeter Institute) as part of Topological Quantum Field Theory Club (I ST\, Lisbon)\n\n\nAbstract\nEach fusion higher category has a "framed S-ma trix" which encodes the commutator of operators of complementary dimension . I will explain how to construct and interpret this pairing\, and I will emphasize that it may fail to exist if you drop semisimplicity requirement s. I will then outline a proof that the framed S-matrix detects (non)degen eracy of the fusion higher category. This is joint work in progress with D avid Reutter.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/43/ END:VEVENT BEGIN:VEVENT SUMMARY:João Faria Martins (University of Leeds) DTSTART:20210924T160000Z DTEND:20210924T170000Z DTSTAMP:20260424T221532Z UID:TQFT/44 DESCRIPTION:Title: Quinn Finite Total Homotopy TQFT as a once-extended TQFT\nby Joã o Faria Martins (University of Leeds) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nQuinn Finite Total Homotopy TQF T is a TQFT that works in any dimension and that depends on the choice of a homotopy finite space $B$ (e.g. $B$ can be the classifying space of a fi nite group or of a finite 2-group). I will report on ongoing joint work w ith Tim Porter on once-extended versions of Quinn Finite total homotopy TQ FT\, and I will show how to compute them for the case when $B$ is the clas sifying space of a finite strict omega-groupoid (represented by a crossed complex).\n\nSome stages of this work were financed by the Leverhulme trus t research project grant: Emergent Physics From Lattice Models of Higher G auge Theory.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Tijana Radenković (Institute of Physics\, Belgrade) DTSTART:20211013T160000Z DTEND:20211013T170000Z DTSTAMP:20260424T221532Z UID:TQFT/45 DESCRIPTION:Title: Topological higher gauge theory - from 2BF to 3BF theory\nby Tija na Radenković (Institute of Physics\, Belgrade) as part of Topological Qu antum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe study a generaliz ation of BF-theories in the context of higher gauge theory. We construct a topological state sum Z\, based on the classical 3BF action for a general semistrict Lie 3-group and a triangulation of a 4-dimensional spacetime m anifold. The 3BF action is constructed using a 2-crossed module which enco des a 3-group (as introduced by Picken and Faria Martins [1])\, while the state sum Z is an example of Porter’s TQFT [2] for d=4 and n=3. In order to verify that the constructed state sum is a topological invariant of th e underlying manifold\, its behavior under Pachner moves is analyzed\, and it is obtained that the state sum Z remains the same. Our results are a g eneralization of the work done by Girelli\, Pfeiffer\, and Popescu [3] for the case of state sum based on the classical 2BF action with the underlyi ng 2-group structure.\n

\n[1] J. Faria Martins and R. Picken\, Diff. Geo m. Appl. 29\, 179 (2011)\, arXiv:0907.2566.\n

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\n[2] T. Porter\, J. Lond. Math. Soc. (2)58\, No. 3\, 723 (1998)\, MR 1678163.\n

\n

\n[3] F. Girelli\, H. Pfeiffer and E. M. Popescu\, Jour. Math. Phys. 49\, 03250 3 (2008)\, arXiv:0708.3051.\n

\n LOCATION:https://stable.researchseminars.org/talk/TQFT/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian R. Williams (University of Edinburgh) DTSTART:20211117T170000Z DTEND:20211117T180000Z DTSTAMP:20260424T221532Z UID:TQFT/46 DESCRIPTION:Title: Exceptional super Lie algebras in twisted M-theory\nby Brian R. W illiams (University of Edinburgh) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nWith Saberi and Raghavendran we con structed\, in the BV formalism\, the minimal\, holomorphic\, twist of 11-d imensional supergravity. Amazingly\, on flat space\, the theory shares a c lose relationship to an exceptional simple super Lie algebra called E(5\,1 0). Motivated by holographic duality\, I’ll turn attention to symmetries of the theories on M2 and M5 branes. In the twisted setting\, we find tha t the superconformal algebra enhances to other infinite-dimensional except ional super Lie algebras. I will discuss further extensions of these excep tional algebras to factorization algebras and applications to pinning down correlation functions in M-theory.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir M. Stojanovic (TU Darmstadt) DTSTART:20211215T170000Z DTEND:20211215T180000Z DTSTAMP:20260424T221532Z UID:TQFT/47 DESCRIPTION:Title: Lie-algebraic aspects of quantum control: gate realization and W-to-G HZ state conversion\nby Vladimir M. Stojanovic (TU Darmstadt) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn this talk I will try to demonstrate the use of Lie-algebraic concepts in t he quantum control of interacting qubit arrays\, with examples from both o perator (gate)- and state control. I will start from the basics of quantum control and briefly review the Lie-algebraic underpinnings of the concept of complete controllability. I will then specialize to qubit arrays with Heisenberg-type interactions\, summarizing the conditions for their comple te controllability and showing a few examples of gate realization. The sec ond part of the talk will be devoted to a rather unconventional use of Lie -algebraic concepts within a dynamical-symmetry-based approach to the dete rministic conversion between W- and Greenberger-Horne-Zeilinger (three-qub it) states. The underlying physical system consists of three neutral atoms subject to several external laser pulses\, where the atomic ground- and a highly-excited Rydberg state play the role of the two relevant logical qu bit states.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Giorgio Trentinaglia (Instituto Superior Técnico\,Lisbon) DTSTART:20220119T170000Z DTEND:20220119T180000Z DTSTAMP:20260424T221532Z UID:TQFT/48 DESCRIPTION:Title: Simplicial vector bundles and representations up to homotopy\nby Giorgio Trentinaglia (Instituto Superior Técnico\,Lisbon) as part of Topo logical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe classi cal Dold–Kan correspondence for simplicial objects in an abelian categor y is one of the cornerstones of homological algebra. When the abelian cate gory is that of vector spaces\, it gives a full identification between sim plicial vector spaces and chain complexes of vector spaces vanishing in ne gative degrees. The Grothendieck construction for fibered categories\, on the other hand\, is a cornerstone of category theory. It relates the fiber ed category point of view with the pseudo-functor point of view and lies a t the heart of the theory of stacks. Our main result can be understood as a far-reaching simultaneous generalization of both ideas within the contex ts of linear algebra and differential geometry. In our result\, simplicial vector spaces and chain complexes of vector spaces are replaced respectiv ely by vector fibrations over a given (higher) Lie groupoid G and by repre sentations up to homotopy of G. (Joint work with Matias del Hoyo.)\n LOCATION:https://stable.researchseminars.org/talk/TQFT/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeffrey C. Morton (SUNY Buffalo State) DTSTART:20220126T170000Z DTEND:20220126T180000Z DTSTAMP:20260424T221532Z UID:TQFT/49 DESCRIPTION:Title: The Fock Pseudomonad: Groupoidifying Second Quantization\nby Jeff rey C. Morton (SUNY Buffalo State) as part of Topological Quantum Field Th eory Club (IST\, Lisbon)\n\n\nAbstract\n

Edward Nelson said "First quant ization is a mystery\, but second quantization is a functor". This functor takes the Hilbert space H representing a quantum mechanical system\, and gives its Fock space F(H)\, representing a multi-particle system with any number of indistinguishable copies of the original system as in quantum fi eld theory (I am considering the bosonic case). In a categorical analysis of the harmonic oscillator\, Vicary revised Nelson's slogan to say "second quantization is a monad" - that is\, the functor in question is equipped with some extra algebraic structure\, making it the "Fock Monad" (F\,$\\et a$\,$\\epsilon$).

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Groupoidification is one of a number of approa ches to "categorifying" quantum-mechanical systems: finding higher-categor ical analogs of those systems. It uses a 2-category Span(Gpd) whose object s are groupoids\, and whose morphisms are "spans". This has had some succe ss in describing extensions of topological field theory to systems with bo undary\, with the "categorified" theory describing the evolution of open s ystems\, which can be composed along their boundaries\, over time. In this talk\, I will use this framework to describe a categorification of F to t he "Fock Pseudomonad" which can be defined in any suitable 2-category\, an d the compatibility of this pseudomonad in Span(Gpd) with that in 2-Hilber t spaces\, and\, under the "degroupoidification" map\, with the usual Fock construction on Hilbert spaces.

\n LOCATION:https://stable.researchseminars.org/talk/TQFT/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Cliff (University of Sherbrooke) DTSTART:20220202T170000Z DTEND:20220202T180000Z DTSTAMP:20260424T221532Z UID:TQFT/50 DESCRIPTION:Title: Moduli spaces of principal 2-group bundles and a categorification of the Freed–Quinn line bundle\nby Emily Cliff (University of Sherbrook e) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAb stract\nA 2-group is a higher categorical analogue of a group\, while a sm ooth 2-group is a higher categorical analogue of a Lie group. An important example is the string 2-group in the sense of Schommer-Pries. We study th e notion of principal bundles for smooth 2-groups\, and investigate the mo duli "space" of such objects.\n\nIn particular in the case of flat princip al bundles for a finite 2-group over a Riemann surface\, we prove that the moduli space gives a categorification of the Freed–Quinn line bundle. T his line bundle has as its global sections the state space of Chern–Simo ns theory for the underlying finite group. We can also use our results to better understand the notion of geometric string structures (as previously studied by Waldorf and Stolz–Teichner).\n\n\nThis is based on joint wor k with Dan Berwick-Evans\, Laura Murray\, Apurva Nakade\, and Emma Phillip s.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Grady (Texas Tech University) DTSTART:20220216T170000Z DTEND:20220216T180000Z DTSTAMP:20260424T221532Z UID:TQFT/51 DESCRIPTION:Title: Deformation classes of invertible field theories and the Freed-Hopkin s conjecture\nby Daniel Grady (Texas Tech University) as part of Topol ogical Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3. 10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico.\n\nA bstract\nIn this talk\, I will discuss a recent result which provides an a ffirmative answer to a conjecture by Freed and Hopkins. The conjecture con cerns a classification of reflection positive invertible field theories. I will begin by reviewing motivation and background on reflection positive theories. Then I will state the conjecture and sketch of the proof\n LOCATION:https://stable.researchseminars.org/talk/TQFT/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitri Pavlov (Texas Tech University) DTSTART:20220330T160000Z DTEND:20220330T170000Z DTSTAMP:20260424T221532Z UID:TQFT/52 DESCRIPTION:Title: The geometric cobordism hypothesis\nby Dmitri Pavlov (Texas Tech University) as part of Topological Quantum Field Theory Club (IST\, Lisbon )\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Insti tuto Superior Técnico).\n\nAbstract\n

I will explain my recent work wit h Daniel Grady on the locality of functorial field theories (arXiv:2011.01 208) and the geometric cobordism hypothesis (arXiv:2111.01095). The latter generalizes the Baez–Dolan cobordism hypothesis to nontopological field theories\, in which bordisms can be equipped with geometric structure\, s uch as smooth maps to a fixed target manifold\, Riemannian metrics\, confo rmal structures\, principal bundles with connection\, or geometric string structures.

\n\n

Applications include

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\nIf time permits\, I will talk about planned work on the nonperturbative quan tization of functorial field theories and generalized Atiyah–Singer-styl e index theorems.

\n LOCATION:https://stable.researchseminars.org/talk/TQFT/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Araújo (Instituto Superior Técnico) DTSTART:20220309T170000Z DTEND:20220309T180000Z DTSTAMP:20260424T221532Z UID:TQFT/53 DESCRIPTION:Title: String diagrams for higher categories\nby Manuel Araújo (Institu to Superior Técnico) as part of Topological Quantum Field Theory Club (IS T\, Lisbon)\n\n\nAbstract\nString diagrams are a powerful computational to ol\, most commonly used in the context of tensor categories and occasional ly bicategories. I will talk about work in progress on extending this to h igher categories. The idea is to define a semistrict n-category as somethi ng which admits composites for labeled string diagrams\, much as one can d efine a strict n-category as something that admits composites for pasting diagrams. This notion of semistrict n-category should be more general than that of a strict n-category\, but not as general as that of a weak n-cate gory. We can show that semistrict 3-categories are the same thing as Gray categories and it is known that every weak 3-category (also called a trica tegory) is equivalent to a Gray category. It is not known whether somethin g similar holds in higher dimensions. I will also try to give an idea of t he usefulness of string diagram calculus in dimensions 3 and 4\, by showin g how it can be used to prove coherence theorems for adjunctions.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Christoph Dorn (University of Oxford) DTSTART:20220316T170000Z DTEND:20220316T180000Z DTSTAMP:20260424T221532Z UID:TQFT/54 DESCRIPTION:Title: Manifold diagrams: Poincaré duality\, singularities\, and smooth str uctures\nby Christoph Dorn (University of Oxford) as part of Topologic al Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 ( 3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbst ract\nWe will pick things up just where we left off last week in Manuel's talk. We will discuss combinatorial and geometric models for manifold diag rams (i.e. higher dimensional generalizations of string diagrams) based on recent joint work with Chris Douglas. We focus on three aspects of the th eory: (1) the geometric duality of manifold diagrams and pasting diagrams\ , whose cells provide a novel "universal" class of shapes for higher categ ory theory\; (2) how to extend the tantalizing connection between classica l singularities and laws of dualizable objects into higher dimensions\, ov ercoming obstructions faced by classical differential singularity theory\; and (3) the conjectural "combinatorialization" of smooth structures\, whi ch would allow us to faithfully represent smooth structures of manifolds i n manifold diagrams\, and thus by purely combinatorial means.\n\nWe ask ou r participants based in the US and Canada to be mindful of the time differ ence\, with the beginning of DST there on March 13th.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Yonatan Harpaz (CNRS at University of Paris 13) DTSTART:20220406T160000Z DTEND:20220406T170000Z DTSTAMP:20260424T221532Z UID:TQFT/55 DESCRIPTION:Title: The cobordism hypothesis in dimension 1\nby Yonatan Harpaz (CNRS at University of Paris 13) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Dep artment\, Instituto Superior Técnico).\n\nAbstract\nThe cobordism hypothe sis is a conjectural characterization of the framed cobordism (∞\,n)-cat egory as the free symmetric monoidal (∞\,n)-category with duals generate d by a single object. After its original formulation by Baez and Dolan in 1995\, a strategy for a proof of the conjecture was put forward by Lurie i n 2009. Though this strategy is very efficient in reducing the general hyp othesis to a relatively concrete statement (Claim 3.4.17 in Lurie's text)\ , a formal proof of this concrete statement has yet to appear in the liter ature. In addition\, this strategy does not cover the 1-dimensional case. In this talk I will describe a way to extend Lurie's strategy to the case of n=1\, in which case the analogue of the missing claim can be proved usi ng\, among other things\, the notion of quasi-unital ∞-categories.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Ángel González Prieto (Universidad Complutense de Madrid) DTSTART:20220413T160000Z DTEND:20220413T170000Z DTSTAMP:20260424T221532Z UID:TQFT/56 DESCRIPTION:Title: Topological Quantum Field Theories for Character Stacks\nby Ánge l González Prieto (Universidad Complutense de Madrid) as part of Topologi cal Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbs tract\nModuli spaces of representations of surface groups (aka character v arieties) are very interesting spaces due to their tight relation with mod uli spaces of Higgs bundles and flat connections. Nowadays\, several appro aches are available in the literature to understand the geometry of these character varieties constructed via geometric invariant theory quotients. Despite these advances\, the geometry of character stacks\, where roughly speaking the group action is not quotiented but still tracked\, remains a mystery.\n\nTo address this problem\, in this talk we shall construct a la x monoidal topological quantum field theory that computes the virtual clas ses of G-representation stacks in the Grothendieck ring of BG-stacks. This tool gives rise to an effective computational method for these virtual cl asses based on topological recursion on the genus of the surface. Time per mitting\, we will also discuss how this construction provides evidence tha t lax monoidal TQFTs represent a new hope in the quantization of algebraic invariants.\n\nJoint work with M. Hablicsek and J. Vogel.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Nezhla Aghaei (University of Southern Denmark) DTSTART:20220420T160000Z DTEND:20220420T170000Z DTSTAMP:20260424T221532Z UID:TQFT/57 DESCRIPTION:Title: Combinatorial quantisation of Supergroup Chern–Simons Theory\nb y Nezhla Aghaei (University of Southern Denmark) as part of Topological Qu antum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd f loor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\ nChern–Simons theories with gauge supergroups appear naturally in string theory and they possess interesting applications in mathematics\, e.g. fo r the construction of knot and link invariants. In my talk I will review t he framework for combinatorial quantization of Chern–Simons theory and e xplain how this framework can be adapted for applications to superalgebras . This will give rise to interesting new observables which can be computed by exploiting the rich representation theory of Lie superalgebras.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Mnev (University of Notre Dame) DTSTART:20220427T160000Z DTEND:20220427T170000Z DTSTAMP:20260424T221532Z UID:TQFT/58 DESCRIPTION:Title: On the Fukaya-Morse A-infinity category\nby Pavel Mnev (Universit y of Notre Dame) as part of Topological Quantum Field Theory Club (IST\, L isbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\nI will sketch the construction of the Fukaya-Morse category of a Riemannian manifold X -- an A-infinity c ategory (a category where associativity of composition holds only "up-to-h omotopy") where the higher composition maps are given in terms of numbers of embedded trees in X\, with edges following the gradient trajectories of certain Morse functions. I will give simple examples and explain differen t approaches to understanding the structure and proving the quadratic rela tions on the structure maps -- (1a) via homotopy transfer\, (1b) effective field theory approach\, (2) topological quantum mechanics approach. The t alk is based on a joint work with O. Chekeres\, A. Losev and D. Youmans\, arXiv:2112.12756.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamie Vicary (University of Cambridge) DTSTART:20220504T160000Z DTEND:20220504T170000Z DTSTAMP:20260424T221532Z UID:TQFT/59 DESCRIPTION:Title: Introducing homotopy.io: A proof assistant for geometrical higher cat egory theory\nby Jamie Vicary (University of Cambridge) as part of Top ological Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n \nAbstract\nWeak higher categories can be difficult to work with algebraic ally\, with the weak structure potentially leading to considerable bureauc racy. Conjecturally\, every weak $\\infty$-category is equivalent to a "se mistrict" one\, in which unitors and associators are trivial\; such a sett ing might reduce the burden of constructing large proofs. In this talk\, I will present the proof assistant homotopy.io\, which allows direct constr uction of composites in a finitely-generated semistrict $(\\infty\,\\infty )$-category. The terms of the proof assistant have an interpretation as st ring diagrams\, and interaction with the proof assistant is entirely geome trical\, by clicking and dragging with the mouse\, completely unlike tradi tional computer algebra systems. I will give an outline of the underlying theoretical foundations\, and demonstrate use of the proof assistant to co nstruct some nontrivial homotopies\, rendered in 2d\, 3d\, and in 4d as mo vies. I will close with some speculations about the possible interaction o f such a system with more traditional type-theoretical approaches. (Joint work with Nathan Corbyn\, Calin Tataru\, Lukas Heidemann\, Nick Hu and Dav id Reutter.)\n LOCATION:https://stable.researchseminars.org/talk/TQFT/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugene Rabinovich (University of Notre Dame) DTSTART:20220517T163000Z DTEND:20220517T173000Z DTSTAMP:20260424T221532Z UID:TQFT/60 DESCRIPTION:Title: Classical Bulk-Boundary Correspondences via Factorization Algebras\nby Eugene Rabinovich (University of Notre Dame) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstrac t\nA factorization algebra is a cosheaf-like local-to-global object which is meant to model the structure present in the observables of classical an d quantum field theories. In the Batalin–Vilkovisky (BV) formalism\, one finds that a factorization algebra of classical observables possesses\, i n addition to its factorization-algebraic structure\, a compatible Poisson bracket of cohomological degree +1. Given a "sufficiently nice" such fact orization algebra on a manifold $N$\, one may associate to it a factorizat ion algebra on $N\\times \\mathbb{R}_{\\geq 0}$. The aim of the talk is to explain the sense in which the latter factorization algebra "knows all th e classical data" of the former. This is the bulk-boundary correspondence of the title. Time permitting\, we will describe how such a correspondence appears in the deformation quantization of Poisson manifolds.\n\nNote unu sual day and time.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Noja (University of Heidelberg) DTSTART:20220525T160000Z DTEND:20220525T170000Z DTSTAMP:20260424T221532Z UID:TQFT/61 DESCRIPTION:Title: The de Rham / Spencer double complex and the geometry of forms on sup ermanifolds\nby Simone Noja (University of Heidelberg) as part of Topo logical Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3 .31 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\ nAbstract\nIntegral forms are characteristic supergeometric objects that a llow us to define a meaningful notion of integration on supermanifolds. In this talk\, I will introduce a double complex of non-commutative sheaves that relates integral forms to the more customary notion of differential f orms. I will then discuss how this framework specializes to so-called cota ngent bundle supermanifolds\, which are relevant to odd symplectic geometr y and BV theory. If time permits\, I will explain how the geometry of form s is related to the problem of splitting a complex supermanifold in this p articular setting.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Nima Moshayedi (University of California\, Berkeley) DTSTART:20220601T160000Z DTEND:20220601T170000Z DTSTAMP:20260424T221532Z UID:TQFT/62 DESCRIPTION:Title: Cutting-Gluing of TQFTs in the Symplectic Cohomological Formalism \nby Nima Moshayedi (University of California\, Berkeley) as part of Topol ogical Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3. 10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\n Abstract\nThe functional integral methods for quantum gauge field theories allows us to pass to a symplectic formalism in order to deal with these o bjects in a rather nice way (the BV formalism). The extension to manifolds with boundary (the BV-BFV formalism)\, recently constructed by Cattaneo-M nev-Reshetikhin\, allows us to talk about cut and glue techniques in the p erturbative symplectic cohomological setting for TQFTs. I will present the idea of the BV-BFV formalism and talk about several interesting connectio ns to e.g. deformation quantization or shifted symplectic structures. More over\, I will talk about some ideas for a higher codimension version.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Marc Lackenby (University of Oxford) DTSTART:20220615T160000Z DTEND:20220615T170000Z DTSTAMP:20260424T221532Z UID:TQFT/63 DESCRIPTION:Title: Knot theory and machine learning\nby Marc Lackenby (University of Oxford) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n \nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Institut o Superior Técnico).\n\nAbstract\nKnot theory is divided into several sub fields. One of these is hyperbolic knot theory\, which is focused on the h yperbolic structure that exists on many knot complements. Another branch o f knot theory is concerned with invariants that have connections to 4-mani folds\, for example the knot signature and Heegaard Floer homology. In my talk\, I will describe a new relationship between these two fields that wa s discovered with the aid of machine learning. Specifically\, we show that the knot signature can be estimated surprisingly accurately in terms of h yperbolic invariants. We introduce a new real-valued invariant called the natural slope of a hyperbolic knot in the 3-sphere\, which is defined in t erms of its cusp geometry. Our main result is that twice the knot signatur e and the natural slope differ by at most a constant times the hyperbolic volume divided by the cube of the injectivity radius. This theorem has app lications to Dehn surgery and to 4-ball genus. We will also present a refi ned version of the inequality where the upper bound is a linear function o f the volume\, and the slope is corrected by terms corresponding to short geodesics that have odd linking number with the knot. My talk will outline the proofs of these results\, as well as describing the role that machine learning played in their discovery.\n\nThis is joint work with Alex Davie s\, Andras Juhasz\, and Nenad Tomasev.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Nezhla Aghaei (University of Southern Denmark) DTSTART:20220509T140000Z DTEND:20220509T150000Z DTSTAMP:20260424T221532Z UID:TQFT/64 DESCRIPTION:Title: Combinatorial quantisation of Supergroup Chern–Simons Theory\nb y Nezhla Aghaei (University of Southern Denmark) as part of Topological Qu antum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd f loor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\ nChern–Simons theories with gauge supergroups appear naturally in string theory and they possess interesting applications in mathematics\, e.g. fo r the construction of knot and link invariants. In my talk I will review t he framework for combinatorial quantization of Chern–Simons theory and e xplain how this framework can be adapted for applications to superalgebras . This will give rise to interesting new observables which can be computed by exploiting the rich representation theory of Lie superalgebras.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Álvaro del Pino Gómez (Utrecht University) DTSTART:20220608T160000Z DTEND:20220608T170000Z DTSTAMP:20260424T221532Z UID:TQFT/65 DESCRIPTION:Title: h-Principles and applications to distributions\nby Álvaro del Pi no Gómez (Utrecht University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\nIn the 1950s\, Sm ale and Hirsch proved that the space of immersions of an m-dimensional man ifold into an n-dimensional manifold is homotopy equivalent\, as long as m < n\, to the space of monomorphisms between the tangent spaces. Any state ment of this form (i.e. a comparison theorem between a space of geometric structures and an associated space that is purely algebraic topological in nature)\, is known as a homotopy principle\, or h-principle.\n\nLater on\ , in the late 60s and early 70s\, Gromov developed (or generalised) variou s techniques capable of proving h-principles. Since then\, these ideas hav e been impactful in the study of many geometric structures (including imme rsions\, submersions\, foliations\, symplectic structures\, contact struct ures\, embeddings\, and Riemannian metrics).\n\nThe goal of the talk will be to sketch some of these techniques and state some consequences in the h omotopical study of tangent distributions (i.e.\, subbundles of the tangen t bundle).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Radmila Sazdanovic (North Carolina State University) DTSTART:20220629T160000Z DTEND:20220629T170000Z DTSTAMP:20260424T221532Z UID:TQFT/66 DESCRIPTION:Title: Bilinear pairings on two-dimensional cobordisms and generalizations o f the Deligne category\nby Radmila Sazdanovic (North Carolina State Un iversity) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\ n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Institu to Superior Técnico).\n\nAbstract\nThe Deligne category of symmetric grou ps is the additive Karoubi closure of the partition category. The partitio n category may be interpreted\, following Comes\, via a particular lineari zation of the category of two-dimensional oriented cobordisms. In this tal k we will use a generalization of this approach to the Deligne category co upled with the universal construction of two-dimensional topological theor ies to construct their multi-parameter monoidal generalizations\, one for each rational function in one variable. This talk is based on joint work w ith M. Khovanov.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Marina Logares (Complutense University of Madrid) DTSTART:20220914T160000Z DTEND:20220914T170000Z DTSTAMP:20260424T221532Z UID:TQFT/67 DESCRIPTION:Title: Hitchin systems\nby Marina Logares (Complutense University of Mad rid) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nLe cture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Su perior Técnico).\n\nAbstract\nHitchin systems are in the core of the inte rsection between integrable systems and gauge theories. These are algebrai c completely integrable systems defined by moduli spaces of (decorated) Hi ggs bundles. In this talk I shall describe several Hitchin systems. This i s based on past and ongoing work with Biswas\, Martens\, Peón-Nieto and S zabó.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Safronov (University of Edinburgh) DTSTART:20220921T160000Z DTEND:20220921T170000Z DTSTAMP:20260424T221532Z UID:TQFT/68 DESCRIPTION:Title: Skein modules and 4d TQFTs\nby Pavel Safronov (University of Edin burgh) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n Lecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\nIt is well-known that the quantum Chern –Simons theory (as formalized by Reshetikhin and Turaev) has a framing a nomaly: to have a functorial dependence on cobordisms\, they have to be eq uipped with an extra tangential structure besides the orientation. Followi ng Walker and Freed–Teleman\, one can view the anomaly of the Chern–Si mons theory as an invertible 4d TQFT\, the Crane–Yetter theory. While th e Chern–Simons theory makes sense only when q\, the quantum parameter\, is a root of unity\, the anomaly theory make sense for any q. I will descr ibe the behavior of this 4d TQFT for generic q and\, in particular\, a des cription of its spaces of states on closed 3-manifolds. This is based on j oint work with Sam Gunningham and David Jordan.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Marko Vojinovic (University of Belgrade) DTSTART:20221026T160000Z DTEND:20221026T170000Z DTSTAMP:20260424T221532Z UID:TQFT/69 DESCRIPTION:Title: Insights into the Standard Model and quantum gravity from higher gaug e theory\nby Marko Vojinovic (University of Belgrade) as part of Topol ogical Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3. 10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\n Abstract\nHigher category theory can be employed to generalize the notion of symmetry\, by passing from a gauge group to the notion of a gauge n-gro up. The n-groups are designed to generalize notions of connection and para llel transport\, from curves to manifolds of dimension higher than one. Th ey also give rise to a class of topological actions called nBF actions. On e can then employ a 3-group as a gauge symmetry and the corresponding 3BF action\, to describe the full Einstein-Cartan theory of gravity coupled to Standard Model fields. Such an action is naturally adapted to the spinfoa m quantization technique\, with the aim to construct a full model of quant um gravity with matter.\n\nOnce constructed\, the properties of the model open up the possibility of a nontrivial unification of all fields. A 3-gro up naturally contains additional novel gauge groups which specify the spec trum of fermions and scalars present in the theory\, just like the ordinar y gauge group specifies the spectrum of gauge bosons in the Yang-Mills the ory. The presence and the properties of new gauge groups have the potentia l to explain fermion families\, and other structure in the matter spectrum of the Standard Model.\n\nThe speaker is visiting Lisbon\, so local parti cipants are invited to attend the talk in person in Room 3.10 (3rd floor M athematics Department).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Fiona Torzewska (University of Leeds) DTSTART:20221116T170000Z DTEND:20221116T180000Z DTSTAMP:20260424T221532Z UID:TQFT/70 DESCRIPTION:Title: Topological quantum field theories and homotopy cobordisms\nby Fi ona Torzewska (University of Leeds) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathem atics Department\, Instituto Superior Técnico).\n\nAbstract\nI will begin by explaining the construction of a category $CofCos$\, whose objects are topological spaces and whose morphisms are cofibrant cospans. Here the id entity cospan is chosen to be of the form $X\\to X\\times [0\,1] \\rightar row X$\, in contrast with the usual identity in the bicategory $Cosp(V)$ o f cospans over a category $V$. The category $CofCos$ has a subcategory $Ho mCob$ in which all spaces are homotopically 1-finitely generated. There ex ist functors into $HomCob$ from a number of categorical constructions whic h are potentially of use for modelling particle trajectories in topologica l phases of matter: embedded cobordism categories and motion groupoids for example. Thus\, functors from $HomCob$ into $Vect$ give representations o f the aforementioned categories. \n\nI will also construct a family of fun ctors $Z_G : HomCob \\to Vect$\, one for each finite group $G$\, showing t hat topological quantum field theories previously constructed by Yetter\, and an untwisted version of Dijkgraaf-Witten\, generalise to functors from $HomCob$. I will construct this functor in such a way that it is clear th e images are finite dimensional vector spaces\, and the functor is explici tly calculable.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Konrad Waldorf (University of Greifswald) DTSTART:20221130T170000Z DTEND:20221130T180000Z DTSTAMP:20260424T221532Z UID:TQFT/71 DESCRIPTION:Title: A representation of the string 2-group\nby Konrad Waldorf (Univer sity of Greifswald) as part of Topological Quantum Field Theory Club (IST\ , Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department \, Instituto Superior Técnico).\n\nAbstract\nThe string 2-group is suppos ed to play the role of the spin group\, but in string theory instead of qu antum mechanics. Several aspects of this analogy are by now well understoo d. In this talk I will talk about joint work with Matthias Ludewig and Pet er Kristel on a further aspect\, namely the representation theory of the s tring 2-group. This was an open problem for a long time. Our solution comb ines higher-categorical topology with operator algebras\, and allows a nea t definition of Stolz-Teichner's "stringor bundle" as an associated 2-vect or bundle.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Konstantin Eder (University of Erlangen–Nürnberg) DTSTART:20221207T170000Z DTEND:20221207T180000Z DTSTAMP:20260424T221532Z UID:TQFT/72 DESCRIPTION:Title: Super Cartan geometry and (loop) quantum supergravity\nby Konstan tin Eder (University of Erlangen–Nürnberg) as part of Topological Quant um Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floo r\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\nIn this talk\, a mathematically rigorous approach toward geometric supergrav ity will be discussed which\, in the physical literature\, is usually know n as the Castellani-D'Auria-Fré approach. To this end\, using tools from supergeometry\, the notion of a super Cartan geometry will be introduced. Interestingly\, in order to consistently incorporate the anticommutative n ature of fermionic fields\, the ordinary category of supermanifolds needs to be generalized in a physically consistent way leading to the notion of so-called enriched supermanifolds. We then apply this formalism to discuss a geometric formulation of (generalized) pure Anti-de Sitter supergravity with N=1\,2 supersymmetry in D=4 modified by an additional Holst term. In this context\, we will also talk about so-called picture changing operato rs (PCO) and how they can be implemented in a mathematically rigorous way. Finally\, an outlook will be given for applications of this formalism to (loop) quantum supergravity and the description of quantum supersymmetric black holes.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Mackaay (University of Algarve) DTSTART:20230125T170000Z DTEND:20230125T180000Z DTSTAMP:20260424T221532Z UID:TQFT/73 DESCRIPTION:Title: 2-Representations of affine type A Soergel bimodules: some observatio ns and examples\nby Marco Mackaay (University of Algarve) as part of T opological Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Roo m 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico). \n\nAbstract\nIn 2010\, Mazorchuk and Miemietz laid the foundations of a s ystematic theory of finitary 2-representations of finitary 2-categories\, which are the categorical analog of finite-dimensional representations of finite-dimensional algebras. In the last couple of years\, this theory has been much further developed and has led to interesting classification res ults for e.g. certain finitary 2-representations of Soergel bimodules of f inite Coxeter type\, which form an important class of examples.\n\nTogethe r with Miemietz and Vaz\, I've recently started to look at 2-representatio ns of Soergel bimodules of affine type A\, which form a 2-category that is no longer finitary but only locally wide finitary\, a generalization whic h was introduced and studied by Marpherson. This has major consequences fo r their 2-representations\, e.g. they now come in 3 different flavors: fin itary\, wide finitary and triangulated.\n\nIn my talk\, I will first very briefly review finitary 2-representation theory of finitary 2-categories a nd recall the example of Soergel bimodules of finite Coxeter type. After t hat\, I will zoom in on Soergel bimodules of affine type A and their three types of 2-representations. I will try to sketch some general features\, but the talk will nevertheless be very example-based\, since our research is still in its early stages.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/73/ END:VEVENT BEGIN:VEVENT SUMMARY:James Macpherson (Instituto Superior Técnico) DTSTART:20230208T170000Z DTEND:20230208T180000Z DTSTAMP:20260424T221532Z UID:TQFT/74 DESCRIPTION:Title: Locally wide quasi-fiat 2-categories and their coalgebra 2-representa tions\nby James Macpherson (Instituto Superior Técnico) as part of To pological Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\ n\nAbstract\nFinitary 2-representation theory\, pioneered by Mazorchuk and Miemietz in 2010\, is a categorification of finite dimensional representa tions of finite dimensional algebras. It primarily studies the 2-represent ation theory of finitary 2-categories\, which are additive\, linear\, Krul l-Schmidt 2-categories with various finiteness conditions. Much progress h as been made in the area since\, including various results that fall under the conceptual banner of 'internal vs. external' - that is\, finding equi valences between arbitrary 'external' 2-representations and 'internal' 2-r epresentations whose data is fully encoded with the finitary 2-category it self.\n\nIn this talk\, I will start by outlining the basic theory of fini tary 2-categories and their finitary 2-representations\, and I will discus s two examples of 'internal' 2-representations\, namely cell 2-representat ions and 2-representations formed of comodule 1-morphisms over a coalgebra 1-morphism. I will then discuss relaxing the finiteness assumptions of fi nitary 2-categories\, resulting in a type of 2-category called 'locally wi de finitary 2-categories'. After discussing some of the difficulties this introduces\, I will focus on a specific type of locally wide finitary 2-ca tegory\, namely locally wide quasi-fiat 2-categories\, and discuss what we know about coalgebra 1-morphisms and their associated 2-representations i n this case.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Freed (Univ. Texas at Austin) DTSTART:20230215T163000Z DTEND:20230215T173000Z DTSTAMP:20260424T221532Z UID:TQFT/75 DESCRIPTION:Title: What is an anomaly?\nby Dan Freed (Univ. Texas at Austin) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nAn omalies in quantum field theory have been the subject of attention for dec ades. In this talk I will dispel some myths: anomalies are tied to symmet ry\, anomalies are tied to fermionic fields\, etc. Then I will explain ho w anomalies - expressed as invertible field theories - are the manifestati on of the projectivity of quantum field theory. My point of view is summa rized by a slogan:\n\n Quantum theory is projective. Quantizat ion is linear.\n\nPlease note the earlier starting time\, half an hour bef ore the usual time.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Geer (Utah State University) DTSTART:20230222T170000Z DTEND:20230222T180000Z DTSTAMP:20260424T221532Z UID:TQFT/76 DESCRIPTION:Title: Non-semisimple TQFTs\nby Nathan Geer (Utah State University) as p art of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\ nIn this talk I will give a general overview of recent work on TQFTs from non-semisimple categories. The main goal of the talk is to give a hint of what is needed to extend the Witten–Reshetikhin–Turaev TQFT to the non -semisimple world.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Young (Utah State University) DTSTART:20230301T170000Z DTEND:20230301T180000Z DTSTAMP:20260424T221532Z UID:TQFT/77 DESCRIPTION:Title: $U_q(\\mathfrak{gl}(1 \\vert 1))$ and $U(1 \\vert 1)$ Chern–Simons theory\nby Matt Young (Utah State University) as part of Topological Q uantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract \nThe goal of this talk is to explain a concrete instance of the theory of non-semisimple TQFT in three dimensions\, as discussed in the talk of Nat han Geer in this seminar on Feb. 22nd\, 2023. I will describe a recent con struction of a TQFT which realizes Chern–Simons theory with gauge superg roup $U(1 \\vert 1)$\, as studied in the physics literature by Rozansky– Saleur and Mikhaylov. In particular\, I'll describe various relative modul ar structures on the category of representations of the quantum group of $ \\mathfrak{gl}(1 \\vert 1)$ which should be seen as non-semisimple analogu es of modular tensor categories associated to the quantum representation t heory of a simple Lie algebra at a root of unity. Based on joint work with Nathan Geer.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Niklas Garner (University of Washington) DTSTART:20230322T170000Z DTEND:20230322T180000Z DTSTAMP:20260424T221532Z UID:TQFT/78 DESCRIPTION:Title: VOAs and Twisted Chern-Simons-Matter TQFTs\nby Niklas Garner (Uni versity of Washington) as part of Topological Quantum Field Theory Club (I ST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Departm ent\, Instituto Superior Técnico).\n\nAbstract\nThe rich interplay betwee n three-dimensional topological quantum field theories (TQFTs) and vertex operator algebras (VOAs) has been a useful bridge in understanding aspects of both subjects. In this talk\, I will describe some aspects of this cor respondence focusing on the simple\, yet surprisingly rich\, examples of C hern-Simons theories based on the Lie superalgebra $\\mathfrak{gl}(1|1)$.\ n LOCATION:https://stable.researchseminars.org/talk/TQFT/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Walker (Microsoft Station Q) DTSTART:20230405T160000Z DTEND:20230405T170000Z DTSTAMP:20260424T221532Z UID:TQFT/79 DESCRIPTION:Title: Two approaches to a universal state sum\nby Kevin Walker (Microso ft Station Q) as part of Topological Quantum Field Theory Club (IST\, Lisb on)\n\n\nAbstract\nI’ll describe two approaches to constructing a univer sal state sum. The first approach (arXiv:2104.02101) is more elementary an d assumes semisimplicity. Special cases of this state sum include Turaev –Viro\, Crane–Yetter\, Douglas–Reutter\, the Reshetikhin–Turaev De hn surgery formula (thought of as a state sum)\, Brown–Arf for $\\mathrm {Pin}_-$ 2-manifolds\, and Dijkgraaf–Witten. The second approach (joint work with David Reutter) is more general and does not assume semisimplicit y. If there’s time I’ll sketch a program to use the non-semisimple sta te sum to reproduce a cluster of non-semi-simple 3-manifold invariants due to many different authors (Lyubashenko\, Kuperberg\, Hennings\, ... Geer\ , Gainutdinov\, Patureau-Mirand\, ... ).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Contreras (Amherst College) DTSTART:20230412T160000Z DTEND:20230412T170000Z DTSTAMP:20260424T221532Z UID:TQFT/80 DESCRIPTION:Title: Frobenius objects in the category of spans and the symplectic categor y\nby Ivan Contreras (Amherst College) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIt is well known that Frob enius algebras are in correspondence with 2-dimensional TQFTs. In this tal k\, we introduce Frobenius objects in any monoidal category\, and in parti cular in the category where objects are sets and morphisms are spans of se ts. We prove the existence of a simplicial set that encodes the data of th e Frobenius structure in this category. This serves as a (simplicial) toy model of the Wehrheim–Woodward construction for the symplectic category. This is part of a program that intends to describe\, in terms of category theory\, the relationship between symplectic groupoids and topological fi eld theory via the Poisson sigma model. Based on joint work with Rajan Meh ta and Molly Keller (Rev. in Math. Phys (34) 10 (2022))\, with Rajan Mehta \, Adele Long and Sophia Marx (https://arxiv.org/abs/2208.14716)\, and ong oing work with Rajan Mehta and Walker Stern.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Creutzig (University of Alberta) DTSTART:20230419T160000Z DTEND:20230419T170000Z DTSTAMP:20260424T221532Z UID:TQFT/81 DESCRIPTION:Title: Ribbon categories associated to gl(1|1)\nby Thomas Creutzig (Univ ersity of Alberta) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn recent seminars you have heard about topologica l field theories associated to gl(1|1). These are TFTs constructed out of ribbon supercategories whose underlying algebra is related to gl(1|1)\, i. e. the quantum supergroup gl(1|1) or the affine VOA of gl(1|1). I will giv e an overview on the representation theory of the affine VOA of gl(1|1) an d explain why its ribbon supercategory coincides with the one of quantum g l(1|1).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Julie Bergner (University of Virginia) DTSTART:20230426T160000Z DTEND:20230426T170000Z DTSTAMP:20260424T221532Z UID:TQFT/83 DESCRIPTION:Title: Models for $(\\infty\,n)$-categories with discreteness conditions \nby Julie Bergner (University of Virginia) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThere are two ways of tur ning Segal spaces into models for up-to-homotopy categories\, or $(\\infty \,1)$-categories: either asking that the space of objects be discrete\, or requiring Rezk's completeness condition. When generalizing to higher $(\\ infty\,n)$-categories\, both of these approaches have been taken to multis implicial models\, in the form of Segal $n$-categories and $n$-fold comple te Segal spaces\, but models given by $\\Theta_n$-diagrams have focused on the completeness conditions. In this talk\, we'll discuss how to get a $\ \Theta_n$-model with discreteness conditions\, but also address the questi on of when these conditions can be mixed and matched with one another.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitri Nikshych (University of New Hampshire) DTSTART:20230503T170000Z DTEND:20230503T180000Z DTSTAMP:20260424T221532Z UID:TQFT/84 DESCRIPTION:Title: Witt groups of braided fusion categories and minimal non-degenerate e xtensions\nby Dmitri Nikshych (University of New Hampshire) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe s ymmetric center of a braided category B consists of all objects of B havin g symmetric\nbraiding with every object of B. The categorical Witt group W (E) of braided fusion categories with the same symmetric center E is obtai ned as the quotient of the monoid of such categories by its submonoid con sisting of Drinfeld centers. I will discuss the structure of this group an d its role in the study of minimal non-degenerate extensions of braided ca tegories. This theory has applications to the classification of braided fu sion 2-categories (which\, in turn\, lead to 4-dimensional TQFTs).\n\nNot e unusual time.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/84/ END:VEVENT BEGIN:VEVENT SUMMARY:David Ben-Zvi (University of Texas\, Austin) DTSTART:20230510T160000Z DTEND:20230510T170000Z DTSTAMP:20260424T221532Z UID:TQFT/85 DESCRIPTION:Title: A TQFT POV on L-functions\nby David Ben-Zvi (University of Texas\ , Austin) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\ n\n\nAbstract\n​I'll discuss a perspective on L-functions modeled on the theory of boundary conditions in extended TQFT\, emerging from my upcomin g work with Yiannis Sakellaridis and Akshay Venkatesh. In particular\, I'l l explain the parallel between L-functions and characters of higher catego rical representations\, and the role of geometric and deformation quantiza tion of shifted symplectic varieties in the theory.\n​\n LOCATION:https://stable.researchseminars.org/talk/TQFT/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Jennifer Brown (Yale University) DTSTART:20230621T160000Z DTEND:20230621T170000Z DTSTAMP:20260424T221532Z UID:TQFT/86 DESCRIPTION:Title: Defect Skein Theories\nby Jennifer Brown (Yale University) as par t of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nT wo field theories can sometimes meet at a codimension one defect\, which c arries the information on how to transition between the bulk theories.\n\n Stratified factorization homology is a tool for constructing such theories with defects from their local coefficient systems. One well-motivated exa mple is parabolic induction\, in which $\\operatorname{Rep}_q G$ is reduce d to the $q$-commutative $\\operatorname{Rep}_q T$ theory via Borel reduct ion along a defect. This is the stacky setting for Fock–Goncharov's clus ter coordinates. It is also a natural context for constructing the quantum A-polynomial.\n\nThe talk will start with an introduction to stratified s paces and factorization homology\, and will include a review of skein rela tions and categories. We will focus on surfaces with line defects\, buildi ng the associated skein theory and discussing how it computes the relevant stratified factorization homology.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Upmeier (University of Aberdeen) DTSTART:20230524T160000Z DTEND:20230524T170000Z DTSTAMP:20260424T221532Z UID:TQFT/87 DESCRIPTION:Title: Invertible TQFTs and Atiyah–Singer index theory\nby Markus Upme ier (University of Aberdeen) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nI will discuss work in progress that con structs a categorification of Atiyah-Singer index theory. My main theorem shows that these new\, categorical indices can be organized into an invert ible TQFT\, which can algebraically be viewed as a categorical group repre sentation of a cobordism category. If time permits\, I will outline how to compute the categorical index topologically.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Haïoun (University of Toulouse) DTSTART:20230517T160000Z DTEND:20230517T170000Z DTSTAMP:20260424T221532Z UID:TQFT/88 DESCRIPTION:Title: Non-semisimple WRT as non-compact fully extended relative TQFTs\n by Benjamin Haïoun (University of Toulouse) as part of Topological Quantu m Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will argue that the Wi tten–Reshetikhin–Turaev-type TQFTs obtained from non-semisimple modula r categories can be obtained from the Cobordism Hypothesis. This is in app arent contradiction with known results\, but I will explain how one can wo rk around these problems using relative TQFTs\, following ideas of Walker\ , Freed–Teleman and Jordan–Safronov. I will present my recent dualizab ility results showing that the Cobordism Hypothesis does give a TQFT from the desired data\, and conjecture that these recover the known non-semisim ple TQFTs. Based on arXiv:2304.12167.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Surya Raghavendran (Perimeter Institute for Theoretical Physics/Un iversity of Toronto) DTSTART:20230705T160000Z DTEND:20230705T170000Z DTSTAMP:20260424T221532Z UID:TQFT/89 DESCRIPTION:Title: Twisted eleven-dimensional supergravity and infinite-dimensional exce ptional simple super Lie algebras\nby Surya Raghavendran (Perimeter In stitute for Theoretical Physics/University of Toronto) as part of Topologi cal Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI'll describe a perturbative BV theory defined on 11-manifolds with a rank 6 transversel y holomorphic foliation and a transverse Calabi–Yau structure. The theor y has an infinite dimensional algebra of gauge symmetries preserving the t rivial background\, which is $L_\\infty$ equivalent to a Lie 2-extension o f the infinite dimensional exceptional simple super Lie algebra E(5|10). C onjecturally\, this theory describes the minimal twist of eleven-dimension al supergravity. After describing this conjecture\, and evidence for it\, I'll describe twisted avatars of the AdS_4 x S^7 and AdS_7 x S^4 backgroun ds\, and how two other infinite dimensional exceptional simple super Lie a lgebras E(1|6) and E(3|6) appear as asymptotic symmetries. Enumerating gra vitons on such backgrounds naturally leads to refinements of generating fu nctions of representation-theoretic significance\, such as the MacMahon fu nction. Time permitting\, I'll explain how our results combined with holog raphic techniques can be used to produce enhancements of familiar vertex a lgebras such as the Heisenberg and Virasoro algebras\, to holomorphic fact orization algebras in three complex dimensions\, and furnish geometric con structions of representations thereof. This talk is based on joint work wi th Ingmar Saberi and Brian Williams.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Etingof (Massachusetts Institute of Technology) DTSTART:20230712T160000Z DTEND:20230712T170000Z DTSTAMP:20260424T221532Z UID:TQFT/90 DESCRIPTION:Title: Lie theory in tensor categories (with applications to modular represe ntation theory)\nby Pavel Etingof (Massachusetts Institute of Technolo gy) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nA bstract\nLet $G$ be a group and $k$ an algebraically closed field of chara cteristic $p$. If $V$ is a finite-dimensional representation of $G$ over $ k$\, then by the classical Krull–Schmidt theorem\, the $n$th tensor powe r of $V$ can be uniquely decomposed into a direct sum of indecomposable re presentations. But we know very little about this decomposition\, even for very small groups\, such as $G = (\\Bbb Z/2)^3$ for $p = 2$ or $G = (\\Bb b Z/3)^2$ for $p = 3$.\n\nFor example\, what can we say about the number $ d_n(V)$ of summands with dimension coprime to $p$? It is easy to show that there is a finite limit $d(V) := \\lim_{n \\to \\infty} d_n(V)^{1/n}$\, b ut what kind of number is this? Is it algebraic or transcendental? Until r ecently\, there were no techniques to solve such questions (and in particu lar the same question about the sum of dimensions of these summands is sti ll wide open). Remarkably\, a new subject which may be called "Lie theory in tensor categories" gives methods to show that $d(V)$ is indeed an algeb raic number\, which moreover has the form\n\\[ d(V) = \\sum_{1 \\leq j \\l eq p/2} n_j(V)[j]_q\, \\]\nwhere $n_j(V)$ is a natural number\, $q := \\ex p(\\pi i/p)$ is a particular root of unity\, and $[j]_q := \\frac{q^j-q^{- j}}{q-q^{-1}}$ is a $q$-number. Moreover\, $d(V \\oplus W) = d(V) + d(W)$ and $d(V \\otimes W) = d(V) d(W)$\, so $d$ is a character of the Green rin g of $G$ over $k$. Finally\, $d_n(V) \\geq C_V d(V)^n$\, for some $0 < C_V \\leq 1$\, and we can give lower bounds for $C_V$. In the talk\, I will e xplain what Lie theory in tensor categories is and how it can be applied t o such problems. This is joint work with K. Coulembier and V. Ostrik.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Kinnear (University of Edinburgh) DTSTART:20230628T160000Z DTEND:20230628T170000Z DTSTAMP:20260424T221532Z UID:TQFT/91 DESCRIPTION:Title: Varying the non-semisimple Crane–Yetter theory over the character s tack\nby Patrick Kinnear (University of Edinburgh) as part of Topologi cal Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nAssociated to a certain subquotient of the category of representations of the small quan tum group at a root of unity is an invertible 4d TQFT known as Crane–Yet ter: it is the anomaly theory of the 3d theory called Witten–Reshetikhin –Turaev. In fact\, the non-semisimplified representation category is inv ertible in the Morita theory of braided tensor categories: under the cobor dism hypothesis this defines a non-semisimple invertible TQFT. Such an inv ertible theory assigns to a closed 3-manifold a 1-dimensional vector space . In this talk\, we define a relative TQFT which can be seen as varying no n-semisimple Crane-Yetter over the character stack: it assigns to a closed 3-manifold $M$ a line bundle on its character stack $\\mathrm{Ch}_G(M)$. We construct this theory by analysing invertibility of a 1-morphism in the Morita theory of symmetric tensor categories\, coming from representation s of Lusztig's quantum group at a root of unity regarded as a bimodule for $\\mathrm{Rep}(G)$ using the quantum Frobenius map. In the talk we will d escribe this 1-morphism and analyse its invertibility and the consequences of this in detail.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Pachol (University of South-Eastern Norway) DTSTART:20230726T160000Z DTEND:20230726T170000Z DTSTAMP:20260424T221532Z UID:TQFT/92 DESCRIPTION:Title: Quantum groups in the digital setting\nby Anna Pachol (University of South-Eastern Norway) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe main idea behind noncommutative geometr y is to “algebralize” geometric notions and then generalize them to no ncommutative algebras. This way noncommutative geometry offers a generalis ed notion of the geometry. Quantum groups or Hopf algebras play the role o f ‘group objects’ in noncommutative geometry and they provide an appro ach to the development of the theory much as Lie groups do in differential geometry.\n\nI will give an introduction to the topic and briefly mention results on classification of all bialgebras and Hopf algebras of dimensio n ≤ 4 over the field $F_2 = \\{0\, 1\\}$. These results can be summarize d as a quiver\, where the vertices are the inequivalent algebras and there is an arrow for each inequivalent bialgebra or Hopf algebra built from th e algebra at the source of the arrow and the dual of the algebra at the ta rget of the arrow. There are 314 distinct bialgebras and\, among them\, 25 Hopf algebras\, with at most one of these from one vertex to another. We found a unique smallest noncommutative and noncocommutative quantum group\ , which is moreover self-dual and resembles a digital version of $U_q(\\ma thfrak{sl}_2)$.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabian Hahner (Heidelberg University) DTSTART:20230719T160000Z DTEND:20230719T170000Z DTSTAMP:20260424T221532Z UID:TQFT/93 DESCRIPTION:Title: Pure spinor techniques in (twisted) supergravity\nby Fabian Hahne r (Heidelberg University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe pure spinor superfield formalism gives a systematic and geometric technique to construct supersymmetric field the ories from algebro-geometric input data. Crucially\, this procedure provid es superfield descriptions where the actions of the supersymmetries are st rict and ompatible with twisting. In this talk\, I will demonstrate the me rits of the formalism using the example of eleven-dimensional supergravity . In particular\, I present a uniform construction of the interacting theo ry and all its twists realizing them as generalizations of Poisson–Chern –Simons theory. In addition to simplifying the computation of twists imm ensely\, this also sheds some new light on the supergeometric origin of th e supergravity theory. The talk is based on joint work with Ingmar Saberi. \n LOCATION:https://stable.researchseminars.org/talk/TQFT/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Walker (Microsoft Station Q) DTSTART:20230914T160000Z DTEND:20230914T170000Z DTSTAMP:20260424T221532Z UID:TQFT/94 DESCRIPTION:Title: Low-dimensional H-bordism and H-modular TQFTs\nby Kevin Walker (M icrosoft Station Q) as part of Topological Quantum Field Theory Club (IST\ , Lisbon)\n\n\nAbstract\nLet H denote a class of manifolds (such as SO (or iented)\, O (unoriented)\, Spin\, Pin+\, Pin-\, manifolds with spin defect s\, etc.). We define a 2+1-dimensional H-modular TQFT to be one which live s on the boundary of a bordism-invariant 3+1-dimensional H-TQFT. Correspon dingly\, we define a H-modular tensor category to be a H-premodular catego ry which leads to a bordism-invariant 3+1-dimensional TQFT. When H = SO\, this reproduces the familiar Witten-Reshetikhin-Turaev TQFTs and correspon ding modular tensor categories. For other examples of H\, non-zero H-bordi sm groups in dimensions 4 or lower lead to interesting complications (anom alies\, mapping class group extensions\, obstructions to defining the H-mo dular theory on all H-manifolds).\n\nPlease note that this is an in-person seminar that we will broadcast online. We encourage local participants to join us in room 3.10 of the mathematics building.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Mnev (University of Notre Dame) DTSTART:20230920T170000Z DTEND:20230920T180000Z DTSTAMP:20260424T221532Z UID:TQFT/95 DESCRIPTION:Title: Why BF theory is not an Atiyah’s TQFT\, and how the BV-BFV approach helps\nby Pavel Mnev (University of Notre Dame) as part of Topologica l Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nBF theory does n ot quite fit into (strict) Atiyah’s axioms. The space of states it assig ns to a boundary is typically infinite-dimensional (which implies that the partition function of $S^1 \\times X$ is infinite). This can be seen (a) as a consequence of noncompactness of the phase space of the theory or (b) as a manifestation of the problem of zero-modes. The BV-BFV formalism is an approach to gauge theories (in particular\, topological ones) combining the Atiyah-Segal functorial picture with the idea of Wilson’s effective action. In this talk I will sketch the construction of BF theory in the B V-BFV language and will explain how it assigns meaningful partition functi ons (satisfying an appropriate gluing property) to all cobordisms.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Costantino (University of Toulouse) DTSTART:20231206T170000Z DTEND:20231206T180000Z DTSTAMP:20260424T221532Z UID:TQFT/96 DESCRIPTION:Title: Stated skein modules of 3-manifolds and TQFTs\nby Francesco Costa ntino (University of Toulouse) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nAfter reviewing the definition of stat ed skein modules for surfaces and 3-manifolds\, I will detail how this rec ent notion allows us to relate topological constructions (related to cut a nd paste techniques) to algebraic ones (for instance\, braided tensor prod ucts of algebra objects in braided categories). I will explain how the sta ted skein algebra of some special surfaces provides a topological descript ion for some notable algebras (e.g. the quantised function ring $O_q(\\mat hfrak{sl}_2)$ or its "transmutation" $BSL_2(q)$). Then I will describe how stated skein moduli of 3-manifolds fit into a TQFT framework\, albeit not a completely standard one. If time permits I will also discuss some unexp ected noninjectivity results in dimension 3. This is joint work with Thang Le.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedram Hekmati (University of Auckland) DTSTART:20231214T170000Z DTEND:20231214T180000Z DTSTAMP:20260424T221532Z UID:TQFT/97 DESCRIPTION:Title: Equivariant Floer homology and its applications\nby Pedram Hekmat i (University of Auckland) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\n\nAbstract\nFloer theory comes in various flavours and has developed into a primary tool in low-dimensional topology. In this ta lk\, I will discuss the construction of an equivariant Seiberg–Witten– Floer homology associated to finite group actions on rational homology 3-s pheres. This gives rise to a series of numerical invariants and I will sur vey some of their applications in knot theory\, to equivariant embeddings and as obstructions to extending group actions to bounding 4-manifolds. Th is is joint work with David Baraglia.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco De Renzi (University of Montpellier) DTSTART:20240110T170000Z DTEND:20240110T180000Z DTSTAMP:20260424T221532Z UID:TQFT/98 DESCRIPTION:Title: Algebraic presentation of cobordisms and TQFTs\nby Marco De Renzi (University of Montpellier) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nIt has long been known that the category of 2-dimensional cobordisms is freely generated by a commutative Frobeniu s algebra\, the circle. This result allows for a complete classification o f TQFTs (Topological Quantum Field Theories) in dimension 2. In this talk I will discuss similar algebraic presentations in dimension 3 and 4 due to Bobtcheva and Piergallini. In both cases\, the fundamental algebraic stru ctures are provided by certain Hopf algebras called BPH algebras. I will a lso present examples of such algebras and the TQFTs they induce. This is a joint work with A. Beliakova\, I. Bobtcheva\, and R. Piergallini.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukas Woike (University of Burgundy) DTSTART:20240124T170000Z DTEND:20240124T180000Z DTSTAMP:20260424T221532Z UID:TQFT/99 DESCRIPTION:Title: An introduction to quantum representations of mapping class groups\nby Lukas Woike (University of Burgundy) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/TQFT/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Nadia Ott (University of Southern Denmark) DTSTART:20240131T170000Z DTEND:20240131T180000Z DTSTAMP:20260424T221532Z UID:TQFT/100 DESCRIPTION:Title: The super period map and the projectedness of supermoduli space\ nby Nadia Ott (University of Southern Denmark) as part of Topological Quan tum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn 2014\, Donagi and W itten proved that supermoduli spaces $\\mathfrak{M}_g$ of genus $g$ super Riemann surfaces are not projected for genus $g \\geq 5$. In joint work wi th Ron Donagi\, we show that $\\mathfrak{M}_g$ is projected\, for all genu s $g$\, away from the so-called bad divisor. In other words\, we show that the complement $U_g$ of $\\mathcal{B} \\subset \\mathfrak{M}_g$ is a proj ected open subscheme of $\\mathfrak{M}_g$. Furthermore\, at least in genus $g = 2$ and $g = 3$\, we show that the super period map defines a project ion $U_g \\to U_{g\,\\mathrm{bos}}$.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukas Müller (Perimeter Institute) DTSTART:20240207T170000Z DTEND:20240207T180000Z DTSTAMP:20260424T221532Z UID:TQFT/101 DESCRIPTION:Title: Topological defects form higher dagger categories\nby Lukas Mül ler (Perimeter Institute) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nRecently\, the study of higher categories o f topological defects in quantum field theory has gained significant atten tion due to their connection to categorical symmetries. These higher categ ories exhibit noteworthy additional structures\, depending upon the specif ic theories and defects under consideration. For instance\, in oriented 2- dimensional field theories\, they organize into a pivotal bicategory. Curr ently\, we lack a comprehensive framework to systematically describe these intricate structures. In my talk I will argue that the theory of higher d agger categories provides such a framework. I will focus on defects within fully extended topological field theories. Except in low dimensions the p icture proposed here is highly conjectural. The talk is partially based on joint work in progress with Bruce Bartlett\, Gio Ferrer\, Brett Hungar\, Theo Johnson-Freyd\, Cameron Krulewski\, Nivedita\, Dave Penneys\, David R eutter\, Claudia Scheimbauer\, Luuk Stehouwer\, and Chetan Vuppulury.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Gunningham (Montana State University) DTSTART:20240221T170000Z DTEND:20240221T180000Z DTSTAMP:20260424T221532Z UID:TQFT/102 DESCRIPTION:Title: Skein theory and the geometric Langlands program\nby Sam Gunning ham (Montana State University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nSkein modules are certain families of vector spaces spanned by embedded links or graphs in a 3-manifold M\, modu lo certain local relations. They can be thought of both as an obstruction to defining a polynomial invariant of knots in M and as an invariant of th e 3-manifold M. In this talk\, I will survey some history\, recent results \, and work in progress on skein modules\, motivated by their role in the geometric Langlands program. I will discuss joint work with (some subsets of) David Ben-Zvi\, David Jordan\, Pavel Safronov\, Monica Vazirani\, and Haiping Yang.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Luuk Stehouwer (Dalhousie University) DTSTART:20240306T170000Z DTEND:20240306T180000Z DTSTAMP:20260424T221532Z UID:TQFT/103 DESCRIPTION:Title: The Categorical Spin-Statistics Theorem: A TQFT Perspective\nby Luuk Stehouwer (Dalhousie University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe spin-statistics theorem is a cornerstone of physics\, linking particle spin to its fermionic or boson ic nature in unitary quantum field theory. This talk presents a novel proo f of this theorem within the framework of unitary TQFTs using so-called da gger categories. Our method draws upon the perspective on dagger categorie s by anti-involutions and Hermitian forms\, which I jointly developed with Jan Steinebrunner. This approach not only provides a clearer understandin g of the spin-statistics theorem\, but also offers valuable insights into symmetric monoidal dagger categories.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Marko Stošić (Instituto Superior Técnico) DTSTART:20240320T170000Z DTEND:20240320T180000Z DTSTAMP:20260424T221532Z UID:TQFT/104 DESCRIPTION:Title: Combinatorics in knot-quiver correspondences\nby Marko Stošić (Instituto Superior Técnico) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will present different versions of th e knot-quiver correspondence related to various knot invariants\, with th e emphasis on combinatorial implications. In particular\, we shall review different enumerative results and integrality properties that are corollar ies of the knot-quiver correspondence\, as well as recent advances regardi ng quivers with higher level nodes.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristina Anghel (University of Leeds) DTSTART:20240410T160000Z DTEND:20240410T170000Z DTSTAMP:20260424T221532Z UID:TQFT/105 DESCRIPTION:Title: A universal coloured Alexander invariant from configurations on oval s in the disc\nby Cristina Anghel (University of Leeds) as part of Top ological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe colou red Jones and Alexander polynomials are quantum invariants that come from representation theory. There are important open problems in quantum topolo gy regarding their geometric information. Our goal is to describe these in variants from a topological viewpoint\, as intersections between submanifo lds in configuration spaces. We show that the Nth coloured Jones and Alexa nder polynomials of a knot can be read off from Lagrangian intersections i n a fixed configuration space. At the asymptotic level\, we geometrically construct a universal ADO invariant for links as a limit of invariants giv en by intersections in configuration spaces. The parallel question of prov iding an invariant unifying the coloured Jones invariants is the subject o f the universal Habiro invariant for knots. The universal ADO invariant th at we construct recovers all of the coloured Alexander invariants (in part icular\, the Alexander polynomial in the first term).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Inbar Klang (Vrije University Amsterdam) DTSTART:20240502T160000Z DTEND:20240502T170000Z DTSTAMP:20260424T221532Z UID:TQFT/106 DESCRIPTION:Title: An algebraic topology perspective on factorization homology\nby Inbar Klang (Vrije University Amsterdam) as part of Topological Quantum Fi eld Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will give an introduction to factorization homology using configuration spaces\, and discuss the non abelian Poincaré duality theorem of Segal\, Salvatore\, Lurie\, and Ayala –Francis​\, which relates factorization homology to mapping spaces. Ti me permitting\, I will also talk about the Ayala–Francis axiomatic appro ach to factorization homology\, which positions factorization homology as a "homology theory for manifolds."\n LOCATION:https://stable.researchseminars.org/talk/TQFT/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Schulz (Johns Hopkins University) DTSTART:20240424T160000Z DTEND:20240424T170000Z DTSTAMP:20260424T221532Z UID:TQFT/107 DESCRIPTION:Title: Spectral networks and G2\nby Sebastian Schulz (Johns Hopkins Uni versity) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n \n\nAbstract\nSpectral networks are a combinatorial tool consisting of lab elled lines on a Riemann surface. They have a surprising amount of applica tions and are intimately linked to non-Abelianization of flat connections\ , Fock–Goncharov cluster coordinates\, exact WKB theory\, etc. After rev iewing this story for the SL(2) and SL(3) case\, I will describe this is i n detail for the group G2. Time permitting\, I will give as an application a concrete parametrization of the nonabelian Hodge correspondence for the Hitchin component of the split real form of G2. This is joint work with A ndy Neitzke.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Carqueville (University of Vienna) DTSTART:20240605T160000Z DTEND:20240605T170000Z DTSTAMP:20260424T221532Z UID:TQFT/108 DESCRIPTION:Title: Orbifold completion of 3-categories\nby Nils Carqueville (Univer sity of Vienna) as part of Topological Quantum Field Theory Club (IST\, Li sbon)\n\n\nAbstract\nWe develop a general theory of 1-\, 2-\, and 3-dimens ional "orbifold completion"\, to describe (generalised) orbifolds of topol ogical quantum field theories as well as all their defects. This can be vi ewed as the "oriented version" of condensation completion. We give a basic introduction to TQFTs and their orbifolds\, and discuss applications whic h include defect TQFTs for state sum models\, Reshethikin-Turaev and Crane -Yetter theory. This is joint work with Lukas Müller.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrien Brochier (Université Paris Cité) DTSTART:20240417T160000Z DTEND:20240417T170000Z DTSTAMP:20260424T221532Z UID:TQFT/109 DESCRIPTION:Title: A classification of modular functors from generalized skein theory\nby Adrien Brochier (Université Paris Cité) as part of Topological Qu antum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nModular functors are collections of projective representations of mapping class groups of surf aces\, compatible with cutting and gluing operations. They can be thought of as categorified\, anomalous 2d topological field theories (TFT) where t he "anomaly" is responsible for the projectiveness of the représentations .\n\nA well-known folklore theorem states that ordinary 2d TFT are classif ied by (commutative) Frobenius algebras. In a similar way\, any modular fu nctor yields a "categorified Frobenius algebra"\, of which ribbon categori es form a large class of examples. In this talk\, we'll explain a necessar y and sufficient condition for such a structure to extend to a modular fun ctor\, formulated in terms of certain generalized skein modules attached t o handlebodies. A key observation is that this is\, indeed\, a condition\, not extra structure\, so that such an extension is essentially unique whe never it exists.\n\nThis construction should be thought of as a far reachi ng generalization of the construction by Masbaum and Roberts of a modular functor from Kauffman skein modules. As a special case it also recovers\, in a purely topological way\, the construction of a modular functor from a (not necessarily semisimple) modular category by Lyubachenko\, and the un iqueness result is new even in those cases. This is based on joint work wi th Lukas Woike.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan-Willem van Ittersum (University of Cologne) DTSTART:20240412T130000Z DTEND:20240412T140000Z DTSTAMP:20260424T221532Z UID:TQFT/110 DESCRIPTION:Title: Shifted symmetric functions\, quasimodular forms and Hamiltonian ope rators\nby Jan-Willem van Ittersum (University of Cologne) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nStarti ng with a counting problem for elements of the symmetric group\, we introd uce the so-called shifted symmetric functions. These functions\, which als o occur naturally in enumerative geometry\, have the remarkable property t hat the corresponding generating series are quasimodular forms. We discuss another family of functions on partitions with the same property. In part icular\, using certain Hamiltonian operators associated to cohomological f ield theories\, we explain how this seemingly different family of function s turns out to be closely related to the shifted symmetric functions.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Pranav Prandit (Tata Institute of Fundamental Research) DTSTART:20240508T160000Z DTEND:20240508T170000Z DTSTAMP:20260424T221532Z UID:TQFT/111 DESCRIPTION:Title: Deformations of objects in higher categories\nby Pranav Prandit (Tata Institute of Fundamental Research) as part of Topological Quantum Fi eld Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will describe a map that a ssociates to every deformation of an object in a higher category a collect ion of generalized symmetries of the object. Building on work by Lurie\, w e will see that the failure of this map to be an equivalence can be quanti fied. Under favorable circumstances\, the map is an equivalence\, and this leads to an explicit description of the space of deformations in terms of solutions to certain equations. I will discuss applications of these resu lts to topological field theory and holomorphic symplectic geometry. This talk is based on joint work with Bhanu Kiran.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Christoph Schweigert (University of Hamburg) DTSTART:20240522T160000Z DTEND:20240522T170000Z DTSTAMP:20260424T221532Z UID:TQFT/112 DESCRIPTION:Title: Traces and higher structures\nby Christoph Schweigert (Universit y of Hamburg) as part of Topological Quantum Field Theory Club (IST\, Lisb on)\n\n\nAbstract\nQuantum topologists are used to thinking about traces i n the framework of pivotal tensor categories and thus in a two-dimensional context to which a two-dimensional graphical calculus can be associated. We explain that traces are already naturally defined for twisted endomorph isms of linear categories\, i.e. in a one-dimensional context. The endomor phisms are twisted by the Nakayama functor which\, for a module category o ver a monoidal category\, is a twisted module functor and hence an inheren tly three-dimensional object. This naturally leads to a three-dimensional graphical calculus. This calculus also has applications to Turaev–Viro t opological field theories with defects.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Wasserman (University of Oxford) DTSTART:20240529T160000Z DTEND:20240529T170000Z DTSTAMP:20260424T221532Z UID:TQFT/113 DESCRIPTION:Title: The Landau-Ginzburg / conformal field theory correspondence\nby Thomas Wasserman (University of Oxford) as part of Topological Quantum Fie ld Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe Landau-Ginzburg (LG) / Co nformal Field Theory (CFT) correspondence predicts a relationship between certain categories of matrix factorisations (for the "LG potential'') and modular tensor categories (for the CFT side). This prediction has its orig in in physics\, and comes from observations about 2-dimensional N=2 supers ymmetric quantum field theory. I will explain how this prediction is to be interpreted mathematically and what difficulties one encounters in doing this. After this I will discuss joint work with Ana Ros Camacho in which w e realise the LG/CFT correspondence for the potentials $x^d$. The main ing redient in this is an enriched category theoretic version of the classical Temperley-Lieb/Jones-Wenzl construction of the representation category of quantum su(2).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang Yang (Technical University of Munich) DTSTART:20240612T160000Z DTEND:20240612T170000Z DTSTAMP:20260424T221532Z UID:TQFT/114 DESCRIPTION:Title: RCFT correlators as equivalences of modular functors\nby Yang Ya ng (Technical University of Munich) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nThe local information of a 2d rat ional conformal field theory (RCFT) is encoded in a vertex operator algebr a\, whose modules constitute a modular fusion category C. The collection o f global observables of the theory is given by conformal blocks and carrie s actions of mapping class groups\, which is described mathematically by a modular functor that assigns the Drinfeld center Z(C) to a circle. The st ring-net construction\, which first appeared in the study of topological p hases of matter\, not only provides such a modular functor but also suppli es a graphical construction of correlators. A generalization of the string -net construction takes a pivotal bicategory as input. When such a bicateg ory is taken to be C (considered as a bicategory with one object)\, it rec overs the modular functor of conformal blocks. On the other hand\, the mod ular functor associated with the Morita bicategory of separable symmetric Frobenius algebras internal to C classifies stratified worldsheets up to " categorical symmetries". In this talk we explain\, using the framework of double categories\, that RCFT correlators exhibit an equivalence between t hese two modular functors. This is in fact a consequence of the functorial ity of the string-net construction: the lax biadjunction between a pivotal bicategory and its orbifold completion induces an equivalence between the ir string-net modular functors.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Catherine Meusburger (University of Erlangen-Nuremberg) DTSTART:20240619T160000Z DTEND:20240619T170000Z DTSTAMP:20260424T221532Z UID:TQFT/115 DESCRIPTION:Title: Quantum double models and Dijkgraaf-Witten TQFT with defects\nby Catherine Meusburger (University of Erlangen-Nuremberg) as part of Topolo gical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe use 3d de fect TQFTs and state sum models with defects to give a gauge theoretical f ormulation of Kitaev's quantum double model (for a finite group) and the ( untwisted) Dijkgraaf-Witten TQFT with defects. This leads to a simple desc ription in terms of embedded quivers\, groupoids and their representations . Defect Dijkgraaf-Witten TQFT is then formulated in terms of spans of gro upoids and their representations.\n\nThis is work in progress with João F aría Martins (University of Leeds).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Agnès Beaudry (University of Colorado Boulder) DTSTART:20240626T160000Z DTEND:20240626T170000Z DTSTAMP:20260424T221532Z UID:TQFT/116 DESCRIPTION:Title: Homotopy theory of parametrized quantum systems\nby Agnès Beaud ry (University of Colorado Boulder) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nIn recent years\, there has been a growing number of applications of stable homotopy theory to condensed ma tter physics\, many of which stem from a conjecture of Kitaev that gapped invertible phases of matter should be classified by the homotopy groups of a spectrum. This gives rise to a mathematical modeling question: how do w e model quantum systems in such a way that this result can be better under stood\, perhaps even proved? In this talk\, I will discuss some aspects of this modeling problem. This is based on joint work with Mike Hermele\, Ju an Moreno\, Markus Pflaum\, Marvin Qi and Daniel Spiegel\, David Stephen\, Xueda Wen.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregor Schaumann (University of Würzburg) DTSTART:20240703T160000Z DTEND:20240703T170000Z DTSTAMP:20260424T221532Z UID:TQFT/117 DESCRIPTION:Title: State spaces in TFT: Quivers and infinite particle algebras\nby Gregor Schaumann (University of Würzburg) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nA topological field theory (TFT) with particles exhibits distinguished state spaces\, where the inco ming and outgoing particles match. These "endo-state spaces" occur natural ly in physical applications and possess interesting mathematical structure s: There is a natural gauge action by conjugation and a natural stabilizat ion map. We will show that the gauge action has a non-trivial orbit struct ure\, leading to quiver moduli spaces\, and the stabilization map leads to a treatment of infinite particle content and AF-algebras.\n\nThe talk wil l be rather introductory and assumes no knowledge of quivers or AF-algebra s.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Minghao Wang (Boston University) DTSTART:20240710T140000Z DTEND:20240710T150000Z DTSTAMP:20260424T221532Z UID:TQFT/118 DESCRIPTION:Title: Feynman graph integrals from topological-holomorphic theories and th eir applications\nby Minghao Wang (Boston University) as part of Topol ogical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nFeynman gra ph integrals of topological field theories have been proved to be ultravio let finite by Axelrod and Singer\, and Kontsevich independently. This resu lt leads to many applications including universal finite type knot invaria nts and the formality of $E_n$ operads. In this talk\, I will extend the f initeness results (and some anomaly cancellation results) to Feynman graph integrals of topological-holomorphic theories on flat spaces. The main te chnique for the proof is compactification of the moduli space of metric gr aphs. As a result\, we can construct many factorization algebras from quan tum topological-holomorphic theories. In the special case of 4d Chern–Si mons theory\, the factorization algebra structure encodes the Yang–Baxte r equation. If time permits\, I will sketch how to extend these results to Feynman graph integrals on Kähler manifolds. Part of this work is joint with Brian Williams.\n\nReference: https://arxiv.org/abs/2401.08113\n\nPle ase note the unusual hour!\n LOCATION:https://stable.researchseminars.org/talk/TQFT/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Kapustin (Caltech) DTSTART:20240724T160000Z DTEND:20240724T170000Z DTSTAMP:20260424T221532Z UID:TQFT/119 DESCRIPTION:Title: Topological invariants of gapped states and cosheaves on sites\n by Anton Kapustin (Caltech) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\nRecently\, an approach to constructing to pological invariants of gapped ground-states of lattice systems has been d eveloped in our joint work with N. Sopenko. It applies to arbitrary gapped states of infinite-volume lattice spin systems with rapidly decaying inte ractions and employs C*-algebraic techniques. In this talk\, I will explai n an interpretation of these invariants as obstructions to gauging\, i.e. to promoting a symmetry to a local symmetry. The key observation is that l ocality on a lattice is an asymptotic notion sensitive only to the large-s cale geometry of the support set. Following Kashiwara and Schapira\, one c an encode locality using a natural Grothendieck topology on a category of semilinear subsets of Eucludean space. Infinitesimal symmetries of a gappe d state form a cosheaf over the corresponding site\, and the topological i nvariants are encoded in its Cech complex.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Clark Barwick (University of Edinburgh) DTSTART:20240814T160000Z DTEND:20240814T170000Z DTSTAMP:20260424T221532Z UID:TQFT/120 DESCRIPTION:Title: Factorization algebras in quite a lot of generality\nby Clark Ba rwick (University of Edinburgh) as part of Topological Quantum Field Theor y Club (IST\, Lisbon)\n\n\nAbstract\nIn the last decade there has been a f lurry of interest in arithmetic quantum field theories​. Since the 1960s \, researchers have identified an analogy between various objects of arith metic geometry and low-dimensional manifolds. For example\, Spec of a numb er ring “looks like” an open 3-manifold\, and primes therein “are” embedded knots. This story has become known as arithmetic topology​. Th e idea of arithmetic QFT is to enrich that analogy by importing tools from physics\, just as with low-dimensional topology. One even dreams of using these tools to study number-theoretic questions (the behavior of L-functi ons\, Langlands dualities\, etc.).\n\nBut the objects of arithmetic geomet ry are not​ manifolds. The tools of topology and differential geometry d o not work directly in arithmetic. So it’s unclear how to translate phys ical concepts to arithmetic settings.\n\nTo this end\, we introduce a mini malist framework for factorization algebras\, where the role of the spacet ime manifold can be played by a geometric object of a very general sort. I n retrospect\, the main idea amounts to a categorification of Borcherds’ approach to vertex algebras.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Monica Vazirani (University of California\, Davis) DTSTART:20240717T160000Z DTEND:20240717T170000Z DTSTAMP:20260424T221532Z UID:TQFT/121 DESCRIPTION:Title: Skeins on tori\nby Monica Vazirani (University of California\, D avis) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\ nAbstract\nWe study skeins on the 2-torus and 3-torus via the representati on theory of the double affine Hecke algebra of type A and its connection to quantum D-modules. As an application we can compute the dimension of th e generic $SL_N$- and $GL_N$-skein module of the 3-torus for arbitrary N. This is joint work with Sam Gunningham and David Jordan.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/121/ END:VEVENT BEGIN:VEVENT SUMMARY:David Ayala (Montana State University) DTSTART:20240807T160000Z DTEND:20240807T170000Z DTSTAMP:20260424T221532Z UID:TQFT/122 DESCRIPTION:Title: Factorization homology of higher categories\nby David Ayala (Mon tana State University) as part of Topological Quantum Field Theory Club (I ST\, Lisbon)\n\n\nAbstract\nThe “alpha” version of factorization homol ogy pairs framed n-manifolds with $E_n$-algebras. This construction gener alizes the classical homology of a manifold\, yields novel results concern ing configuration spaces of points in a manifold\, and supplies a sort of state-sum model for sigma-models (i.e.\, mapping spaces) to (n-1)-connecte d targets. This “alpha” version of factorization homology novelly ext ends Poincaré duality\, shedding light on deformation theory and dualitie s among field theories. Being defined using homotopical mathematical foun dations\, “alpha” factorization homology is manifestly functorial and continuous in all arguments\, notably in moduli of manifolds and embedding s between them\, and it satisfies a local-to-global expression that is inh erently homotopical in nature. \n\nNow\, $E_n$-algebras can be characteri zed as $(\\infty\,n)$-categories equipped with an (n-1)-connected functor from a point. The (full) “beta” version of factorization homology pai rs framed n-manifolds with pointed $(\\infty\,n)$-categories with adjoints . Applying 0th homology\, or $\\pi_0$\, recovers a version of the string net construction on surfaces\, as well as skein modules of 3-manifolds. I n some sense\, the inherently homotopical nature of (full) “beta” fact orization homology affords otherwise unforeseen continuity in all argument s\, and local-to-global expressions. \n\nIn this talk\, I will outline a definition of “beta” factorization homology\, focusing on low-dimensio ns and on suitably reduced $(\\infty\,n)$-categories (specifically\, braid ed monoidal categories). I will outline some examples\, and demonstrate s ome features of factorization homology. Some of this material is establis hed in the literature\, some a work in progress\, and some conjectural — the status of each assertion will be made clear. I will be especially in terested in targeting this talk to those present\, and so will welcome com ments and questions.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Jackson Van Dyke (Technical University of Munich) DTSTART:20240731T160000Z DTEND:20240731T170000Z DTSTAMP:20260424T221532Z UID:TQFT/123 DESCRIPTION:Title: Geometric quantization\, fusion categories\, and Rozansky–Witten t heory\nby Jackson Van Dyke (Technical University of Munich) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI wil l begin by reviewing geometric and deformation quantization of a symplecti c vector space. The goal will be to explain an analogy between these objec ts and Rozansky–Witten theory (along with a certain four-dimensional TQF T). This analogy will factor through an analogy concerning three-dimension al TQFTs generated by pointed fusion categories. Throughout\, there will b e an emphasis on equivariance and anomalies.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Tashi Walde (Technical University of Munich) DTSTART:20240821T160000Z DTEND:20240821T170000Z DTSTAMP:20260424T221532Z UID:TQFT/124 DESCRIPTION:Title: Assembly of constructible factorization algebras\nby Tashi Walde (Technical University of Munich) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nThe theory of factorization algebra s\, and particularly that of constructible factorization algebras\, is exp ected to be very well behaved. For example\, it has long been “known” that the assignment taking a stratified manifold to its category of constr uctible factorization algebras satisfies gluing\, i.e.\, is itself a sheaf . Unfortunately\, this and other related facts about factorization algebra s have long been “folklore knowledge”\, but with no proofs available.\ n\nIn this talk I will report on recent work with Eilind Karlsson and Clau dia I. Scheimbauer\, where we close some of these gaps in the literature\, including the aforementioned gluing result.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Colleen Delaney (Purdue University) DTSTART:20240828T160000Z DTEND:20240828T170000Z DTSTAMP:20260424T221532Z UID:TQFT/125 DESCRIPTION:Title: An efficient* classical algorithm for some quantum invariants of 3-m anifolds\nby Colleen Delaney (Purdue University) as part of Topologica l Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe will share so me recent results that are instructive for approaching the classification of 3d TQFTs and topological order by computational complexity. We show tha t the Turaev-Viro-Barrett-Westbury state sum TQFT invariants of 3-manifold s that arise from Tambara-Yamagami fusion categories can actually be compu ted in polynomial time on a classical computer\, provided that there is a bound on the first Betti number. On the other hand\, if we don’t insist on a bound on the first Betti number\, then the invariants should be NP-ha rd to compute. This talk is based on joint work with Clément Maria and Er ic Samperton.\n\nPlease note that this session will not be recorded.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/125/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaël Rouquier (UCLA) DTSTART:20240904T160000Z DTEND:20240904T170000Z DTSTAMP:20260424T221532Z UID:TQFT/126 DESCRIPTION:Title: 2-Representation theory of gl(1|1)\nby Raphaël Rouquier (UCLA) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstr act\n2-Representations of simple Lie algebras are expected to lead to 4-di mensional TQFTs\, as envisioned by Crane and Frenkel. The tensor product o f 2-representations introduces homotopical phenomena which disappear when considering instead the case of the super Lie algebra gl(1|1). I will disc uss how to construct parts of the structure of a braided monoidal 2-catego ry associated to gl(1|1)\, and how this compares with the known 4-dimensio nal Heegaard–Floer TQFT.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Elliott (Amherst College) DTSTART:20240911T150000Z DTEND:20240911T160000Z DTSTAMP:20260424T221532Z UID:TQFT/127 DESCRIPTION:Title: Topological twists of superconformal field theory\nby Chris Elli ott (Amherst College) as part of Topological Quantum Field Theory Club (IS T\, Lisbon)\n\n\nAbstract\nIn quantum field theory\, "twisting" is a proce dure for producing new theories from old\, where the new theories have par ticularly nice symmetry properties (for example\, topological quantum fiel d theories). The twisting construction involves the choice of a nilpotent element of a super Lie algebra that acts on the theory. I will discuss joi nt work with Owen Gwilliam and Matteo Lotito on twisting for theories with an action of a superconformal algebra and the appearance of interesting a lgebraic structures such as vertex algebras and $E_n$ algebras.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Thang Le (Georgia Institute of Technology) DTSTART:20240918T160000Z DTEND:20240918T170000Z DTSTAMP:20260424T221532Z UID:TQFT/128 DESCRIPTION:Title: Algebraic structures of skein algebras\nby Thang Le (Georgia Ins titute of Technology) as part of Topological Quantum Field Theory Club (IS T\, Lisbon)\n\n\nAbstract\nWe will survey some results of stated $SL_n$ sk ein algebras and show how to use them to study the ordinary skein algebras of surfaces. We will discuss the integrality of the skein algebra\, the i njectivity of the cutting homomorphism\, and the structure of the skein al gebras of the bigon and the triangle. The talk is based on joint work with F. Costantino\, J. Korinman\, A. Sikora\, and T. Yu.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Kristel (Hausdorff Center for Mathematics) DTSTART:20241009T090000Z DTEND:20241009T100000Z DTSTAMP:20260424T221532Z UID:TQFT/129 DESCRIPTION:Title: 2-vector bundles\nby Peter Kristel (Hausdorff Center for Mathema tics) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\ nAbstract\nI will introduce the notion of 2-vector bundles\, which are a c ategorified version of vector bundles. This notion is based on the idea th at the bicategory of 2-vector spaces is the bicategory of algebras\, bimod ules\, and intertwiners. I will recall the definition of that bicategory\, which leads into the definition of 2-vector bundles. As time permits\, I will discuss connections to string geometry\, and extended TQFT\, and clas sifying results. This is all based on work with Matthias Ludewig and Konra d Waldorf.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/129/ END:VEVENT BEGIN:VEVENT SUMMARY:William Stewart (Technical University of Munich) DTSTART:20241016T090000Z DTEND:20241016T100000Z DTSTAMP:20260424T221532Z UID:TQFT/130 DESCRIPTION:Title: Domain walls and oplax natural transformations\nby William Stewa rt (Technical University of Munich) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nI will review the notion of a top ological (or gapped) domain wall between topological quantum field theorie s and illustrate an equivalence between domain walls and oplax natural tra nsformations. I will show how this provides a reformulation of Lurie's cob ordism hypothesis with singularities.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Ödül Tetik (University of Vienna) DTSTART:20241030T100000Z DTEND:20241030T110000Z DTSTAMP:20260424T221532Z UID:TQFT/131 DESCRIPTION:Title: Yoga with twisted stratifications\nby Ödül Tetik (University o f Vienna) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\ n\n\nAbstract\nLinked spaces\, originally motivated by applications to TQF Ts\, simultaneously simplify and generalise stratified spaces. I will brie fly introduce the concept and the accompanying exit-path quasi-category co nstruction. To exhibit the nontriviality of the generalisation\, I will th en consider some fundamental categories (as in "fundamental groupoid") of linked spaces and realise\, from a "twist" of the complement of the trefoi l knot with a point defect\, a two-object category where the hom-set is th e modular group PSL(2\,Z) and argue that there is no stratified space with this fundamental category.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Hofer (University of Hamburg) DTSTART:20241120T100000Z DTEND:20241120T110000Z DTSTAMP:20260424T221532Z UID:TQFT/132 DESCRIPTION:Title: CFT/TFT correspondence beyond semisimplicity\nby Aaron Hofer (Un iversity of Hamburg) as part of Topological Quantum Field Theory Club (IST \, Lisbon)\n\n\nAbstract\nSince the 1980s\, it has been well known that th ere is a close relationship between two-dimensional conformal field theori es and three-dimensional topological field theories. This CFT/TFT correspo ndence provides a tractable example of holography as well as a first examp le of the symmetry TFT framework.\n\nThe Fuchs-Runkel-Schweigert construct ion is a mathematically precise incarnation of this correspondence and pro vides a rigorous construction of correlators for rational CFTs using 3D TF Ts of Reshetikhin-Turaev type. In this talk\, I will review the FRS constr uction and explain how it can be generalized to non-rational CFTs using th e non-semisimple 3D TFTs of De Renzi\, Gainutdinov\, Geer\, Patureau-Miran d\, and Runkel.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Theodoros Lagiotis (University of Edinburgh) DTSTART:20241218T100000Z DTEND:20241218T110000Z DTSTAMP:20260424T221532Z UID:TQFT/133 DESCRIPTION:Title: Noncompact 3d TQFTs from non-semisimple modular categories\nby T heodoros Lagiotis (University of Edinburgh) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nPerhaps the most (mathema tically) well understood 3d TQFT is that of Reshetikhin–Turaev. Famously \, the input data for their construction is that of a semisimple modular t ensor category (MTC). Attempts at generalizing this construction to the no n-semisimple case date back to the 90's with work of Hennings\, Lyubashenk o and Kerler–Lyubashenko. However\, only partial results were achieved. This was until De Renzi et al. defined a 3d TQFT from such non-semisimple modular categories. Importantly\, they had to impose an admissibility cond ition on the cobordism categories they use. My work has been in the direct ion of defining a once-extended 3d TQFT from this data. However\, Bartlett et al. proved that such TQFTs are classified by semisimple modular catego ries. We will investigate the most natural method of circumventing this. T his will lead to the notion of noncompact TQFT. I will then proceed to tal k about my work on constructing such a TQFT from the data of a (potentiall y) non-semisimple MTC\, with an emphasis on the key ingredients of this co nstruction. Time permitting\, I will also discuss how to extract 3-manifol d invariants and a modified trace from such a noncompact TQFT.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Maciej Borodzik (Institute of Mathematics\, Polish Academy of Scie nces) DTSTART:20241211T110000Z DTEND:20241211T120000Z DTSTAMP:20260424T221532Z UID:TQFT/134 DESCRIPTION:Title: Equivariant Khovanov homotopy type\nby Maciej Borodzik (Institut e of Mathematics\, Polish Academy of Sciences) as part of Topological Quan tum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nGiven a periodic link L\, we construct a group action on the Khovanov homotopy type defined by L ipshitz and Sarkar. As a result\, we prove that the annular Khovanov homol ogy of the quotient link has no larger rank than the Khovanov homology of the periodic link. This is a joint work with Wojciech Politarczyk and Mari thania Silvero.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthias Ludewig (University of Greifswald) DTSTART:20250205T100000Z DTEND:20250205T110000Z DTSTAMP:20260424T221532Z UID:TQFT/135 DESCRIPTION:Title: The stringor bundle and the spinor bundle on loop space\nby Matt hias Ludewig (University of Greifswald) as part of Topological Quantum Fie ld Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe explain the construction o f the stringor bundle on a string manifold recently given in joint work wi th Peter Kristel and Konrad Waldorf. We start by discussing the spinor bun dle on the loop space of a string manifold\, together with its fusion prod uct. Then we explain how the stringor bundle on the manifold itself can be obtained using a regression procedure.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Clement Delcamp (IHES) DTSTART:20250402T090000Z DTEND:20250402T100000Z DTSTAMP:20260424T221532Z UID:TQFT/136 DESCRIPTION:Title: Topological symmetry and duality in quantum lattice models\nby C lement Delcamp (IHES) as part of Topological Quantum Field Theory Club (IS T\, Lisbon)\n\n\nAbstract\nDefining internal symmetry in a quantum theory through the lens of topological defects opens the door to generalised noti ons of symmetry\, including some arising from non-invertible transformatio ns\, and enables a calculus that leverages well-established methods from t opological quantum field theory. In d spatial dimensions\, the framework o f fusion d-category theory is believed to offer an axiomatisation for fini te non-invertible symmetries. Though seemingly exotic\, such non-invertibl e symmetries can be shown to naturally arise as dual symmetries upon gaugi ng invertible symmetries. In this talk\, I will present a framework to sys tematically investigate these aspects in quantum lattice models.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Ingo Runkel (University of Hamburg) DTSTART:20250423T090000Z DTEND:20250423T100000Z DTSTAMP:20260424T221532Z UID:TQFT/137 DESCRIPTION:Title: Topological symmetries and their gaugings in 2d CFT and 3d TFT\n by Ingo Runkel (University of Hamburg) as part of Topological Quantum Fiel d Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe study of topological defec ts in quantum field theory has seen a wealth of activity recently leading to many interesting insights\, for example the explicit realisation of no n-invertible topological defects in higher dimensional QFTs via the gaugin g of higher form symmetries\, or the description of the higher algebraic s tructures inherent in these topological defects. In this talk\, I would li ke to focus on low-dimensional examples\, where such defects and their pro perties have been investigated for some time already. I would like to exhi bit some of the properties of topological defects in two-dimensional confo rmal field theory and in three-dimensional topological field theory\, an d show some of the structural insights into 2d CFT and 3d TFT one can gain with the help of defects. In this way\, the well-understood low-dimension al case might serve as a source of ideas and as a test case for higher dim ensional constructions.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Bertrand Patureau-Mirand (Université de Bretagne-Sud) DTSTART:20250430T090000Z DTEND:20250430T100000Z DTSTAMP:20260424T221532Z UID:TQFT/138 DESCRIPTION:Title: Weaving 4-Dimensional TQFTs with Ribbon Categories\nby Bertrand Patureau-Mirand (Université de Bretagne-Sud) as part of Topological Quant um Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will describe some re quirements on a non semi-simple ribbon category that ensure its admissible skein modules form the state spaces of a 3+1-dimensional TQFT.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Cris Negron (University of Southern California) DTSTART:20250716T160000Z DTEND:20250716T170000Z DTSTAMP:20260424T221532Z UID:TQFT/139 DESCRIPTION:Title: $(3-\\epsilon)$-dimensional TQFTs from derived quantum group represe ntations\nby Cris Negron (University of Southern California) as part o f Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI wi ll discuss joint work with Agustina Czenky. We introduce a $(3-\\epsilon)$ -dimensional TQFTs which is generated\, in some sense\, by the derived cat egory of quantum group representations. This TQFT is valued in the $\\inft y$-category of dg vector spaces\, and the value on a genus $g$ surface is a $g$-th iterate of the Hochschild cohomology for the aforementioned categ ory. I will explain how this TQFT arises as a derived variant of the usual Reshetikhin–Turaev theory and\, if time allows\, I will discuss the pos sibility of introducing local systems into the theory. Our interest in loc al systems comes from proposed relationships with 4-dimensional non-topolo gical QFT.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Joshua Sussan (CUNY Medgar Evers) DTSTART:20250723T160000Z DTEND:20250723T170000Z DTSTAMP:20260424T221532Z UID:TQFT/140 DESCRIPTION:Title: Symmetries of link homology\nby Joshua Sussan (CUNY Medgar Evers ) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbs tract\nWe construct an action of $\\mathfrak{sl}(2)$ on equivariant Khovan ov–Rozansky link homology. We will discuss some topological application s and show how the construction simplifies in characteristic p. This is joint with You Qi\, Louis-Hadrien Robert\, and Emmanuel Wagner.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Rajan Mehta (Smith College) DTSTART:20250703T083000Z DTEND:20250703T093000Z DTSTAMP:20260424T221532Z UID:TQFT/141 DESCRIPTION:Title: 2-Segal sets as combinatorial models for algebras\nby Rajan Meht a (Smith College) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nRoughly\, 2-Segal sets are simplicial sets such tha t higher-dimensional simplices can be uniquely described by triangulated p olygons formed out of 2-simplices. In a sense that I will make precise\, 2 -Segal sets can be viewed as categorified associative algebras. As a TQFT Club member\, you might ask\, “Are there 2-Segal sets that correspond to (commutative) Frobenius algebras?” The answer is yes\, commutativity an d Frobenius structures come from asking the simplicial set to possess addi tional compatible structure maps. I’ll give an overview of these corresp ondences as well as some background as to how I arrived at this topic from the world of Poisson geometry. This is based on joint works with Ivan Co ntreras\, Walker Stern\, and Sophia Marx.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Rhea Palak Bakshi (University of California\, Santa Barbara) DTSTART:20250730T160000Z DTEND:20250730T170000Z DTSTAMP:20260424T221532Z UID:TQFT/142 DESCRIPTION:Title: On the structure of skein modules\nby Rhea Palak Bakshi (Univers ity of California\, Santa Barbara) as part of Topological Quantum Field Th eory Club (IST\, Lisbon)\n\n\nAbstract\nSkein modules were introduced by J ózef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman br acket skein module (KBSM) is the most extensively studied of all. However\ , computing the KBSM of a 3-manifold is known to be notoriously hard\, esp ecially over the ring of Laurent polynomials. With the goal of finding a d efinite structure of the KBSM over this ring\, several conjectures and the orems were stated over the years for KBSMs. We show that some of these con jectures\, and even theorems\, are not true. In this talk I will briefly d iscuss a counterexample to Marche’s generalisation of Witten’s conject ure. I will show that a theorem stated by Przytycki in 1999 about the KBSM of the connected sum of two handlebodies does not hold. I will also give the exact structure of the KBSM of the connected sum of two solid tori and show that it is isomorphic to the KBSM of a genus two handlebody modulo s ome specific handle sliding relations. Moreover\, these handle sliding rel ations can be written in terms of Chebyshev polynomials.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Harshit Yadav (University of Alberta) DTSTART:20250806T160000Z DTEND:20250806T170000Z DTSTAMP:20260424T221532Z UID:TQFT/143 DESCRIPTION:Title: Modular tensor categories via local modules\nby Harshit Yadav (U niversity of Alberta) as part of Topological Quantum Field Theory Club (IS T\, Lisbon)\n\n\nAbstract\nGiven a commutative algebra $A$ in a braided mo noidal category $C$\, the category of local A-modules\, $C_A^\\mathrm{loc} $\, is defined as a subcategory of the category $C_A$ of right $A$-modules in C. Pareigis showed that $C_A^\\mathrm{loc}$\, which is important for s tudying vertex operator algebra extensions\, is a braided monoidal categor y under very general conditions. In this setting\, I will present a criter ion for $C_A^\\mathrm{loc}$ to be a rigid monoidal category. When $C$ is p ivotal/ribbon\, I will also discuss when the category $C_A$ is pivotal and when $C_A^\\mathrm{loc}$ is ribbon.\n\nAs an application\, I will show th at when $C$ is a modular tensor category and $A$ is a commutative simple s ymmetric Frobenius algebra in $C$\, then $C_A^\\mathrm{loc}$ is a modular tensor category. Furthermore\, I will discuss methods to construct such co mmutative algebras using simple currents and the Witt group of non-degener ate braided finite tensor categories. This presentation is based on joint work with Kenichi Shimizu.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/143/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Lauda (University of Southern California) DTSTART:20250813T160000Z DTEND:20250813T170000Z DTSTAMP:20260424T221532Z UID:TQFT/144 DESCRIPTION:Title: Nonsemisimple Topological Quantum Computation\nby Aaron Lauda (U niversity of Southern California) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nSince the foundational work of Free dman\, Kitaev\, Larsen\, and Wang\, it has been understood that 3-dimensio nal topological quantum field theories (TQFTs)\, described via modular ten sor categories\, provide a universal model for fault-tolerant topological quantum computation. These TQFTs\, derived from quantum groups at roots of unity\, achieve modularity by semisimplifying their representation catego ries—discarding objects with quantum trace zero. The resulting semisimpl e categories describe anyons whose braiding enables robust quantum computa tion.\n\nThis talk explores recent advances in low-dimensional topology\, focusing on the use of nonsemisimple categories that retain quantum trace zero objects to construct new TQFTs. These nonsemisimple TQFTs surpass the ir semisimple counterparts\, distinguishing topological features inaccessi ble to the latter. For physical applications\, unitarity is essential\, en suring Hom spaces form Hilbert spaces. We present joint work with Nathan G eer\, Bertrand Patureau-Mirand\, and Joshua Sussan\, where nonsemisimple T QFTs are equipped with a Hermitian structure. This framework introduces Hi lbert spaces with possibly indefinite metrics\, presenting new challenges. \n\nWe further discuss collaborative work with Sung Kim\, Filippo Iulianel li\, and Sussan\, demonstrating that nonsemisimple TQFTs enable universal quantum computation at roots of unity where semisimple theories fail. Spec ifically\, we show how Ising anyons within this framework achieve universa lity through braiding alone. The resulting braiding operations are deeply connected to the Lawrence–Krammer–Bigelow representations\, with the H ermitian structure providing a nondegenerate inner product grounded in qua ntum algebra.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/144/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Plavnik (Indiana University) DTSTART:20250820T160000Z DTEND:20250820T170000Z DTSTAMP:20260424T221532Z UID:TQFT/145 DESCRIPTION:Title: The homotopy coherent classification of fusion 2-categories\nby Julia Plavnik (Indiana University) as part of Topological Quantum Field Th eory Club (IST\, Lisbon)\n\n\nAbstract\nFusion 2-categories are a higher c ategorical analog of fusion categories that have gained a lot of attention in the last years because of their importance in many fields of math and physics\, such as TQFTs\, condensed matter physics and high energy physic s. The classifiction of fusion (1-) categories is a very active research a rea and has provided new examples and led to the development of new invari ants and tools to understand these categories. \n\nIn this talk\, we will present a parametrization of multifusion 2-categories in terms of lower ca tegorical data\, involving braided fusion categories\, group theory\, and cohomological data. If time allows\, we will also show some applications o f this result. This is a joint work in with T. Décoppet\, T. Johnson-Frey d\, P. Huston\, D. Nikshych\, D. Penneys\, D. Reutter\, and M. Yu.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack Romö (University of Leeds) DTSTART:20250827T160000Z DTEND:20250827T170000Z DTSTAMP:20260424T221532Z UID:TQFT/146 DESCRIPTION:Title: Homotopy bicategories of $(\\infty\,2)$-categories\nby Jack Rom ö (University of Leeds) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nAcross the multitude of definitions for a hi gher category\, a dividing line can be found between two major camps of mo del. On one side lives the ‘algebraic’ models\, like Bénabou’s bica tegories\, tricategories following Gurski and the models of Batanin and Le inster\, Trimble and Penon. On the other end\, one finds the ‘non-algebr aic’ models\, including more homotopy-theoretic ones like quasicategorie s\, Segal n-categories\, complete n-fold Segal spaces and more. The bridge s between these models remain somewhat mysterious. Progress has been made in certain instances\, as seen in the work of Tamsamani\, Leinster\, Lack and Paoli\, Cottrell\, Campbell\, Nikolaus and others. Developing comparis ons between these forms of higher category has relevance to topological qu antum field theories in relating the work done on fully extended TQFTs usi ng homotopy theoretic models of higher category\, such as Lurie's proof-sk etch of the Cobordism Hypothesis conducted using n-fold Segal spaces\, and the large body of work on extended TQFTs using algebraic models of higher category\, such as symmetric monoidal bicategories.\n\nNonetheless\, the correspondence remains incomplete\; indeed\, for instance\, there is no fu lly verified means in the literature to take an 'algebraic’ homotopy n-c ategory of any known model of $(\\infty\, n)$-category for general n. One might see this as an extension of the fundamental n-groupoid of a homotopy type\, a statement I will make precise. In this talk\, I will explore cur rent work in the problem of taking homotopy bicategories of non-algebraic $(\\infty\, 2)$-categories\, including a construction of my own. If time p ermits\, I will discuss the connections of this problem to topological qua ntum field theories.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Voronov (University of Minnesota) DTSTART:20250910T150000Z DTEND:20250910T160000Z DTSTAMP:20260424T221532Z UID:TQFT/147 DESCRIPTION:Title: The superstring measure on the moduli spaces of genus-zero super Rie mann surfaces\nby Alexander Voronov (University of Minnesota) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI w ill present a computation of tree-level superstring measures on the moduli spaces of genus-zero super Riemann surfaces with Neveu–Schwarz (NS) and Ramond punctures. The answer in the NS case is not new\, but it is done u sing first principles\, i.e.\, exclusively complex algebraic supergeometry and\, in particular\, the super Mumford isomorphism. The answer in the Ra mond case is totally new\, but we do not quite have it. This is joint work with S. Cacciatori and S. Grushevsky: published in the NS case and in-pro gress in the Ramond case.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Jones (North Carolina State University) DTSTART:20250903T160000Z DTEND:20250903T170000Z DTSTAMP:20260424T221532Z UID:TQFT/148 DESCRIPTION:Title: Levin–Wen models: a mathematician's perspective from the boundary< /a>\nby Corey Jones (North Carolina State University) as part of Topologic al Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nTopological qua ntum many-body systems on the lattice are characterized by having the prop erty that their low energy effective theories are TQFTs. Levin–Wen model s are classes of spin systems on the 2D lattice whose low energy effective theories are Turaev–Viro TQFTs. The problem (from a mathematician's per spective) is that low energy effective theories are not at all well-define d! This leads to the question: for systems that (supposedly) exhibit topol ogical order\, how can we see the emergent TQFT directly on the lattice in the infinite volume limit? We will discuss our recently proposed approach to mathematically formalize the ideas of topological holography in terms of boundary algebras\, and explain how this provides a solution for system s with local topological order.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Dionne Ibarra (Monash University) DTSTART:20250917T090000Z DTEND:20250917T100000Z DTSTAMP:20260424T221532Z UID:TQFT/149 DESCRIPTION:Title: Octahedral fully augmented links and the TV volume conjecture\nb y Dionne Ibarra (Monash University) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nTuraev–Viro (TV) invariants are 3-manifold invariants\, defined for a given fixed integer $r$ and $2r$-th root of unity. Chen and Yang extended the definition of TV-invariants to pseudo 3-manifolds and introduced a volume conjecture for TV-invariants wh ich states that for the case of $r$-th roots of unity where $r$ is odd and $M$ is hyperbolic\, the TV invariants of $M$ grow exponentially and deter mine the volume of $M$.\n\nThe Witten–Reshetikhin–Turaev (WRT) 3-manif old invariants (also known as the Chern–Simons 3-manifold invariants)\, are defined for a given fixed integer $r$\, and a $2r$-th root of unity. T he existence of such invariants were predicted by Witten in his work on Ch ern–Simons gauge theory and topological quantum field theory. They were constructed by Reshetikhin and Turaev by using representation theory and K irby calculus. Later\, Lickorish gave a skein theoretic definition. These invariants were also originally defined for closed orientable 3-manifolds\ , but were recently extended to link complements. Furthermore\, Belletti\, Detcherry\, Kalfagianni\, and Yang provided an explicit formula relating the TV invariant to the WRT invariant of link complements in a closed orie ntable 3-manifold and used this formula to prove the TV volume conjecture for octahedral link complements in the connected sums of $S^2 \\times S^1$ called fundamental shadow links.\n\nIn contrast\, fully augmented links a re links in $S^3$ whose complements have nice geometric properties. For in stance\, Agol and Thurston showed that fully augmented links can be decomp osed into totally geodesic\, right-angled ideal polyhedra. In this talk\, we will present a geometric description of the relationship between octahe dral fully augmented links and fundamental shadow links and we will outlin e an alternative proof\, using the colored Jones polynomial\, to prove the TV volume conjecture for octahedral fully augmented links with no half-tw ists. This is joint work with Emma McQuire and Jessica Purcell.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Norbury (University of Melbourne) DTSTART:20251001T090000Z DTEND:20251001T100000Z DTSTAMP:20260424T221532Z UID:TQFT/151 DESCRIPTION:Title: Super volumes of the moduli space of super Riemann surfaces\nby Paul Norbury (University of Melbourne) as part of Topological Quantum Fiel d Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will present the super volum es of the moduli space of super Riemann surfaces. They will be defined usi ng a family of finite measures on the moduli space of genus $g$ curves. Th ese measures are in turn given by a construction analogous to the classica l construction of the Weil–Petersson metric\, using the extra data of a spin structure. The total measure gives the volume of the moduli space of super curves and can be calculated via a deep relationship with the KdV eq uation.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/151/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiro Lee Tanaka (Texas State University) DTSTART:20251126T100000Z DTEND:20251126T110000Z DTSTAMP:20260424T221532Z UID:TQFT/152 DESCRIPTION:Title: Broken\nby Hiro Lee Tanaka (Texas State University) as part of T opological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe'll t alk about joint work with Jacob Lurie regarding moduli stacks of geometric objects developing natural breaks. If time allows\, I'll end with some sp eculation regarding a 3-D TFT arising from various G2 manifolds.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/152/ END:VEVENT BEGIN:VEVENT SUMMARY:César Galindo (Universidad de los Andes) DTSTART:20251029T170000Z DTEND:20251029T180000Z DTSTAMP:20260424T221532Z UID:TQFT/153 DESCRIPTION:Title: A manifestly Morita-invariant construction of Turaev–Viro invarian ts\nby César Galindo (Universidad de los Andes) as part of Topologica l Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe present a bic ategorical state sum construction for 3-manifold invariants. Using the piv otal bicategory of spherical module categories over a spherical fusion cat egory\, we construct invariants that manifestly preserve Morita equivalenc e. Our main result shows that this bicategorical invariant recovers the st andard Turaev–Viro invariant\, thereby proving Morita invariance of Tura ev–Viro invariants without appealing to the Reshetikhin–Turaev constru ction.\n\nThis is joint work with Jürgen Fuchs\, David Jaklitsch\, and Ch ristoph Schweigert.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne-Laure Thiel (Université de Bourgogne) DTSTART:20251203T100000Z DTEND:20251203T110000Z DTSTAMP:20260424T221532Z UID:TQFT/154 DESCRIPTION:Title: On faithful representations of the braid group\nby Anne-Laure Th iel (Université de Bourgogne) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe famous Burau representation of the braid group is known to be unfaithful for braids with at least five stran ds. In the early 2000s\, two constructions were provided to fix faithfulne ss: the first being the Lawrence–Krammer–Bigelow linear representation \, hence proving linearity of braid groups\, and the second being the Khov anov–Seidel categorical representation. In this talk\, based on joint wo rk in progress with Licata\, Queffelec\, and Wagner\, I will investigate t he interplay between these two representations.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Huston (University of Leeds) DTSTART:20251022T160000Z DTEND:20251022T170000Z DTSTAMP:20260424T221532Z UID:TQFT/155 DESCRIPTION:Title: Algebraic techniques in 3-cateories of (2+1)D topological defects\nby Peter Huston (University of Leeds) as part of Topological Quantum Fi eld Theory Club (IST\, Lisbon)\n\n\nAbstract\nTopological phases of matter in (2+1)D should naturally form a 3-category\, in which k-morphisms repre sent defects of codimension k. By the cobordism hypothesis\, the 3-categor ies of (2+1)D topological order with a fixed anomaly are each equivalent t o the 3-category of fusion categories enriched over a corresponding UMTC. In ongoing work with Fiona Burnell\, we introduce algebraic techniques for concrete computations in 3-categories of (2+1)D topological order\, inclu ding a tunneling approach to the classification of point defects which gen eralizes the use of braiding to identify anyon types. We then apply these techniques to compute ground state degeneracy and classify low energy exci tations in a class of fracton-like (2+1)D topological defect networks.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/155/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Putrov (The Abdus Salam International Centre for Theoretical Physics) DTSTART:20251217T170000Z DTEND:20251217T180000Z DTSTAMP:20260424T221532Z UID:TQFT/157 DESCRIPTION:Title: A relationship between gauge theories with finite and continuous gau ge groups.\nby Pavel Putrov (The Abdus Salam International Centre for Theoretical Physics) as part of Topological Quantum Field Theory Club (IST \, Lisbon)\n\n\nAbstract\nI will discuss certain relations between 3-dimen sional topological gauge theories with continuous and finite gauge groups\ , commonly known as Chern–Simons and Dijkgraaf–Witten theories respect ively. The relations of this form appear when the continuous and finite ga uge groups are the same algebraic group considered over the complex/real n umbers and a finite field\, respectively. In this talk\, I will focus on t he SU(2) example and consider the relationship on the level of the corresp onding invariants of closed 3-manifolds: Witten–Reshetikhin–Turaev and Dijkgraaf–Witten invariants.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincentas Mulevicius (University of Vienna) DTSTART:20260128T170000Z DTEND:20260128T180000Z DTSTAMP:20260424T221532Z UID:TQFT/158 DESCRIPTION:Title: Categorical 4-manifold invariants from trisection diagrams\nby V incentas Mulevicius (University of Vienna) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nTrisections give a diagram matic description of smooth 4-manifolds\, similar to Heegaard splittings i n dimension three. In this talk\, I will describe new 4-manifold invariant s defined from trisection diagrams using categorical data. The input consi sts of three spherical fusion categories\, a semisimple bimodule category with a bimodule trace\, and a pivotal functor into the category of bimodul e endofunctors.\n\nThe construction works by labelling the trisection diag rams with the categorical data and evaluating them using a diagrammatic ca lculus for bimodule categories. The details of this procedure ensures that the result is invariant under moves on trisections yielding the same 4-ma nifold. This construction generalises existing Hopf algebraic trisection i nvariants due to Chaidez--Cotler--Cui and recovers the Crane--Yetter and B ärenz--Barrett invariants as special cases. I will outline the main idea s of the construction and briefly discuss examples and connections to TQFT s.\n\nBased on the work 2511.19384 with Catherine Meusburger (FAU) and Fio na Torzewska (Bristol).\n LOCATION:https://stable.researchseminars.org/talk/TQFT/158/ END:VEVENT BEGIN:VEVENT SUMMARY:Angela Tabiri (African Institute for Mathematical Sciences Ghana) DTSTART:20251210T170000Z DTEND:20251210T180000Z DTSTAMP:20260424T221532Z UID:TQFT/159 DESCRIPTION:Title: Decomposable surfaces and plane curves which are quantum homogeneous spaces\nby Angela Tabiri (African Institute for Mathematical Sciences Ghana) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\ n\nAbstract\nDecomposable plane curves of degree up to 5 were shown to be quantum homogeneous spaces by Brown and Tabiri. It was conjectured that al l decomposable plane curves of any degree are quantum homogeneous spaces. In this talk\, we will discuss recent results which show that decomposable surfaces and plane curves of any degree are quantum homogeneous spaces. O ther algebras such as the reduced algebra will be constructed and its prop erties discussed.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxine Calle (University of Pennsylvania) DTSTART:20260123T160000Z DTEND:20260123T170000Z DTSTAMP:20260424T221532Z UID:TQFT/160 DESCRIPTION:Title: Nested cobordisms and TQFTs\nby Maxine Calle (University of Penn sylvania) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\ n\n\nAbstract\nA well-known folklore theorem classifies 2-dimensional topo logical quantum field theories (TQFTs) in terms of Frobenius algebras\, pr oviding a unifying link between topology\, algebra\, and physics. In this talk\, we explore what happens when the usual cobordism category is replac ed by a category of nested cobordisms\, in which 2-dimensional surfaces ar e equipped with embedded 1-dimensional submanifolds. We study symmetric mo noidal functors out of this category and the resulting algebraic structure s they encode. This talk is based on joint work with R. Hoekzema\, L. Murr ay\, N. Pacheco-Tallaj\, C. Rovi\, and S. Sridhar.\n\nPlease note the chan ge of day and time!\n LOCATION:https://stable.researchseminars.org/talk/TQFT/160/ END:VEVENT BEGIN:VEVENT SUMMARY:Constantin Teleman (University of California\, Berkeley) DTSTART:20260304T170000Z DTEND:20260304T180000Z DTSTAMP:20260424T221532Z UID:TQFT/161 DESCRIPTION:Title: Reshetikhin–Turaev theories are fully local\nby Constantin Tel eman (University of California\, Berkeley) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will review two results pertaining to 3-dimensional Reshetikhin–Turaev TQFTs\, defined from modu lar tensor categories M. These theories were not constructed as “fully l ocal” TQFTs (in the framework of Lurie’s Cobordism Hypothesis): no alg ebraic structures were assigned to points. (The obstruction was the Witt c lass of M.) Kevin Walker solved the locality problem in the setting of ano malous theories. A ‘no-go’ theorem (joint with Dan Freed) showed that\ , if localized as linear theories\, these RT theories did not admit local topological boundary conditions\, and could therefore not be generated fro m a point by this method. (The group-like case had been addressed by Kapus tin and Saulina.) In recent work with Freed and Claudia Scheimbauer\, we d isplayed a fully local realization of these theories\, by objects in a tar get 3-category which enlarges that of fusion categories. This allowed us t o settle some conjectures relating orientations and spherical structures.\ n LOCATION:https://stable.researchseminars.org/talk/TQFT/161/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan-Ramón Gómez-García (Institut de Mathématiques de Jussieu- Paris Rive Gauche) DTSTART:20260211T100000Z DTEND:20260211T110000Z DTSTAMP:20260424T221532Z UID:TQFT/162 DESCRIPTION:Title: Defect skein theory\, parabolic restriction and the Turaev coproduct \nby Juan-Ramón Gómez-García (Institut de Mathématiques de Jussieu -Paris Rive Gauche) as part of Topological Quantum Field Theory Club (IST\ , Lisbon)\n\n\nAbstract\nInspired by Jaeger’s composition formula for th e HOMFLY polynomial\, Turaev defined a coproduct on the HOMFLY skein algeb ra of a framed surface S\, turning it into a bialgebra. Jaeger’s formula can be viewed as a universal version of the restriction of the defining r epresentation from GL_m+n to GL_m x GL_n. The restriction functor\, howeve r\, is not braided\, and therefore there is a priori no reason for the ind uced linear map between the corresponding skein algebras to be multiplicat ive. In this talk\, I will address this problem using defect skein theory and the formalism of parabolic restriction.\n\nIn the first part of the ta lk\, I will introduce skein theory for 3-manifolds with both surface and l ine defects. Local relations near the defects are produced from the algebr aic data of a central algebra (codimension 1) and a centred bimodule (codi mension 2). Examples of such structures are provided by the formalism of p arabolic restriction. In the second part of the talk\, I will explain how to construct a universal version of this formalism. Finally\, we will see how Turaev’s coproduct extends to the entire skein category using the pr evious constructions.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Thiago Paiva (Beijing University) DTSTART:20260318T140000Z DTEND:20260318T150000Z DTSTAMP:20260424T221532Z UID:TQFT/163 DESCRIPTION:Title: A simpler braid description for all links in the 3-sphere\nby Th iago Paiva (Beijing University) as part of Topological Quantum Field Theor y Club (IST\, Lisbon)\n\n\nAbstract\nBy Alexander's theorem\, every link i n the 3-sphere can be represented as the closure of a braid. Lorenz links and twisted torus links are two families that have been extensively studie d and are well-described in terms of braids. In this talk\, we will presen t a natural generalization of Lorenz links and twisted torus links that pr oduces all links in the 3-sphere. This provides a simpler braid descriptio n for all links in the 3-sphere.\n\nJoint seminar with CEMS.UL.\n LOCATION:https://stable.researchseminars.org/talk/TQFT/163/ END:VEVENT END:VCALENDAR