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:20260422T225721Z UID:TQFT/1 DESCRIPTION:Title: Hid den algebraic structures in topology\nby Sergei Gukov (California Inst itute of Technology) as part of Topological Quantum Field Theory Club (IST \, Lisbon)\n\n\nAbstract\nWhich 4-manifold invariants can detect the Gluck twist? And\, which 3-manifold invariants can detect the difference betwee n surgeries on mutant knots? What is the most powerful topological quantum field theory (TQFT)? Guided by questions like these\, we will look for ne w invariants of 3-manifolds and smooth 4-manifolds. Traditionally\, a cons truction of many such invariants and TQFTs involves a choice of certain al gebraic structure\, so that one can talk about "invariants for SU(2)" or a "TQFT defined by a given Frobenius algebra." Surprisingly\, recent develo pments lead to an opposite phenomenon\, where algebraic structures are lab eled 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. Explain ing these intriguing connections between topology and algebra will be the main goal of this talk.\n LOCATION:https://researchseminars.org/talk/TQFT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Danica Kosanović (Max-Planck Institut für Mathematik) DTSTART:20200529T160000Z DTEND:20200529T170000Z DTSTAMP:20260422T225721Z UID:TQFT/2 DESCRIPTION:Title: Kno t invariants from homotopy theory\nby Danica Kosanović (Max-Planck In stitut für Mathematik) as part of Topological Quantum Field Theory Club ( IST\, Lisbon)\n\n\nAbstract\nThe embedding calculus of Goodwillie and Weis s is a certain homotopy theoretic technique for studying spaces of embeddi ngs. When applied to the space of knots this method gives a sequence of kn ot invariants which are conjectured to be universal Vassiliev invariants. This is remarkable since such invariants have been constructed only ration ally so far and many questions about possible torsion remain open. In this talk I will present a geometric viewpoint on the embedding calculus\, whi ch enables explicit computations. In particular\, we prove that these knot invariants are surjective maps\, confirming a part of the universality co njecture\, and we also confirm the full conjecture rationally\, using some recent results in the field. Hence\, these invariants are at least as goo d as configuration space integrals.\n LOCATION:https://researchseminars.org/talk/TQFT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Khovanov (Columbia University) DTSTART:20200619T160000Z DTEND:20200619T170000Z DTSTAMP:20260422T225721Z UID:TQFT/3 DESCRIPTION:Title: Int roduction to foam evaluation\nby Mikhail Khovanov (Columbia University ) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbs tract\nFoam evaluation was discovered by Louis-Hardrien Robert and Emmanue l Wagner slightly over three years ago. It's a remarkable formula assignin g a symmetric function to a foam\, that is\, to a decorated 2-dimensional CW-complex embedded in three-space. We'll explain their formula in the 3-c olor case in the context of unoriented foams and discuss its relation to K ronheimer-Mrowka homology of graphs and the four-color theorem.\n LOCATION:https://researchseminars.org/talk/TQFT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:John Huerta (IST and CAMGSD) DTSTART:20200605T160000Z DTEND:20200605T170000Z DTSTAMP:20260422T225721Z UID:TQFT/4 DESCRIPTION:Title: Bun dle Gerbes on Supermanifolds\nby John Huerta (IST and CAMGSD) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nBun dle gerbes are a generalization of line bundles that play an important rol e in constructing WZW models with boundary. With an eye to applications fo r WZW models with superspace target\, we describe the classification of bu ndle gerbes on supermanifolds\, and sketch a proof of their existence for large families of super Lie groups.\n LOCATION:https://researchseminars.org/talk/TQFT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Marko Stošić (Instituto Superior Técnico and CAMGSD) DTSTART:20200626T160000Z DTEND:20200626T170000Z DTSTAMP:20260422T225721Z UID:TQFT/5 DESCRIPTION:Title: Rat ional and algebraic links and knots-quivers correspondence\nby Marko S tošić (Instituto Superior Técnico and CAMGSD) as part of Topological Qu antum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will start with a brief overview of knots-quivers correspondence\, where colored HOMFLY-PT\n (or BPS) invariants of the knot are expressed as motivic Donaldson-Thomas invariants of a corresponding quiver.\nThis deep conjectural relationship already had some surprising applications.\nIn this talk I will focus on sh owing that the knots-quivers correspondence holds for rational links\, as well as much larger class of arborescent links (algebraic links in the sen se of Conway). This is done by extending the correspondence to tangles\, a nd showing that the set of tangles satisfying tangles-quivers corresponden ce is closed under the tangle addition operation.\n\nThis talk is based on joint work with Paul Wedrich.\n LOCATION:https://researchseminars.org/talk/TQFT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Antti Kupiainen (University of Helsinki) DTSTART:20200612T160000Z DTEND:20200612T170000Z DTSTAMP:20260422T225721Z UID:TQFT/6 DESCRIPTION:Title: Int egrability of Liouville Conformal Field Theory\nby Antti Kupiainen (Un iversity of Helsinki) as part of Topological Quantum Field Theory Club (IS T\, Lisbon)\n\n\nAbstract\nA. Polyakov introduced Liouville Conformal Fiel d theory (LCFT) in 1981 as a way to put a natural measure on the set of Ri emannian metrics over a two dimensional manifold. Ever since\, the work of Polyakov has echoed in various branches of physics and mathematics\, rang ing from string theory to probability theory and geometry.\nIn the context of 2D quantum gravity models\, Polyakov’s approach is conjecturally equ ivalent to the scaling limit of Random Planar Maps and through the Alday-G aiotto-Tachikava correspondence LCFT is conjecturally related to certain 4 D Yang-Mills theories. Through the work of Dorn\,Otto\, Zamolodchikov and Zamolodchikov and Teschner LCFT is believed to be to a certain extent inte grable.\n\nI will review a probabilistic construction of LCFT developed to gether with David\, Rhodes and Vargas and recent proofs of the integrabili ty of LCFT:\n\n-The proof in a joint work with Rhodes and Vargas of the DO ZZ formula\n(Annals of Mathematics\, 81-166\,191 (2020))\n\n-The proof in a joint work with Guillarmou\, Rhodes and Vargas of the\nbootstrap conject ure for LCFT (arXiv:2005.11530).\n LOCATION:https://researchseminars.org/talk/TQFT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ezra Getzler (Northwestern University) DTSTART:20200724T160000Z DTEND:20200724T170000Z DTSTAMP:20260422T225721Z UID:TQFT/7 DESCRIPTION:Title: Glu ing local gauge conditions in BV quantum field theory\nby Ezra Getzler (Northwestern University) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\n\nAbstract\nIn supersymmetric sigma models\, there is frequently no global choice of Lagrangian submanifold for BV quantization. I will take the superparticle\, a toy version of the Green Schwarz supers tring\, as my example\, and show how to extend the light-cone gauge to the physically relevant part of phase space. This involves extending a formul a of Mikhalkov and A. Schwarz that generalizes the prescription of Batalin and Vilkovisky for the construction of the functional integral.\n\nThis i s joint work with S. Pohorence.\n LOCATION:https://researchseminars.org/talk/TQFT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexis Virelizier (Université de Lille) DTSTART:20200911T160000Z DTEND:20200911T170000Z DTSTAMP:20260422T225721Z UID:TQFT/8 DESCRIPTION:Title: Hom otopy Quantum Field Theories\nby Alexis Virelizier (Université de Lil le) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nA bstract\nHomotopy quantum field theories (HQFTs) generalize topological qu antum field theories (TQFTs) by replacing manifolds by maps from manifolds 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 aspherical\, th at is $X = K(G\, 1)$ for some group $G$\, then this cohomological HQFT is related to the Dijkgraaf-Witten invariant and is computed as a Turaev-Viro state sum via the category of $G$-graded vector spaces. More generally\, the state sum Turaev-Viro TQFT and the surgery Reshetikhin-Turaev TQFT ext end to HQFTs (using graded fusion categories) which are related via the gr aded categorical center.
This is joint work with V. Turaev.\n LOCATION:https://researchseminars.org/talk/TQFT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Ricardo Campos (CNRS - University of Montpellier) DTSTART:20200710T160000Z DTEND:20200710T170000Z DTSTAMP:20260422T225721Z UID:TQFT/9 DESCRIPTION:Title: The homotopy type of associative and commutative algebras\nby Ricardo Cam pos (CNRS - University of Montpellier) as part of Topological Quantum Fiel d Theory Club (IST\, Lisbon)\n\n\nAbstract\nGiven a topological space\, ho w much of its homotopy type is captured by its algebra of singular cochain s? The experienced rational homotopy theorist will argue that one should c onsider instead a commutative algebra of forms. This raises the more algeb raic question "Given a dg commutative algebra\, how much of its homotopy t ype (quasi-isomorphism type) is contained in its associative part?" Despit e its elementary formulation\, this question turns out to be surprisingly subtle and has important consequences.\nIn this talk\, I will show how one can use operadic deformation theory to give an affirmative answer in char acteristic zero.\nWe will also see how the Koszul duality between Lie alge bras and commutative algebras allows us to use similar arguments to deduce that under good conditions Lie algebras are determined by the (associativ e algebra structure of) their universal enveloping algebras.\n\n\n(Joint w ith Dan Petersen\, Daniel Robert-Nicoud and Felix Wierstra and based on ar Xiv:1904.03585)\n LOCATION:https://researchseminars.org/talk/TQFT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Boavida de Brito (Instituto Superior Técnico and CAMGSD) DTSTART:20200717T160000Z DTEND:20200717T170000Z DTSTAMP:20260422T225721Z UID:TQFT/10 DESCRIPTION:Title: Ga lois symmetries of knot spaces\nby Pedro Boavida de Brito (Instituto S uperior Técnico and CAMGSD) as part of Topological Quantum Field Theory C lub (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 spa ce of all knots. The path components of this space form a finitely generat ed abelian group which is\, conjecturally\, a universal receptacle for int egral finite-type knot invariants. The added Galois symmetry allows us to extract new information about its homotopy and homology beyond characteris tic zero. I will then discuss some work in progress concerning higher-dime nsional variants.\n\nThis is joint work with Geoffroy Horel.\n LOCATION:https://researchseminars.org/talk/TQFT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:André Henriques (University of Oxford) DTSTART:20200925T160000Z DTEND:20200925T170000Z DTSTAMP:20260422T225721Z UID:TQFT/11 DESCRIPTION:Title: Re ps of relative mapping class groups via conformal nets\nby André Henr iques (University of Oxford) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nGiven a surface with boundary Σ\, its r elative mapping class group is the quotient of Diff(Σ) by the subgroup of maps which are isotopic to the identity via an isotopy that fixes the bou ndary pointwise. (If Σ has no boundary\, then that's the usual mapping cl ass group\; if Σ is a disc\, then that's the group Diff(S¹) of diffeomor phisms of S¹.)\n\nConformal nets are one of the existing axiomatizations of chiral conformal field theory (vertex operator algebras being another o ne). We will show that\, given an arbitrary conformal net and a surface wi th boundary Σ\, we get a continuous projective unitary representation of the relative mapping class group (orientation reversing elements act by an ti-unitaries). When the conformal net is rational and Σ is a closed surfa ce (i.e. ∂Σ = ∅)\, then these representations are finite dimensional and well known. When the conformal net is not rational\, then we must requ ire ∂Σ ≠ ∅ for these representations to be defined. We will try to explain what goes wrong when Σ is a closed surface and the conformal net is not rational.
\n\nThe material presented in this talk is partially based on my paper arXiv:1409.8672 with Arthur Bartels and Chris Douglas.\n LOCATION:https://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:20260422T225721Z UID:TQFT/13 DESCRIPTION:Title: Co unting Monster Potentials\nby Davide Masoero (Group of Mathematical Ph ysics\, University of Lisbon) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe monster potentials were introduced by  Bazhanov-Lukyanov-Zamolodchikov in the framework of the ODE/IM corres pondence. They should in fact be in 1:1 correspondence with excited states of the Quantum KdV model (an Integrable Conformal Field Theory) since the y are the most general potentials whose spectral determinant solves the Be the Ansatz equations of such a theory. By studying the large momentum limi t of the monster potentials\, I retrieve that:\n\n1) The poles of the mons ter potentials asymptotically condensate about the complex equilibria of t he ground state potential.\n\n2) The leading correction to such asymptotic s is described by the roots of Wronskians of Hermite polynomials.\n\nThis allows me  to associate to each partition of N a unique monster potential with N roots\, of which I compute the spectrum. As a consequence\, I prov e up to a few mathematical technicalities that\, fixed an integer N\, the number of monster potentials with N roots coincide with the number of inte ger partitions of N\, which is the dimension of the level N subspace of th e quantum KdV model. In striking accordance with the ODE/IM correspondence .\n\nThe talk is based on the preprint https://arxiv.org/abs/2009.14638 \ , written in collaboration with Riccardo Conti (Group of Mathematical Phys ics of Lisbon University).\n LOCATION:https://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:20260422T225721Z UID:TQFT/14 DESCRIPTION:Title: Mi rror symmetry for Painlevé surfaces\nby Tom Sutherland (Group of Math ematical Physics\, University of Lisbon) as part of Topological Quantum Fi eld Theory Club (IST\, Lisbon)\n\n\nAbstract\nThis talk will survey aspect s of mirror symmetry for ten families of non-compact hyperkähler manifold s on which the dynamics of one of the Painlevé equations is naturally def ined. They each have a pair of natural realisations: one as the complement of a singular fibre of a rational elliptic surface and another as the com plement of a triangle of lines in a (singular) cubic surface. The two real isations relate closely to a space of stability conditions and a cluster v ariety of a quiver respectively\, providing a perspective on SYZ mirror sy mmetry for these manifolds. I will discuss joint work in progress with Hel ge Ruddat studying the canonical basis of theta functions on these cubic s urfaces.\n LOCATION:https://researchseminars.org/talk/TQFT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Shapiro (University of Notre Dame) DTSTART:20201009T160000Z DTEND:20201009T170000Z DTSTAMP:20260422T225721Z UID:TQFT/15 DESCRIPTION:Title: Cl uster realization of quantum groups and higher Teichmüller theory\nby Alexander Shapiro (University of Notre Dame) as part of Topological Quant um Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nQuantum higher Teichmü ller theory\, as described by Fock and Goncharov\, endows a quantum charac ter variety on a surface $S$ with a cluster structure. The latter allows o ne to construct a canonical representation of the character variety\, whic h happens to be equivariant with respect to an action of the mapping class group of $S$. It was conjectured by the authors that these representation s behave well with respect to cutting and gluing of surfaces\, which in tu rn yields an analogue of a modular functor. In this talk\, I will show how the quantum group and its positive representations arise in this context. I will also explain how the modular functor conjecture is related to the closedness of positive representations under tensor products as well as to the non-compact analogue of the Peter-Weyl theorem. If time permits\, I w ill say a few words about the proof of the conjecture.\n\nThis talk is bas ed on joint works with Gus Schrader.\n LOCATION:https://researchseminars.org/talk/TQFT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Miranda Cheng (University of Amsterdam) DTSTART:20201016T160000Z DTEND:20201016T170000Z DTSTAMP:20260422T225721Z UID:TQFT/16 DESCRIPTION:Title: Qu antum modular forms and $3$-manifolds\nby Miranda Cheng (University of Amsterdam) as part of Topological Quantum Field Theory Club (IST\, Lisbon )\n\n\nAbstract\nQuantum modular forms are functions on rational numbers t hat have rather mysterious weak modular properties. Mock modular forms and false theta functions are examples of holomorphic functions on the upper- half plane which lead to quantum modular forms. Inspired by the $3d-3d$ co rrespondence in string theory\, new topological invariants named homologic al blocks for (in particular plumbed) three-manifolds have been proposed a few years ago. My talk aims to explain the recent observations on the qua ntum modular properties of the homological blocks\, as well as the relatio n to logarithmic vertex algebras.\n\nThe talk will be based on a series of work in collaboration with Sungbong Chun\, Boris Feigin\, Francesca Ferra ri\, Sergei Gukov\, Sarah Harrison\, and Gabriele Sgroi.\n LOCATION:https://researchseminars.org/talk/TQFT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Mackaay (University of Algarve) DTSTART:20201106T170000Z DTEND:20201106T180000Z DTSTAMP:20260422T225721Z UID:TQFT/17 DESCRIPTION:Title: Th e double-centralizer theorem in 2-representation theory and its applicatio ns\nby Marco Mackaay (University of Algarve) as part of Topological Qu antum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nFinitary birepresent ation theory of finitary bicategories is a categorical analog of finite-di mensional representation theory of finite-dimensional algebras. The role o f the simples is played by the so-called simple transitive birepresentatio ns and the classification of the latter\, for any given finitary bicategor y\, is a fundamental problem in finitary birepresentation theory (the clas sification problem). \nAfter briefly reviewing the basics of birepresentat ion theory\, I will explain an analog of the double centralizer theorem fo r finitary bicategories\, which was inspired by Etingof and Ostrik's doubl e centralizer theorem for tensor categories. As an application\, I will sh ow how it can be used to (almost completely) solve the classification prob lem for Soergel bimodules in any finite Coxeter type.\n LOCATION:https://researchseminars.org/talk/TQFT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:João Faria Martins (University of Leeds) DTSTART:20201030T170000Z DTEND:20201030T180000Z DTSTAMP:20260422T225721Z UID:TQFT/18 DESCRIPTION:Title: Cr ossed modules\, homotopy 2-types\, knotted surfaces and welded knots\n by João Faria Martins (University of Leeds) as part of Topological Quantu m Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will review the constr uction of invariants of knots\, loop braids and knotted surfaces derived f rom finite crossed modules. I will also show a method to calculate the alg ebraic homotopy 2-type of the complement of a knotted surface $\\Sigma$ em bedded in the 4-sphere from a movie presentation of $\\Sigma$. This will e ntail a categorified form of the Wirtinger relations for a knot group. Alo ng the way I will also show applications to welded knots in terms of a biq uandle related to the homotopy 2-type of the complement of the tube of a w elded knots.\n\nThe last stages of this talk are part of the framework of the Leverhulme Trust research project grant: RPG-2018-029: “Emergent Ph ysics From Lattice Models of Higher Gauge Theory.\n LOCATION:https://researchseminars.org/talk/TQFT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Tudor Dimofte (University of California\, Davis) DTSTART:20201120T170000Z DTEND:20201120T180000Z DTSTAMP:20260422T225721Z UID:TQFT/19 DESCRIPTION:Title: $3 d$ A and B models and link homology\nby Tudor Dimofte (University of C alifornia\, Davis) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will discuss some current work (with Garner\, Hi lburn\, Oblomkov\, and Rozansky) on new and old constructions of HOMFLY-PT link homology in physics and mathematics\, and new connections among them . In particular\, we relate the classic proposal of Gukov-Schwarz-Vafa\, i nvolving 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 re view general aspects of $3d$ TQFT's\, in particular the "$3d$ A and B mode ls" that play a role here\, and how link homology appears in them.\n LOCATION:https://researchseminars.org/talk/TQFT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Ostrik (University of Oregon) DTSTART:20201204T170000Z DTEND:20201204T180000Z DTSTAMP:20260422T225721Z UID:TQFT/20 DESCRIPTION:Title: Tw o dimensional topological field theories and partial fractions\nby Vic tor Ostrik (University of Oregon) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/TQFT/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Penka Georgieva (Sorbonne Université) DTSTART:20201218T170000Z DTEND:20201218T180000Z DTSTAMP:20260422T225721Z UID:TQFT/21 DESCRIPTION:Title: Kl ein TQFT and real Gromov-Witten invariants\nby Penka Georgieva (Sorbon ne Université) as part of Topological Quantum Field Theory Club (IST\, Li sbon)\n\n\nAbstract\nIn this talk I will explain how the Real Gromov-Witte n theory of local 3-folds with base a Real curve gives rise to an extensio n of a 2d Klein TQFT. The latter theory is furthermore semisimple which al lows for complete computation from the knowledge of a few basic elements w hich can be computed explicitly. As a consequence of the explicit expressi ons we find in the Calabi-Yau case\, we obtain the expected Gopukumar-Vafa formula and relation to SO/Sp Chern-Simons theory.\n LOCATION:https://researchseminars.org/talk/TQFT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Dragović (Univ. Texas at Dallas) DTSTART:20201113T170000Z DTEND:20201113T180000Z DTSTAMP:20260422T225721Z UID:TQFT/22 DESCRIPTION:Title: El lipsoidal billiards\, extremal polynomials\, and partitions\nby Vladim ir Dragović (Univ. Texas at Dallas) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\n

A comprehensive study of peri odic trajectories of the billiards within ellipsoids in the d-dimensional Euclidean space is presented. The novelty of the approach is based on a re lationship established between the periodic billiard trajectories and the extremal polynomials of the Chebyshev type on the systems of d intervals o n the real line. Classification of periodic trajectories is based on a ne w combinatorial object: billiard partitions.

\n

The case study of tra jectories of small periods T\, d ≤ T ≤ 2d is given. In particular\, it is proven that all d-periodic trajectories are contained in a coordinate- hyperplane and that for a given ellipsoid\, there is a unique set of caust ics which generates d + 1-periodic trajectories. A complete catalog of bil liard trajectories with small periods is provided for d = 3.

\n

The talk is based on the following papers:

\n

V. Dragović\, M. Radnović \, Periodic ellipsoidal billiard trajectories and extremal polynomials\, Communications Mathematical Physics\, 2019\, Vol. 372\, p. 183-211.

\n< p>G. Andrews\, V. Dragović\, M. Radnović\, Combinatorics of the periodic billiards within quadrics\, \narXiv: 1908.01026\, The Ramanujan Journal\, DOI: 10.1007/s11139-020-00346-y.

\n LOCATION:https://researchseminars.org/talk/TQFT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Brent Pym (McGill University) DTSTART:20210115T170000Z DTEND:20210115T180000Z DTSTAMP:20260422T225721Z UID:TQFT/23 DESCRIPTION:Title: Mu ltiple zeta values in deformation quantization\nby Brent Pym (McGill U niversity) as part of Topological Quantum Field Theory Club (IST\, Lisbon) \n\n\nAbstract\nIn 1997\, Kontsevich gave a universal solution to the defo rmation quantization problem in mathematical physics: starting from any Po isson manifold (the classical phase space)\, it produces a noncommutative algebra of quantum observables by deforming the ordinary\nmultiplication o f functions. His formula is a Feynman expansion whose Feynman integrals gi ve periods of the moduli space of marked holomorphic disks. I will describ e joint work with Peter Banks and Erik Panzer\, in which we prove that Kon tsevich's integrals evaluate to integer-linear\ncombinations of multiple z eta values\, building on Francis Brown's theory of polylogarithms on the m oduli space of genus zero curves.\n LOCATION:https://researchseminars.org/talk/TQFT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Beliakova (University of Zürich) DTSTART:20201211T170000Z DTEND:20201211T180000Z DTSTAMP:20260422T225721Z UID:TQFT/24 DESCRIPTION:Title: Cy clotomic expansions of the $gl_N$ knot invariants\nby Anna Beliakova ( University of Zürich) as part of Topological Quantum Field Theory Club (I ST\, Lisbon)\n\n\nAbstract\nNewton’s interpolation is a method to recons truct a function from its values at different points. In the talk I will e xplain how one can use this method to construct an explicit basis for the center of quantum $gl_N$ and to show that the universal $gl_N$ knot invari ant expands in this basis. This will lead us to an explicit construction o f the so-called unified invariants for integral homology 3-spheres\, that dominate all Witten-Reshetikhin-Turaev invariants. This is a joint work wi th Eugene Gorsky\, that generalizes famous results of Habiro for $sl_2$.\n LOCATION:https://researchseminars.org/talk/TQFT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Severin Bunk (Univ. Hamburg) DTSTART:20210129T170000Z DTEND:20210129T180000Z DTSTAMP:20260422T225721Z UID:TQFT/25 DESCRIPTION:Title: Un iversal Symmetries of Gerbes and Smooth Higher Group Extensions\nby Se verin Bunk (Univ. Hamburg) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\n\nAbstract\nGerbes are geometric objects describing th e third integer cohomology group of a manifold and the B-field in string t heory\; they can essentially be understood as bundles of categories whose fibre is equivalent to the category of vector spaces. Starting from a hand s-on example\, I will explain gerbes and their categorical features. The m ain topic of this talk will then be the study of symmetries of gerbes in a universal manner. We will see that these symmetries are completely encode d in an extension of smooth 2-groups. In the last part\, I will survey how this construction can be used to provide a new smooth model for the strin g group\, via a theory of group extensions in $\\infty$-topoi.\n LOCATION:https://researchseminars.org/talk/TQFT/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Renee Hoekzema (Univ. Oxford) DTSTART:20210122T170000Z DTEND:20210122T180000Z DTSTAMP:20260422T225721Z UID:TQFT/26 DESCRIPTION:Title: Ma nifolds with odd Euler characteristic and higher orientability\nby Ren ee Hoekzema (Univ. Oxford) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\n\nAbstract\nOrientable manifolds have even Euler chara cteristic unless the dimension is a multiple of 4. I give a generalisation of this theorem: $k$-orientable manifolds have even Euler characteristic (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 the $i^{ \\rm th}$ Stiefel-Whitney class vanishes for all $0 < i < 2^k$. This theor em is strict for $k=0\,1\,2\,3$\, but whether there exist 4-orientable man ifolds with an odd Euler characteristic is a new open question. Such manif olds would have dimensions that are a multiple of 32. I discuss manifolds of dimension high powers of 2 and present the results of calculations on t he cohomology of the second Rosenfeld plane\, a special 64-dimensional man ifold with odd Euler characteristic.\n LOCATION:https://researchseminars.org/talk/TQFT/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Elias (Univ. Oregon) DTSTART:20210226T170000Z DTEND:20210226T180000Z DTSTAMP:20260422T225721Z UID:TQFT/27 DESCRIPTION:Title: In troduction to the Hecke category and the diagonalization of the full twist \nby Ben Elias (Univ. Oregon) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nThe group algebra of the symmetric group has a large commutative subalgebra generated by Young-Jucys-Murphy e lements\, which acts diagonalizably on any irreducible representation. The goal of this talk is to give an accessible introduction to the categorifi cation of this story. The main players are: Soergel bimodules\, which cate gorify the Hecke algebra of the symmetric group\; Rouquier complexes\, whi ch categorify the braid group where Young-Jucys-Murphy elements live\; and the Elias-Hogancamp theory of categorical diagonalization\, which allows one to construct projections to "eigencategories."\n LOCATION:https://researchseminars.org/talk/TQFT/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Vaz (Université Catholique de Louvain\, Belgium) DTSTART:20210108T170000Z DTEND:20210108T180000Z DTSTAMP:20260422T225721Z UID:TQFT/28 DESCRIPTION:Title: Ca tegorification of Verma Modules in low-dimensional topology\nby Pedro Vaz (Université Catholique de Louvain\, Belgium) as part of Topological Q uantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn this talk I will review the program of categorification of Verma modules and explain their applications to low-dimensional topology\, namely to the construction of Khovanov invariants for links in the solid torus via a categorification of the blob algebra.\n\nThe material presented spreads along several collabo rations with Abel Lacabanne\, and Grégoire Naisse.\n LOCATION:https://researchseminars.org/talk/TQFT/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Florio Ciaglia (MPI Leipzig) DTSTART:20210212T170000Z DTEND:20210212T180000Z DTSTAMP:20260422T225721Z UID:TQFT/29 DESCRIPTION:Title: A groupoid-based perspective on quantum mechanics\nby Florio Ciaglia (MP I 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 th eoretical investigation of the foundations and mathematical formalism of q uantum mechanics which is based on Schwinger’s “Symbolism of atomic me asurement” [8] on the physical side\, and on the notion of groupoid on t he mathematical side. I will start by reviewing the “development” of q uantum mechanics and its formalism starting from Schrödinger’s wave mec hanics\, passing through the Hilbert space quantum mechanics\, and arrivin g at the $C^∗$-algebraic formulation of quantum mechanics in order to gi ve an intuitive idea of what is the “place” of the groupoid-based appr oach to quantum theories presented here. Then\, after (what I hope will be ) a highly digestible introduction to the notion of groupoid\, I will revi ew two historic experimental instances in which the shadow of the structur e of groupoid may be glimpsed\, namely\, the Ritz-Rydberg combination prin ciple\, and the Stern-Gerlach experiment. The last part of the talk will b e devoted to building a bridge between the groupoid-based approach to quan tum mechanics and the more familiar $C^∗$-algebraic one by analysing how to obtain a (possibly) non-commutative algebra out of a given groupoid. T wo relevant examples will be discussed\, and some comment on future direct ions (e.g.\, the composition of systems) will close the talk. The material presented is part of an ongoing project developed together with Dr. 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].

\n

References

\n

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

\n

[2] F. M. Ciaglia\, F. Di Cosmo\, A. Ibort\, and G. Marmo. Schwinger’s Pict ure of Quantum Mechanics. International Journal of Geometric Methods in Mo dern Physics\, 17(04):2050054 (14)\, 2020.

\n

[3] F. M. Ciaglia\, F . Di Cosmo\, A. Ibort\, and G. Marmo. Schwinger’s Picture of Quantum Mec hanics IV: Composition and independence. International Journal of Geometri c Methods in Modern Physics\, 17(04):2050058 (34)\, 2020.

\n

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

\n

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

\n

[6] F. M. Ciaglia\, A. Ibort\, and G. Mar mo. Schwinger’s Picture of Quantum Mechanics II: Algebras and Observable s. International Journal of Geometric Methods in Modern Physics\, 16(09):1 950136 (32)\, 2019.

\n

[7] F. M. Ciaglia\, A. Ibort\, and G. Marmo. Schwinger’s Picture of Quantum Mechanics III: The Statistical Interpret ation. International Journal of Geometric Methods in Modern Physics\, 16(1 1):1950165 (37)\, 2019.

\n

[8] J. Schwinger. Quantum Mechanics\, Sym bolism of Atomic Measurements. Springer-Verlag\, Berlin\, 2001.

\n LOCATION:https://researchseminars.org/talk/TQFT/29/ END:VEVENT BEGIN:VEVENT SUMMARY:David Reutter (MPI Bonn) DTSTART:20210219T170000Z DTEND:20210219T180000Z DTSTAMP:20260422T225721Z UID:TQFT/30 DESCRIPTION:Title: Se misimple topological field theories in even dimensions\nby David Reutt er (MPI Bonn) as part of Topological Quantum Field Theory Club (IST\, Lisb on)\n\n\nAbstract\nA major open problem in quantum topology is the constru ction of an oriented 4-dimensional topological quantum field theory (TQFT) in the sense of Atiyah-Segal which is sensitive to exotic smooth structur e. More generally\, how much manifold topology can a TQFT see? \n\nIn this talk\, I will answer this question for semisimple field theories in even dimensions — I will sketch a proof that such field theories can at most see the stable diffeomorphism type of a manifold and conversely\, that if two sufficiently finite manifolds are not stably diffeomorphic then they c an be distinguished by semisimple field theories. In this context\, `semis implicity' is a certain algebraic condition applying to all currently know n examples of vector-space-valued TQFTs\, including `unitary field theorie s’\, and `once-extended field theories' which assign algebras or linear categories to codimension 2 manifolds. I will discuss implications in dime nsion 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 category\, as a guiding example.\n\nThis is based on arXiv:2001.02288 and joint work in progress with Chris Schommer-Pries.\n LOCATION:https://researchseminars.org/talk/TQFT/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Ikshu Neithalath (UCLA\, California) DTSTART:20210312T170000Z DTEND:20210312T180000Z DTSTAMP:20260422T225721Z UID:TQFT/31 DESCRIPTION:Title: Sk ein Lasagna modules of 2-handlebodies\nby Ikshu Neithalath (UCLA\, Cal ifornia) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n \n\nAbstract\nMorrison\, Walker and Wedrich recently defined a generalizat ion of Khovanov-Rozansky homology to links in the boundary of a 4-manifold . \nWe will discuss recent joint work with Ciprian Manolescu on computing the "skein lasagna module\," a basic part of MWW's invariant\, for a certa in class of 4-manifolds.\n LOCATION:https://researchseminars.org/talk/TQFT/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Owen Gwilliam (Univ. Massachusetts\, Amherst) DTSTART:20210305T140000Z DTEND:20210305T150000Z DTSTAMP:20260422T225721Z UID:TQFT/32 DESCRIPTION:Title: Bu lk-boundary correspondences with factorization algebras\nby Owen Gwill iam (Univ. Massachusetts\, Amherst) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nFactorization algebras provide a flexible language for describing the observables of a perturbative QFT\, a s shown in joint work with Kevin Costello. Those constructions extend to a manifold with boundary for a special class of theories. I will discuss wo rk 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 version fo r higher abelian CS theory on an oriented smooth manifold of dimension $4n +3$ with boundary a complex manifold of complex dimension $2n+1$. Given ti me\, I will discuss how this framework leads to a concrete construction of the center of higher enveloping algebras of Lie algebras\, in work with G reg Ginot and Brian Williams.\n\nPLEASE NOTE THE UNUSUAL TIME!\n LOCATION:https://researchseminars.org/talk/TQFT/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabio di Cosmo (Instituto de Ciencias Matemáticas\, Madrid) DTSTART:20210319T170000Z DTEND:20210319T174000Z DTSTAMP:20260422T225721Z UID:TQFT/33 DESCRIPTION:Title: St atistical Interpretation in the Schwinger’s picture of Quantum Mechanics \nby Fabio di Cosmo (Instituto de Ciencias Matemáticas\, Madrid) as p art of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\ nIn this talk I will illustrate some ideas about the statistical interpret ation in the Schwinger’s picture of Quantum Mechanics. After a brief int roduction on the postulates assumed in this framework\, I will recall the basic ingredients of Connes’ non commutative integration theory. This la nguage allows me to define\, on one hand quantum measures on the groupoid associated with the quantum systems\, and on the other weights on the corr esponding groupoid von-Neumann algebra. In particular\, quantum measures a re a generalization of measures on sigma-algebras which is suited for the description of interference phenomena. Then\, the final part of the talk w ill be devoted to the statistical interpretation associated with both situ ations.\n\nFirst part of a double session\, followed by a 20 minute break for coffee and discussion\, before the second speaker\, Pedro Resende.\n LOCATION:https://researchseminars.org/talk/TQFT/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Resende (Instituto Superior Técnico\, Lisbon) DTSTART:20210319T180000Z DTEND:20210319T184000Z DTSTAMP:20260422T225721Z UID:TQFT/34 DESCRIPTION:Title: An abstract theory of physical measurements\nby Pedro Resende (Instituto Superior Técnico\, Lisbon) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nSince its early days\, quantum mechanics has forced physicists to consider the interaction between quantum systems and classically described experimental devices — a fundamental tenet fo r Bohr was that the results of measurements need to be communicated using the language of classical physics.\n\nSeveral decades of progress have led to improved understanding\, but the tension between “quantum” and “ classical” persists. Ultimately\, how is classical information extracted from a measurement? Is classical information fundamental\, as in Wheeler ’s “it from bit”? In this talk\, which is based on ongoing work [1]\ , I approach the problem mathematically by considering spaces whose points are measurements\, abstractly conceived in terms of the classical informa tion they produce. Concretely\, measurement spaces are stably Gelfand quan tales [2] equipped with a compatible sober topology\, but essentially thei r definition hinges on just two binary operations\, called composition and disjunction\, whose intuitive meanings are fairly clear. Despite their si mplicity\, these spaces have interesting mathematical properties. C*-algeb ras yield measurement spaces of “quantum type\,” and Lie groupoids giv e us spaces of “classical type\,” such as those which are associated w ith a specific experimental apparatus. The latter also yield a connection to Schwinger’s selective measurements\, which have been recast in groupo id language by Ciaglia et al.\nAn interaction between the two types\, prov iding 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 measur ements performed with a Stern–Gerlach apparatus.\n\nReferences\n\n[1] P. Resende\, An abstract theory of physical measurements (2021)\, available at \nhttps://arxiv.org/abs/2102.01712.\n\n[2] P. Resende\, The many groupo ids of a stably Gelfand quantale\, J. Algebra 498 (2018)\, 197–210\, \nD OI 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.2017.12. 001. MR3742593\n\nSecond part of a double session\, followed by a 20 minut e discussion period.\n LOCATION:https://researchseminars.org/talk/TQFT/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Roger Picken (Instituto Superior Técnico\, Lisbon) DTSTART:20210409T160000Z DTEND:20210409T170000Z DTSTAMP:20260422T225721Z UID:TQFT/35 DESCRIPTION:Title: Li nk invariants from finite crossed modules and a lifting of the Eisermann i nvariant\nby Roger Picken (Instituto Superior Técnico\, Lisbon) as pa rt of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\n This talk is based on work with João Faria Martins (Univ. Leeds) [1] and several projects with students. I will describe the construction of an inv ariant of tangles and framed tangles which takes values in an arbitrary cr ossed module of finite groups. This involves the fundamental crossed modul e associated to a natural topological pair coming from a knot diagram\, an d a suitable class of morphisms from this fundamental crossed module to th e chosen finite crossed module. Our construction includes all rack and qua ndle cohomology (framed) link invariants\, as well as the Eisermann invari ant of knots [2-3]\, for which we also find a lifting. The Eisermann invar iant detects information about a suitable choice of meridian and longitude in the knot complement boundary.\n\n

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

\n LOCATION:https://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:20260422T225721Z UID:TQFT/36 DESCRIPTION:Title: Qu antum differential equations\, qKZ difference equations\, and helices\ nby Giordano Cotti (Grupo de Física Matemática\, Universidade de Lisboa) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbst ract\nQuantum differential equations (qDEs) are a rich object attached to complex smooth projective varieties. They encode information on their enum erative geometry\, topology and (conjecturally) on their algebraic geometr y. In occasion of the 1998 ICM in Berlin\, B.Dubrovin conjectured an intri guing connection between the enumerative geometry of a Fano manifold $X$ w ith algebro-geometric properties of exceptional collections in the derived category $D_b(X)$. Under the assumption of semisimplicity of the quantum cohomology of $X$\, the conjecture prescribes an explicit form for local i nvariants of $QH^*(X)$\, the so-called “monodromy data”\, in terms of Gram matrices and characteristic classes of objects of exceptional collect ions. In this talk I will discuss an equivariant analog of these relations \, focusing on the example of projective spaces. The study of the equivari ant quantum differential equations for partial flag varieties has been ini tiated by V.Tarasov and A.Varchenko in 2017. They discovered the existence of a system of compatible qKZ difference equations\, which have made the study of the quantum differential equations easier than in the non-equivar iant case. I will establish relations between the monodromy data of the jo int system of the equivariant qDE and qKZ equations for $\\mathbb{P}^n$ an d characteristic classes of objects of the derived category of T-equivaria nt coherent sheaves on $\\mathbb{P}^n$.\n\nBased on joint works with B.Dub rovin\, D.Guzzetti and A.Varchenko.\n LOCATION:https://researchseminars.org/talk/TQFT/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Si Li (Tsinghua University) DTSTART:20210514T080000Z DTEND:20210514T090000Z DTSTAMP:20260422T225721Z UID:TQFT/37 DESCRIPTION:Title: Ge ometry of Localized Effective Theories and Algebraic Index\nby Si Li ( Tsinghua University) as part of Topological Quantum Field Theory Club (IST \, Lisbon)\n\n\nAbstract\nWe describe a general framework to study the qua ntum geometry of -models when they are effectively localized to small quan tum fluctuations around constant maps. Such effective theories have exact descriptions at all loops in terms of target geometry and can be rigorousl y formulated. We illustrate this idea by the example of topological quantu m mechanics which will lead to an explicit construction of the universal t race map on periodic cyclic chains of matrix Weyl algebras. As an applicat ion\, we explain how to implement the idea of exact semi-classical approxi mation into a proof of the algebraic index theorem using Gauss Manin conne ction.\n\nThis is joint work with Zhengping Gui and Kai Xu.\nZhengping Gui \, Si Li\, Kai Xu\,\nGeometry of Localized Effective Theories\, Exact Semi -classical Approximation and the Algebraic Index\nhttps://arxiv.org/pdf/19 11.11173\n LOCATION:https://researchseminars.org/talk/TQFT/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabian Haiden (Mathematical Institute\, University of Oxford) DTSTART:20210625T160000Z DTEND:20210625T170000Z DTSTAMP:20260422T225721Z UID:TQFT/38 DESCRIPTION:Title: Ca tegorical Kähler Geometry\nby Fabian Haiden (Mathematical Institute\, University of Oxford) as part of Topological Quantum Field Theory Club (I ST\, Lisbon)\n\n\nAbstract\nThis is a report on joint work in progress wit h L. Katzarkov\, M. Kontsevich\, and P. Pandit. The Homological Mirror Sym metry conjecture is stated as an equivalence of triangulated categories\, one coming from algebraic geometry and the other from symplectic topology. An enhancement of the conjecture also identifies stability conditions (in the sense of Bridgeland) on these categories. We adopt the point of view that triangulated (DG/A-infinity) categories are non-commutative spaces of an algebraic nature. A stability condition can then be thought of as the analog of a Kähler class or polarization. Many\, often still conjectural\ , constructions of stability conditions hint at a richer structure which w e think of as analogous to a Kähler metric. For instance\, a type of Dona ldson and Uhlenbeck-Yau theorem is expected to hold. I will discuss these examples and common features among them\, leading to a tentative definitio n.\n LOCATION:https://researchseminars.org/talk/TQFT/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruce Bartlett (Stellenbosch University) DTSTART:20210521T160000Z DTEND:20210521T170000Z DTSTAMP:20260422T225721Z UID:TQFT/39 DESCRIPTION:Title: As ymptotics of the classical and quantum $6j$ symbols\nby Bruce Bartlet t (Stellenbosch University) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\nThe classical (resp. quantum) 6j symbols are real numbers which encode the associator information for the tensor ca tegory of representations of SU(2) (resp. the quantum group of SU(2) at le vel k). They form the building blocks for the Turaev-Viro 3-dimensional TQ FT. I will review the intriguing asymptotic formula for these symbols in terms of the geometry of a Euclidean tetrahedron (in the classical case) o r a spherical tetrahedron (in the quantum case)\, due to Ponzano-Regge and Taylor-Woodward respectively. There is a wonderful integral formula for t he square of the classical 6j symbols as a group integral over SU(2)\, and I will report on investigations into a similar conjectural integral formu la for the quantum 6j symbols. In the course of these investigations\, we observed and proved a certain reciprocity formula for the Wigner derivativ e for spherical tetrahedra. Joint with Hosana Ranaivomanana.\n LOCATION:https://researchseminars.org/talk/TQFT/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Melnikov (International Institute of Physics) DTSTART:20210528T160000Z DTEND:20210528T170000Z DTSTAMP:20260422T225721Z UID:TQFT/40 DESCRIPTION:Title: En tanglement and complexity from TQFT\nby Dmitry Melnikov (International Institute of Physics) as part of Topological Quantum Field Theory Club (I ST\, Lisbon)\n\n\nAbstract\nIn the 1990s Aravind proposed that topological links can be used to classify different patterns of quantum entanglement. One way this connection can be investigated is through an appropriate qua ntum mechanical definition of knots. I will start from the category theory definition of a TQFT and derive a relation between measures of quantum en tanglement and topological invariants of links. We will see how patterns o f quantum entanglement emerge in the TQFT picture. Meanwhile\, complexity is a complementary measure of quantum correlations. In the TQFT case\, it can also be related to topological invariants. I will discuss a few defini tions of complexity for several families of knots and links.\n LOCATION:https://researchseminars.org/talk/TQFT/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Saemann (Heriot-Watt University) DTSTART:20210507T160000Z DTEND:20210507T170000Z DTSTAMP:20260422T225721Z UID:TQFT/41 DESCRIPTION:Title: Ad justed Higher Gauge Theory: Connections and Parallel Transport\nby Chr istian Saemann (Heriot-Watt University) as part of Topological Quantum Fie ld Theory Club (IST\, Lisbon)\n\n\nAbstract\nOrdinary higher gauge theory suffers from the problem that all the curvature forms but the top degree o ne\, which are called fake curvatures\, have to vanish. If this condition was omitted\, the gauge structure\, the underlying higher principal bundle and the corresponding parallel transport would be inconsistent. For vanis hing fake curvatures\, however\, one can locally gauge away the non-abelia n parts of the higher connection\, ending up with a connection on an abeli an gerbe. This is clearly unsatisfactory for non-topological higher gauge theories. A solution to this problem is what we call "adjusted higher gaug e theory"\, in which the usual definition of the curvatures is adjusted by additional data. This lifts the requirement for vanishing fake curvatures . Moreover\, it matches constructions of theoretical physicists in the con text of supergravity. In this talk\, I will review the above points and sa y a few words about my motivation for studying adjusted higher gauge theor ies.\n LOCATION:https://researchseminars.org/talk/TQFT/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Ingmar Saberi (University of Heidelberg) DTSTART:20210604T160000Z DTEND:20210604T170000Z DTSTAMP:20260422T225721Z UID:TQFT/42 DESCRIPTION:Title: Tw ists of supergravity theories via algebraic geometry\nby Ingmar Saberi (University of Heidelberg) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\nTwists of supersymmetric field theories h ave been the source of an enormous amount of new mathematics\, including ( just for example) Seiberg-Witten theory and mirror symmetry. It is reasona ble to expect that twists of supergravity theories will exhibit even riche r structure\, but they remain comparatively unexplored\, largely due to th eir intricacy. For example\, a holomorphically twisted version of the AdS/ CFT correspondence was proposed by Kevin Costello and Si Li\, motivated by constructions in topological string theory and the work of Bershadsky-Cec otti-Ooguri-Vafa\; Costello and Li conjectured a connection between their version of BCOV theory and the type IIB supergravity theory\, but did not verify this connection directly. I will show that the pure spinor superfie ld technique\, which has been known for some time in the physics literatur e\, can be used to elegantly and economically construct supersymmetric the ories\, as well as to swiftly compute their twists. In each case\, the res ulting structures are governed by the classical algebraic geometry of cert ain affine varieties. If time permits\, I'll discuss the examples of type IIB supergravity and eleven-dimensional supergravity in some detail.\n LOCATION:https://researchseminars.org/talk/TQFT/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Theo Johnson-Freyd (Dalhousie University and Perimeter Institute) DTSTART:20210618T160000Z DTEND:20210618T170000Z DTSTAMP:20260422T225721Z UID:TQFT/43 DESCRIPTION:Title: Hi gher S-matrices\nby Theo Johnson-Freyd (Dalhousie University and Perim eter Institute) as part of Topological Quantum Field Theory Club (IST\, Li sbon)\n\n\nAbstract\nEach fusion higher category has a "framed S-matrix" w hich encodes the commutator of operators of complementary dimension. I wil l explain how to construct and interpret this pairing\, and I will emphasi ze that it may fail to exist if you drop semisimplicity requirements. I wi ll then outline a proof that the framed S-matrix detects (non)degeneracy o f the fusion higher category. This is joint work in progress with David Re utter.\n LOCATION:https://researchseminars.org/talk/TQFT/43/ END:VEVENT BEGIN:VEVENT SUMMARY:João Faria Martins (University of Leeds) DTSTART:20210924T160000Z DTEND:20210924T170000Z DTSTAMP:20260422T225721Z UID:TQFT/44 DESCRIPTION:Title: Qu inn Finite Total Homotopy TQFT as a once-extended TQFT\nby João Faria Martins (University of Leeds) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nQuinn Finite Total Homotopy TQFT is a TQFT that works in any dimension and that depends on the choice of a homot opy finite space $B$ (e.g. $B$ can be the classifying space of a finite gr oup or of a finite 2-group). I will report on ongoing joint work with Tim Porter on once-extended versions of Quinn Finite total homotopy TQFT\, an d I will show how to compute them for the case when $B$ is the classifying space of a finite strict omega-groupoid (represented by a crossed complex ).\n\nSome stages of this work were financed by the Leverhulme trust resea rch project grant: Emergent Physics From Lattice Models of Higher Gauge Th eory.\n LOCATION:https://researchseminars.org/talk/TQFT/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Tijana Radenković (Institute of Physics\, Belgrade) DTSTART:20211013T160000Z DTEND:20211013T170000Z DTSTAMP:20260422T225721Z UID:TQFT/45 DESCRIPTION:Title: To pological higher gauge theory - from 2BF to 3BF theory\nby Tijana Rade nković (Institute of Physics\, Belgrade) as part of Topological Quantum F ield Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe study a generalization o f BF-theories in the context of higher gauge theory. We construct a topolo gical state sum Z\, based on the classical 3BF action for a general semist rict Lie 3-group and a triangulation of a 4-dimensional spacetime manifold . The 3BF action is constructed using a 2-crossed module which encodes a 3 -group (as introduced by Picken and Faria Martins [1])\, while the state s um Z is an example of Porter’s TQFT [2] for d=4 and n=3. In order to ver ify that the constructed state sum is a topological invariant of the under lying manifold\, its behavior under Pachner moves is analyzed\, and it is obtained that the state sum Z remains the same. Our results are a generali zation of the work done by Girelli\, Pfeiffer\, and Popescu [3] for the ca se of state sum based on the classical 2BF action with the underlying 2-gr oup structure.\n

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

\n

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

\n

\n[3] F. Gir elli\, H. Pfeiffer and E. M. Popescu\, Jour. Math. Phys. 49\, 032503 (2008 )\, arXiv:0708.3051.\n

\n LOCATION:https://researchseminars.org/talk/TQFT/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian R. Williams (University of Edinburgh) DTSTART:20211117T170000Z DTEND:20211117T180000Z DTSTAMP:20260422T225721Z UID:TQFT/46 DESCRIPTION:Title: Ex ceptional super Lie algebras in twisted M-theory\nby Brian R. Williams (University of Edinburgh) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\n\nAbstract\nWith Saberi and Raghavendran we constructe d\, in the BV formalism\, the minimal\, holomorphic\, twist of 11-dimensio nal supergravity. Amazingly\, on flat space\, the theory shares a close re lationship to an exceptional simple super Lie algebra called E(5\,10). Mot ivated by holographic duality\, I’ll turn attention to symmetries of the theories on M2 and M5 branes. In the twisted setting\, we find that the s uperconformal algebra enhances to other infinite-dimensional exceptional s uper Lie algebras. I will discuss further extensions of these exceptional algebras to factorization algebras and applications to pinning down correl ation functions in M-theory.\n LOCATION:https://researchseminars.org/talk/TQFT/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir M. Stojanovic (TU Darmstadt) DTSTART:20211215T170000Z DTEND:20211215T180000Z DTSTAMP:20260422T225721Z UID:TQFT/47 DESCRIPTION:Title: Li e-algebraic aspects of quantum control: gate realization and W-to-GHZ stat e conversion\nby Vladimir M. Stojanovic (TU Darmstadt) as part of Topo logical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn this ta lk I will try to demonstrate the use of Lie-algebraic concepts in the quan tum control of interacting qubit arrays\, with examples from both operator (gate)- and state control. I will start from the basics of quantum contro l and briefly review the Lie-algebraic underpinnings of the concept of com plete controllability. I will then specialize to qubit arrays with Heisenb erg-type interactions\, summarizing the conditions for their complete cont rollability and showing a few examples of gate realization. The second par t of the talk will be devoted to a rather unconventional use of Lie-algebr aic concepts within a dynamical-symmetry-based approach to the determinist ic conversion between W- and Greenberger-Horne-Zeilinger (three-qubit) sta tes. The underlying physical system consists of three neutral atoms subjec t to several external laser pulses\, where the atomic ground- and a highly -excited Rydberg state play the role of the two relevant logical qubit sta tes.\n LOCATION:https://researchseminars.org/talk/TQFT/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Giorgio Trentinaglia (Instituto Superior Técnico\,Lisbon) DTSTART:20220119T170000Z DTEND:20220119T180000Z DTSTAMP:20260422T225721Z UID:TQFT/48 DESCRIPTION:Title: Si mplicial vector bundles and representations up to homotopy\nby Giorgio Trentinaglia (Instituto Superior Técnico\,Lisbon) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe classical Dol d–Kan correspondence for simplicial objects in an abelian category is on e of the cornerstones of homological algebra. When the abelian category is that of vector spaces\, it gives a full identification between simplicial vector spaces and chain complexes of vector spaces vanishing in negative degrees. The Grothendieck construction for fibered categories\, on the oth er hand\, is a cornerstone of category theory. It relates the fibered cate gory point of view with the pseudo-functor point of view and lies at the h eart of the theory of stacks. Our main result can be understood as a far-r eaching simultaneous generalization of both ideas within the contexts of l inear algebra and differential geometry. In our result\, simplicial vector spaces and chain complexes of vector spaces are replaced respectively by vector fibrations over a given (higher) Lie groupoid G and by representati ons up to homotopy of G. (Joint work with Matias del Hoyo.)\n LOCATION:https://researchseminars.org/talk/TQFT/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeffrey C. Morton (SUNY Buffalo State) DTSTART:20220126T170000Z DTEND:20220126T180000Z DTSTAMP:20260422T225721Z UID:TQFT/49 DESCRIPTION:Title: Th e Fock Pseudomonad: Groupoidifying Second Quantization\nby Jeffrey C. Morton (SUNY Buffalo State) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\n

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

\n\n

Groupoidification is one of a number of approaches to "categorifying" quantum-mechanical systems: finding higher-categorical an alogs of those systems. It uses a 2-category Span(Gpd) whose objects are g roupoids\, and whose morphisms are "spans". This has had some success in d escribing extensions of topological field theory to systems with boundary\ , with the "categorified" theory describing the evolution of open systems\ , which can be composed along their boundaries\, over time. In this talk\, I will use this framework to describe a categorification of F to the "Foc k Pseudomonad" which can be defined in any suitable 2-category\, and the c ompatibility of this pseudomonad in Span(Gpd) with that in 2-Hilbert space s\, and\, under the "degroupoidification" map\, with the usual Fock constr uction on Hilbert spaces.

\n LOCATION:https://researchseminars.org/talk/TQFT/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Cliff (University of Sherbrooke) DTSTART:20220202T170000Z DTEND:20220202T180000Z DTSTAMP:20260422T225721Z UID:TQFT/50 DESCRIPTION:Title: Mo duli spaces of principal 2-group bundles and a categorification of the Fre ed–Quinn line bundle\nby Emily Cliff (University of Sherbrooke) as p art of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\ nA 2-group is a higher categorical analogue of a group\, while a smooth 2- group is a higher categorical analogue of a Lie group. An important exampl e is the string 2-group in the sense of Schommer-Pries. We study the notio n of principal bundles for smooth 2-groups\, and investigate the moduli "s pace" of such objects.\n\nIn particular in the case of flat principal bund les for a finite 2-group over a Riemann surface\, we prove that the moduli space gives a categorification of the Freed–Quinn line bundle. This lin e bundle has as its global sections the state space of Chern–Simons theo ry for the underlying finite group. We can also use our results to better understand the notion of geometric string structures (as previously studie d by Waldorf and Stolz–Teichner).\n\n\nThis is based on joint work with Dan Berwick-Evans\, Laura Murray\, Apurva Nakade\, and Emma Phillips.\n LOCATION:https://researchseminars.org/talk/TQFT/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Grady (Texas Tech University) DTSTART:20220216T170000Z DTEND:20220216T180000Z DTSTAMP:20260422T225721Z UID:TQFT/51 DESCRIPTION:Title: De formation classes of invertible field theories and the Freed-Hopkins conje cture\nby Daniel Grady (Texas Tech 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 this talk\, I will discuss a recent result which provides an affirmat ive answer to a conjecture by Freed and Hopkins. The conjecture concerns a classification of reflection positive invertible field theories. I will b egin by reviewing motivation and background on reflection positive theorie s. Then I will state the conjecture and sketch of the proof\n LOCATION:https://researchseminars.org/talk/TQFT/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitri Pavlov (Texas Tech University) DTSTART:20220330T160000Z DTEND:20220330T170000Z DTSTAMP:20260422T225721Z UID:TQFT/52 DESCRIPTION:Title: Th e geometric cobordism hypothesis\nby Dmitri Pavlov (Texas Tech Univers ity) 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\n

I will explain my recent work with Danie l Grady on the locality of functorial field theories (arXiv:2011.01208) an d the geometric cobordism hypothesis (arXiv:2111.01095). The latter genera lizes the Baez–Dolan cobordism hypothesis to nontopological field theori es\, in which bordisms can be equipped with geometric structure\, such as smooth maps to a fixed target manifold\, Riemannian metrics\, conformal st ructures\, principal bundles with connection\, or geometric string structu res.

\n\n

Applications include

\n\n\n\n


\nIf time p ermits\, I will talk about planned work on the nonperturbative quantizatio n of functorial field theories and generalized Atiyah–Singer-style index theorems.

\n LOCATION:https://researchseminars.org/talk/TQFT/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Araújo (Instituto Superior Técnico) DTSTART:20220309T170000Z DTEND:20220309T180000Z DTSTAMP:20260422T225721Z UID:TQFT/53 DESCRIPTION:Title: St ring diagrams for higher categories\nby Manuel Araújo (Instituto Supe rior Técnico) as part of Topological Quantum Field Theory Club (IST\, Lis bon)\n\n\nAbstract\nString diagrams are a powerful computational tool\, mo st commonly used in the context of tensor categories and occasionally bica tegories. I will talk about work in progress on extending this to higher c ategories. The idea is to define a semistrict n-category as something whic h admits composites for labeled string diagrams\, much as one can define a strict n-category as something that admits composites for pasting diagram s. This notion of semistrict n-category should be more general than that o f a strict n-category\, but not as general as that of a weak n-category. W e can show that semistrict 3-categories are the same thing as Gray categor ies and it is known that every weak 3-category (also called a tricategory) is equivalent to a Gray category. It is not known whether something simil ar holds in higher dimensions. I will also try to give an idea of the usef ulness of string diagram calculus in dimensions 3 and 4\, by showing how i t can be used to prove coherence theorems for adjunctions.\n LOCATION:https://researchseminars.org/talk/TQFT/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Christoph Dorn (University of Oxford) DTSTART:20220316T170000Z DTEND:20220316T180000Z DTSTAMP:20260422T225721Z UID:TQFT/54 DESCRIPTION:Title: Ma nifold diagrams: Poincaré duality\, singularities\, and smooth structures \nby Christoph Dorn (University of Oxford) as part of Topological Quan tum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd flo or\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\nW e will pick things up just where we left off last week in Manuel's talk. W e will discuss combinatorial and geometric models for manifold diagrams (i .e. higher dimensional generalizations of string diagrams) based on recent joint work with Chris Douglas. We focus on three aspects of the theory: ( 1) the geometric duality of manifold diagrams and pasting diagrams\, whose cells provide a novel "universal" class of shapes for higher category the ory\; (2) how to extend the tantalizing connection between classical singu larities and laws of dualizable objects into higher dimensions\, overcomin g obstructions faced by classical differential singularity theory\; and (3 ) the conjectural "combinatorialization" of smooth structures\, which woul d allow us to faithfully represent smooth structures of manifolds in manif old diagrams\, and thus by purely combinatorial means.\n\nWe ask our parti cipants based in the US and Canada to be mindful of the time difference\, with the beginning of DST there on March 13th.\n LOCATION:https://researchseminars.org/talk/TQFT/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Yonatan Harpaz (CNRS at University of Paris 13) DTSTART:20220406T160000Z DTEND:20220406T170000Z DTSTAMP:20260422T225721Z UID:TQFT/55 DESCRIPTION:Title: Th e cobordism hypothesis in dimension 1\nby Yonatan Harpaz (CNRS at Univ ersity of Paris 13) 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 cobordism hypothesis is a conjectural characterization of the framed cobordism (∞\,n)-category a s the free symmetric monoidal (∞\,n)-category with duals generated 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 in 2009. Though this strategy is very efficient in reducing the general hypothesis to a relatively concrete statement (Claim 3.4.17 in Lurie's text)\, a for mal proof of this concrete statement has yet to appear in the literature. 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 using\, am ong other things\, the notion of quasi-unital ∞-categories.\n LOCATION:https://researchseminars.org/talk/TQFT/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Ángel González Prieto (Universidad Complutense de Madrid) DTSTART:20220413T160000Z DTEND:20220413T170000Z DTSTAMP:20260422T225721Z UID:TQFT/56 DESCRIPTION:Title: To pological Quantum Field Theories for Character Stacks\nby Ángel Gonz ález Prieto (Universidad Complutense de Madrid) 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\ nModuli spaces of representations of surface groups (aka character varieti es) are very interesting spaces due to their tight relation with moduli sp aces of Higgs bundles and flat connections. Nowadays\, several approaches are available in the literature to understand the geometry of these charac ter varieties constructed via geometric invariant theory quotients. Despit e these advances\, the geometry of character stacks\, where roughly speaki ng the group action is not quotiented but still tracked\, remains a myster y.\n\nTo address this problem\, in this talk we shall construct a lax mono idal topological quantum field theory that computes the virtual classes of G-representation stacks in the Grothendieck ring of BG-stacks. This tool gives rise to an effective computational method for these virtual classes based on topological recursion on the genus of the surface. Time permittin g\, we will also discuss how this construction provides evidence that lax monoidal TQFTs represent a new hope in the quantization of algebraic invar iants.\n\nJoint work with M. Hablicsek and J. Vogel.\n LOCATION:https://researchseminars.org/talk/TQFT/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Nezhla Aghaei (University of Southern Denmark) DTSTART:20220420T160000Z DTEND:20220420T170000Z DTSTAMP:20260422T225721Z UID:TQFT/57 DESCRIPTION:Title: Co mbinatorial quantisation of Supergroup Chern–Simons Theory\nby Nezhl a Aghaei (University of Southern Denmark) as part of Topological Quantum F ield Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\nChern –Simons theories with gauge supergroups appear naturally in string theor y and they possess interesting applications in mathematics\, e.g. for the construction of knot and link invariants. In my talk I will review the fra mework for combinatorial quantization of Chern–Simons theory and explain how this framework can be adapted for applications to superalgebras. This will give rise to interesting new observables which can be computed by ex ploiting the rich representation theory of Lie superalgebras.\n LOCATION:https://researchseminars.org/talk/TQFT/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Mnev (University of Notre Dame) DTSTART:20220427T160000Z DTEND:20220427T170000Z DTSTAMP:20260422T225721Z UID:TQFT/58 DESCRIPTION:Title: On the Fukaya-Morse A-infinity category\nby Pavel Mnev (University of No tre Dame) 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\nI will sketch the construction of the Fukaya-Morse category of a Riemannian manifold X -- an A-infinity category (a category where associativity of composition holds only "up-to-homotopy ") where the higher composition maps are given in terms of numbers of embe dded trees in X\, with edges following the gradient trajectories of certai n Morse functions. I will give simple examples and explain different appro aches to understanding the structure and proving the quadratic relations o n the structure maps -- (1a) via homotopy transfer\, (1b) effective field theory approach\, (2) topological quantum mechanics approach. The talk is based on a joint work with O. Chekeres\, A. Losev and D. Youmans\, arXiv:2 112.12756.\n LOCATION:https://researchseminars.org/talk/TQFT/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamie Vicary (University of Cambridge) DTSTART:20220504T160000Z DTEND:20220504T170000Z DTSTAMP:20260422T225721Z UID:TQFT/59 DESCRIPTION:Title: In troducing homotopy.io: A proof assistant for geometrical higher category t heory\nby Jamie Vicary (University of Cambridge) as part of Topologica l Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3 rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstr act\nWeak higher categories can be difficult to work with algebraically\, with the weak structure potentially leading to considerable bureaucracy. C onjecturally\, every weak $\\infty$-category is equivalent to a "semistric t" one\, in which unitors and associators are trivial\; such a setting mig ht reduce the burden of constructing large proofs. In this talk\, I will p resent the proof assistant homotopy.io\, which allows direct construction of composites in a finitely-generated semistrict $(\\infty\,\\infty)$-cate gory. The terms of the proof assistant have an interpretation as string di agrams\, and interaction with the proof assistant is entirely geometrical\ , by clicking and dragging with the mouse\, completely unlike traditional computer algebra systems. I will give an outline of the underlying theoret ical foundations\, and demonstrate use of the proof assistant to construct some nontrivial homotopies\, rendered in 2d\, 3d\, and in 4d as movies. I will close with some speculations about the possible interaction of such a system with more traditional type-theoretical approaches. (Joint work wi th Nathan Corbyn\, Calin Tataru\, Lukas Heidemann\, Nick Hu and David Reut ter.)\n LOCATION:https://researchseminars.org/talk/TQFT/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugene Rabinovich (University of Notre Dame) DTSTART:20220517T163000Z DTEND:20220517T173000Z DTSTAMP:20260422T225721Z UID:TQFT/60 DESCRIPTION:Title: Cl assical Bulk-Boundary Correspondences via Factorization Algebras\nby E ugene 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\nAbstract\nA fa ctorization algebra is a cosheaf-like local-to-global object which is mean t to model the structure present in the observables of classical and quant um field theories. In the Batalin–Vilkovisky (BV) formalism\, one finds that a factorization algebra of classical observables possesses\, in addit ion to its factorization-algebraic structure\, a compatible Poisson bracke t of cohomological degree +1. Given a "sufficiently nice" such factorizati on algebra on a manifold $N$\, one may associate to it a factorization alg ebra on $N\\times \\mathbb{R}_{\\geq 0}$. The aim of the talk is to explai n the sense in which the latter factorization algebra "knows all the class ical data" of the former. This is the bulk-boundary correspondence of the title. Time permitting\, we will describe how such a correspondence appear s in the deformation quantization of Poisson manifolds.\n\nNote unusual da y and time.\n LOCATION:https://researchseminars.org/talk/TQFT/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Noja (University of Heidelberg) DTSTART:20220525T160000Z DTEND:20220525T170000Z DTSTAMP:20260422T225721Z UID:TQFT/61 DESCRIPTION:Title: Th e de Rham / Spencer double complex and the geometry of forms on supermanif olds\nby Simone Noja (University of Heidelberg) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.31 (3r d floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstra ct\nIntegral forms are characteristic supergeometric objects that allow us to define a meaningful notion of integration on supermanifolds. In this t alk\, I will introduce a double complex of non-commutative sheaves that re lates integral forms to the more customary notion of differential forms. I will then discuss how this framework specializes to so-called cotangent b undle supermanifolds\, which are relevant to odd symplectic geometry and B V theory. If time permits\, I will explain how the geometry of forms is re lated to the problem of splitting a complex supermanifold in this particul ar setting.\n LOCATION:https://researchseminars.org/talk/TQFT/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Nima Moshayedi (University of California\, Berkeley) DTSTART:20220601T160000Z DTEND:20220601T170000Z DTSTAMP:20260422T225721Z UID:TQFT/62 DESCRIPTION:Title: Cu tting-Gluing of TQFTs in the Symplectic Cohomological Formalism\nby Ni ma Moshayedi (University of California\, Berkeley) 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\nThe functional integral methods for quantum gauge field theories allows us to pass to a symplectic formalism in order to deal with these objects in a rather nice way (the BV formalism). The extension to manifolds with b oundary (the BV-BFV formalism)\, recently constructed by Cattaneo-Mnev-Res hetikhin\, allows us to talk about cut and glue techniques in the perturba tive symplectic cohomological setting for TQFTs. I will present the idea o f the BV-BFV formalism and talk about several interesting connections to e .g. deformation quantization or shifted symplectic structures. Moreover\, I will talk about some ideas for a higher codimension version.\n LOCATION:https://researchseminars.org/talk/TQFT/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Marc Lackenby (University of Oxford) DTSTART:20220615T160000Z DTEND:20220615T170000Z DTSTAMP:20260422T225721Z UID:TQFT/63 DESCRIPTION:Title: Kn ot theory and machine learning\nby Marc Lackenby (University of Oxford ) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nLectu re held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Super ior Técnico).\n\nAbstract\nKnot theory is divided into several subfields. One of these is hyperbolic knot theory\, which is focused on the hyperbol ic structure that exists on many knot complements. Another branch of knot theory is concerned with invariants that have connections to 4-manifolds\, for example the knot signature and Heegaard Floer homology. In my talk\, I will describe a new relationship between these two fields that was disco vered with the aid of machine learning. Specifically\, we show that the kn ot signature can be estimated surprisingly accurately in terms of hyperbol ic invariants. We introduce a new real-valued invariant called the natural slope of a hyperbolic knot in the 3-sphere\, which is defined in terms of its cusp geometry. Our main result is that twice the knot signature and t he natural slope differ by at most a constant times the hyperbolic volume divided by the cube of the injectivity radius. This theorem has applicatio ns to Dehn surgery and to 4-ball genus. We will also present a refined ver sion of the inequality where the upper bound is a linear function of the v olume\, and the slope is corrected by terms corresponding to short geodesi cs that have odd linking number with the knot. My talk will outline the pr oofs of these results\, as well as describing the role that machine learni ng played in their discovery.\n\nThis is joint work with Alex Davies\, And ras Juhasz\, and Nenad Tomasev.\n LOCATION:https://researchseminars.org/talk/TQFT/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Nezhla Aghaei (University of Southern Denmark) DTSTART:20220509T140000Z DTEND:20220509T150000Z DTSTAMP:20260422T225721Z UID:TQFT/64 DESCRIPTION:Title: Co mbinatorial quantisation of Supergroup Chern–Simons Theory\nby Nezhl a Aghaei (University of Southern Denmark) as part of Topological Quantum F ield Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\nChern –Simons theories with gauge supergroups appear naturally in string theor y and they possess interesting applications in mathematics\, e.g. for the construction of knot and link invariants. In my talk I will review the fra mework for combinatorial quantization of Chern–Simons theory and explain how this framework can be adapted for applications to superalgebras. This will give rise to interesting new observables which can be computed by ex ploiting the rich representation theory of Lie superalgebras.\n LOCATION:https://researchseminars.org/talk/TQFT/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Álvaro del Pino Gómez (Utrecht University) DTSTART:20220608T160000Z DTEND:20220608T170000Z DTSTAMP:20260422T225721Z UID:TQFT/65 DESCRIPTION:Title: h- Principles and applications to distributions\nby Álvaro del Pino Góm ez (Utrecht University) as part of Topological Quantum Field Theory Club ( IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Depart ment\, Instituto Superior Técnico).\n\nAbstract\nIn the 1950s\, Smale and Hirsch proved that the space of immersions of an m-dimensional manifold i nto an n-dimensional manifold is homotopy equivalent\, as long as m < n\, to the space of monomorphisms between the tangent spaces. Any statement of this form (i.e. a comparison theorem between a space of geometric structu res and an associated space that is purely algebraic topological in nature )\, is known as a homotopy principle\, or h-principle.\n\nLater on\, in th e late 60s and early 70s\, Gromov developed (or generalised) various techn iques capable of proving h-principles. Since then\, these ideas have been impactful in the study of many geometric structures (including immersions\ , submersions\, foliations\, symplectic structures\, contact structures\, embeddings\, and Riemannian metrics).\n\nThe goal of the talk will be to s ketch some of these techniques and state some consequences in the homotopi cal study of tangent distributions (i.e.\, subbundles of the tangent bundl e).\n LOCATION:https://researchseminars.org/talk/TQFT/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Radmila Sazdanovic (North Carolina State University) DTSTART:20220629T160000Z DTEND:20220629T170000Z DTSTAMP:20260422T225721Z UID:TQFT/66 DESCRIPTION:Title: Bi linear pairings on two-dimensional cobordisms and generalizations of the D eligne category\nby Radmila Sazdanovic (North Carolina State Universit y) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nLect ure held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Supe rior Técnico).\n\nAbstract\nThe Deligne category of symmetric groups is t he additive Karoubi closure of the partition category. The partition categ ory may be interpreted\, following Comes\, via a particular linearization of the category of two-dimensional oriented cobordisms. In this talk we wi ll use a generalization of this approach to the Deligne category coupled w ith the universal construction of two-dimensional topological theories to construct their multi-parameter monoidal generalizations\, one for each ra tional function in one variable. This talk is based on joint work with M. Khovanov.\n LOCATION:https://researchseminars.org/talk/TQFT/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Marina Logares (Complutense University of Madrid) DTSTART:20220914T160000Z DTEND:20220914T170000Z DTSTAMP:20260422T225721Z UID:TQFT/67 DESCRIPTION:Title: Hi tchin systems\nby Marina Logares (Complutense University of Madrid) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nLecture h eld in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbstract\nHitchin systems are in the core of the intersectio n between integrable systems and gauge theories. These are algebraic compl etely integrable systems defined by moduli spaces of (decorated) Higgs bun dles. In this talk I shall describe several Hitchin systems. This is based on past and ongoing work with Biswas\, Martens\, Peón-Nieto and Szabó.\ n LOCATION:https://researchseminars.org/talk/TQFT/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Safronov (University of Edinburgh) DTSTART:20220921T160000Z DTEND:20220921T170000Z DTSTAMP:20260422T225721Z UID:TQFT/68 DESCRIPTION:Title: Sk ein modules and 4d TQFTs\nby Pavel Safronov (University of Edinburgh) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Instituto Superio r Técnico).\n\nAbstract\nIt is well-known that the quantum Chern–Simons theory (as formalized by Reshetikhin and Turaev) has a framing anomaly: t o have a functorial dependence on cobordisms\, they have to be equipped wi th an extra tangential structure besides the orientation. Following Walker and Freed–Teleman\, one can view the anomaly of the Chern–Simons theo ry as an invertible 4d TQFT\, the Crane–Yetter theory. While the Chern –Simons theory makes sense only when q\, the quantum parameter\, is a ro ot of unity\, the anomaly theory make sense for any q. I will describe the behavior of this 4d TQFT for generic q and\, in particular\, a descriptio n of its spaces of states on closed 3-manifolds. This is based on joint wo rk with Sam Gunningham and David Jordan.\n LOCATION:https://researchseminars.org/talk/TQFT/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Marko Vojinovic (University of Belgrade) DTSTART:20221026T160000Z DTEND:20221026T170000Z DTSTAMP:20260422T225721Z UID:TQFT/69 DESCRIPTION:Title: In sights into the Standard Model and quantum gravity from higher gauge theor y\nby Marko Vojinovic (University of Belgrade) 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\nHigher category theory can be employed to generalize the notion of symm etry\, by passing from a gauge group to the notion of a gauge n-group. The n-groups are designed to generalize notions of connection and parallel tr ansport\, from curves to manifolds of dimension higher than one. They also give rise to a class of topological actions called nBF actions. One can t hen employ a 3-group as a gauge symmetry and the corresponding 3BF action\ , to describe the full Einstein-Cartan theory of gravity coupled to Standa rd Model fields. Such an action is naturally adapted to the spinfoam quant ization technique\, with the aim to construct a full model of quantum grav ity with matter.\n\nOnce constructed\, the properties of the model open up the possibility of a nontrivial unification of all fields. A 3-group natu rally contains additional novel gauge groups which specify the spectrum of fermions and scalars present in the theory\, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. Th e presence and the properties of new gauge groups have the potential to ex plain fermion families\, and other structure in the matter spectrum of the Standard Model.\n\nThe speaker is visiting Lisbon\, so local participants are invited to attend the talk in person in Room 3.10 (3rd floor Mathemat ics Department).\n LOCATION:https://researchseminars.org/talk/TQFT/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Fiona Torzewska (University of Leeds) DTSTART:20221116T170000Z DTEND:20221116T180000Z DTSTAMP:20260422T225721Z UID:TQFT/70 DESCRIPTION:Title: To pological quantum field theories and homotopy cobordisms\nby Fiona Tor zewska (University of Leeds) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics D epartment\, Instituto Superior Técnico).\n\nAbstract\nI will begin by exp laining the construction of a category $CofCos$\, whose objects are topolo gical spaces and whose morphisms are cofibrant cospans. Here the identity cospan is chosen to be of the form $X\\to X\\times [0\,1] \\rightarrow X$\ , in contrast with the usual identity in the bicategory $Cosp(V)$ of cospa ns over a category $V$. The category $CofCos$ has a subcategory $HomCob$ i n which all spaces are homotopically 1-finitely generated. There exist fun ctors into $HomCob$ from a number of categorical constructions which are p otentially of use for modelling particle trajectories in topological phase s of matter: embedded cobordism categories and motion groupoids for exampl e. Thus\, functors from $HomCob$ into $Vect$ give representations of the a forementioned categories. \n\nI will also construct a family of functors $ Z_G : HomCob \\to Vect$\, one for each finite group $G$\, showing that top ological quantum field theories previously constructed by Yetter\, and an untwisted version of Dijkgraaf-Witten\, generalise to functors from $HomCo b$. I will construct this functor in such a way that it is clear the image s are finite dimensional vector spaces\, and the functor is explicitly cal culable.\n LOCATION:https://researchseminars.org/talk/TQFT/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Konrad Waldorf (University of Greifswald) DTSTART:20221130T170000Z DTEND:20221130T180000Z DTSTAMP:20260422T225721Z UID:TQFT/71 DESCRIPTION:Title: A representation of the string 2-group\nby Konrad Waldorf (University of Greifswald) as part of Topological Quantum Field Theory Club (IST\, Lisbo n)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, Inst ituto Superior Técnico).\n\nAbstract\nThe string 2-group is supposed to p lay the role of the spin group\, but in string theory instead of quantum m echanics. Several aspects of this analogy are by now well understood. In t his talk I will talk about joint work with Matthias Ludewig and Peter Kris tel on a further aspect\, namely the representation theory of the string 2 -group. This was an open problem for a long time. Our solution combines hi gher-categorical topology with operator algebras\, and allows a neat defin ition of Stolz-Teichner's "stringor bundle" as an associated 2-vector bund le.\n LOCATION:https://researchseminars.org/talk/TQFT/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Konstantin Eder (University of Erlangen–Nürnberg) DTSTART:20221207T170000Z DTEND:20221207T180000Z DTSTAMP:20260422T225721Z UID:TQFT/72 DESCRIPTION:Title: Su per Cartan geometry and (loop) quantum supergravity\nby Konstantin Ede r (University of Erlangen–Nürnberg) as part of Topological Quantum Fiel d Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 (3rd floor\, Mat hematics Department\, Instituto Superior Técnico).\n\nAbstract\nIn this t alk\, a mathematically rigorous approach toward geometric supergravity wil l be discussed which\, in the physical literature\, is usually known as th e Castellani-D'Auria-Fré approach. To this end\, using tools from superge ometry\, the notion of a super Cartan geometry will be introduced. Interes tingly\, in order to consistently incorporate the anticommutative nature o f fermionic fields\, the ordinary category of supermanifolds needs to be g eneralized in a physically consistent way leading to the notion of so-call ed enriched supermanifolds. We then apply this formalism to discuss a geom etric formulation of (generalized) pure Anti-de Sitter supergravity with N =1\,2 supersymmetry in D=4 modified by an additional Holst term. In this c ontext\, we will also talk about so-called picture changing operators (PCO ) and how they can be implemented in a mathematically rigorous way. Finall y\, an outlook will be given for applications of this formalism to (loop) quantum supergravity and the description of quantum supersymmetric black h oles.\n LOCATION:https://researchseminars.org/talk/TQFT/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Mackaay (University of Algarve) DTSTART:20230125T170000Z DTEND:20230125T180000Z DTSTAMP:20260422T225721Z UID:TQFT/73 DESCRIPTION:Title: 2- Representations of affine type A Soergel bimodules: some observations and examples\nby Marco Mackaay (University of Algarve) 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\nIn 2010\, Mazorchuk and Miemietz laid the foundations of a systemat ic theory of finitary 2-representations of finitary 2-categories\, which a re the categorical analog of finite-dimensional representations of finite- dimensional algebras. In the last couple of years\, this theory has been m uch further developed and has led to interesting classification results fo r e.g. certain finitary 2-representations of Soergel bimodules of finite C oxeter type\, which form an important class of examples.\n\nTogether with Miemietz and Vaz\, I've recently started to look at 2-representations of S oergel bimodules of affine type A\, which form a 2-category that is no lon ger finitary but only locally wide finitary\, a generalization which was i ntroduced and studied by Marpherson. This has major consequences for their 2-representations\, e.g. they now come in 3 different flavors: finitary\, wide finitary and triangulated.\n\nIn my talk\, I will first very briefly review finitary 2-representation theory of finitary 2-categories and reca ll the example of Soergel bimodules of finite Coxeter type. After that\, 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 stil l in its early stages.\n LOCATION:https://researchseminars.org/talk/TQFT/73/ END:VEVENT BEGIN:VEVENT SUMMARY:James Macpherson (Instituto Superior Técnico) DTSTART:20230208T170000Z DTEND:20230208T180000Z DTSTAMP:20260422T225721Z UID:TQFT/74 DESCRIPTION:Title: Lo cally wide quasi-fiat 2-categories and their coalgebra 2-representations\nby James Macpherson (Instituto Superior Técnico) 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\nFinitary 2-representation theory\, pioneered by Mazorchuk and Miemie tz in 2010\, is a categorification of finite dimensional representations o f finite dimensional algebras. It primarily studies the 2-representation t heory of finitary 2-categories\, which are additive\, linear\, Krull-Schmi dt 2-categories with various finiteness conditions. Much progress has been made in the area since\, including various results that fall under the co nceptual banner of 'internal vs. external' - that is\, finding equivalence s between arbitrary 'external' 2-representations and 'internal' 2-represen tations whose data is fully encoded with the finitary 2-category itself.\n \nIn this talk\, I will start by outlining the basic theory of finitary 2- categories and their finitary 2-representations\, and I will discuss two e xamples of 'internal' 2-representations\, namely cell 2-representations an d 2-representations formed of comodule 1-morphisms over a coalgebra 1-morp hism. I will then discuss relaxing the finiteness assumptions of finitary 2-categories\, resulting in a type of 2-category called 'locally wide fini tary 2-categories'. After discussing some of the difficulties this introdu ces\, I will focus on a specific type of locally wide finitary 2-category\ , namely locally wide quasi-fiat 2-categories\, and discuss what we know a bout coalgebra 1-morphisms and their associated 2-representations in this case.\n LOCATION:https://researchseminars.org/talk/TQFT/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Freed (Univ. Texas at Austin) DTSTART:20230215T163000Z DTEND:20230215T173000Z DTSTAMP:20260422T225721Z UID:TQFT/75 DESCRIPTION:Title: Wh at is an anomaly?\nby Dan Freed (Univ. Texas at Austin) as part of Top ological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nAnomalies in quantum field theory have been the subject of attention for decades. In this talk I will dispel some myths: anomalies are tied to symmetry\, an omalies are tied to fermionic fields\, etc. Then I will explain how anoma lies - expressed as invertible field theories - are the manifestation of t he projectivity of quantum field theory. My point of view is summarized b y a slogan:\n\n Quantum theory is projective. Quantization is linear.\n\nPlease note the earlier starting time\, half an hour before the usual time.\n LOCATION:https://researchseminars.org/talk/TQFT/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Geer (Utah State University) DTSTART:20230222T170000Z DTEND:20230222T180000Z DTSTAMP:20260422T225721Z UID:TQFT/76 DESCRIPTION:Title: No n-semisimple TQFTs\nby Nathan Geer (Utah State University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn thi s talk I will give a general overview of recent work on TQFTs from non-sem isimple 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-semisi mple world.\n LOCATION:https://researchseminars.org/talk/TQFT/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Young (Utah State University) DTSTART:20230301T170000Z DTEND:20230301T180000Z DTSTAMP:20260422T225721Z UID:TQFT/77 DESCRIPTION:Title: $U _q(\\mathfrak{gl}(1 \\vert 1))$ and $U(1 \\vert 1)$ Chern–Simons theory< /a>\nby Matt Young (Utah State 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\nThe g oal of this talk is to explain a concrete instance of the theory of non-se misimple TQFT in three dimensions\, as discussed in the talk of Nathan Gee r in this seminar on Feb. 22nd\, 2023. I will describe a recent constructi on of a TQFT which realizes Chern–Simons theory with gauge supergroup $U (1 \\vert 1)$\, as studied in the physics literature by Rozansky–Saleur and Mikhaylov. In particular\, I'll describe various relative modular stru ctures on the category of representations of the quantum group of $\\mathf rak{gl}(1 \\vert 1)$ which should be seen as non-semisimple analogues of m odular tensor categories associated to the quantum representation theory o f a simple Lie algebra at a root of unity. Based on joint work with Nathan Geer.\n LOCATION:https://researchseminars.org/talk/TQFT/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Niklas Garner (University of Washington) DTSTART:20230322T170000Z DTEND:20230322T180000Z DTSTAMP:20260422T225721Z UID:TQFT/78 DESCRIPTION:Title: VO As and Twisted Chern-Simons-Matter TQFTs\nby Niklas Garner (University of Washington) as part of Topological Quantum Field Theory Club (IST\, Li sbon)\n\nLecture held in Room 3.10 (3rd floor\, Mathematics Department\, I nstituto Superior Técnico).\n\nAbstract\nThe rich interplay between three -dimensional topological quantum field theories (TQFTs) and vertex operato r algebras (VOAs) has been a useful bridge in understanding aspects of bot h subjects. In this talk\, I will describe some aspects of this correspond ence focusing on the simple\, yet surprisingly rich\, examples of Chern-Si mons theories based on the Lie superalgebra $\\mathfrak{gl}(1|1)$.\n LOCATION:https://researchseminars.org/talk/TQFT/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Walker (Microsoft Station Q) DTSTART:20230405T160000Z DTEND:20230405T170000Z DTSTAMP:20260422T225721Z UID:TQFT/79 DESCRIPTION:Title: Tw o approaches to a universal state sum\nby Kevin Walker (Microsoft Stat ion Q) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n \nAbstract\nI’ll describe two approaches to constructing a universal sta te sum. The first approach (arXiv:2104.02101) is more elementary and assum es semisimplicity. Special cases of this state sum include Turaev–Viro\, Crane–Yetter\, Douglas–Reutter\, the Reshetikhin–Turaev Dehn surger y 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 semisimplicity. If the re’s time I’ll sketch a program to use the non-semisimple state sum to reproduce a cluster of non-semi-simple 3-manifold invariants due to many different authors (Lyubashenko\, Kuperberg\, Hennings\, ... Geer\, Gainutd inov\, Patureau-Mirand\, ... ).\n LOCATION:https://researchseminars.org/talk/TQFT/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Contreras (Amherst College) DTSTART:20230412T160000Z DTEND:20230412T170000Z DTSTAMP:20260422T225721Z UID:TQFT/80 DESCRIPTION:Title: Fr obenius objects in the category of spans and the symplectic category\n by Ivan Contreras (Amherst College) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nIt is well known that Frobenius a lgebras are in correspondence with 2-dimensional TQFTs. In this talk\, we introduce Frobenius objects in any monoidal category\, and in particular i n the category where objects are sets and morphisms are spans of sets. We prove the existence of a simplicial set that encodes the data of the Frobe nius structure in this category. This serves as a (simplicial) toy model o f the Wehrheim–Woodward construction for the symplectic category. This i s part of a program that intends to describe\, in terms of category theory \, the relationship between symplectic groupoids and topological field the ory via the Poisson sigma model. Based on joint work with Rajan Mehta and Molly Keller (Rev. in Math. Phys (34) 10 (2022))\, with Rajan Mehta\, Adel e Long and Sophia Marx (https://arxiv.org/abs/2208.14716)\, and ongoing wo rk with Rajan Mehta and Walker Stern.\n LOCATION:https://researchseminars.org/talk/TQFT/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Creutzig (University of Alberta) DTSTART:20230419T160000Z DTEND:20230419T170000Z DTSTAMP:20260422T225721Z UID:TQFT/81 DESCRIPTION:Title: Ri bbon categories associated to gl(1|1)\nby Thomas Creutzig (University of Alberta) as part of Topological Quantum Field Theory Club (IST\, Lisbon )\n\n\nAbstract\nIn recent seminars you have heard about topological 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 give an ov erview on the representation theory of the affine VOA of gl(1|1) and expla in why its ribbon supercategory coincides with the one of quantum gl(1|1). \n LOCATION:https://researchseminars.org/talk/TQFT/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Julie Bergner (University of Virginia) DTSTART:20230426T160000Z DTEND:20230426T170000Z DTSTAMP:20260422T225721Z UID:TQFT/83 DESCRIPTION:Title: Mo dels for $(\\infty\,n)$-categories with discreteness conditions\nby Ju lie Bergner (University of Virginia) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThere are two ways of turning Se gal spaces into models for up-to-homotopy categories\, or $(\\infty\,1)$-c ategories: either asking that the space of objects be discrete\, or requir ing Rezk's completeness condition. When generalizing to higher $(\\infty\, n)$-categories\, both of these approaches have been taken to multisimplici al models\, in the form of Segal $n$-categories and $n$-fold complete Sega l spaces\, but models given by $\\Theta_n$-diagrams have focused on the co mpleteness conditions. In this talk\, we'll discuss how to get a $\\Theta_ n$-model with discreteness conditions\, but also address the question of w hen these conditions can be mixed and matched with one another.\n LOCATION:https://researchseminars.org/talk/TQFT/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitri Nikshych (University of New Hampshire) DTSTART:20230503T170000Z DTEND:20230503T180000Z DTSTAMP:20260422T225721Z UID:TQFT/84 DESCRIPTION:Title: Wi tt groups of braided fusion categories and minimal non-degenerate extensio ns\nby Dmitri Nikshych (University of New Hampshire) as part of Topolo gical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe symmetri c center of a braided category B consists of all objects of B having symme tric\nbraiding with every object of B. The categorical Witt group W(E) of braided fusion categories with the same symmetric center E is obtained as the quotient of the monoid of such categories by its submonoid consisting of Drinfeld centers. I will discuss the structure of this group and its r ole in the study of minimal non-degenerate extensions of braided categorie s. This theory has applications to the classification of braided fusion 2- categories (which\, in turn\, lead to 4-dimensional TQFTs).\n\nNote unusu al time.\n LOCATION:https://researchseminars.org/talk/TQFT/84/ END:VEVENT BEGIN:VEVENT SUMMARY:David Ben-Zvi (University of Texas\, Austin) DTSTART:20230510T160000Z DTEND:20230510T170000Z DTSTAMP:20260422T225721Z UID:TQFT/85 DESCRIPTION:Title: A TQFT POV on L-functions\nby David Ben-Zvi (University of Texas\, Austi n) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAb stract\n​I'll discuss a perspective on L-functions modeled on the theory of boundary conditions in extended TQFT\, emerging from my upcoming work with Yiannis Sakellaridis and Akshay Venkatesh. In particular\, I'll expla in the parallel between L-functions and characters of higher categorical r epresentations\, and the role of geometric and deformation quantization of shifted symplectic varieties in the theory.\n​\n LOCATION:https://researchseminars.org/talk/TQFT/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Jennifer Brown (Yale University) DTSTART:20230621T160000Z DTEND:20230621T170000Z DTSTAMP:20260422T225721Z UID:TQFT/86 DESCRIPTION:Title: De fect Skein Theories\nby Jennifer Brown (Yale University) as part of To pological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nTwo fiel d theories can sometimes meet at a codimension one defect\, which carries the information on how to transition between the bulk theories.\n\nStratif ied factorization homology is a tool for constructing such theories with d efects from their local coefficient systems. One well-motivated example is parabolic induction\, in which $\\operatorname{Rep}_q G$ is reduced to th e $q$-commutative $\\operatorname{Rep}_q T$ theory via Borel reduction alo ng a defect. This is the stacky setting for Fock–Goncharov's cluster coo rdinates. It is also a natural context for constructing the quantum A-poly nomial.\n\nThe talk will start with an introduction to stratified spaces a nd factorization homology\, and will include a review of skein relations a nd categories. We will focus on surfaces with line defects\, building the associated skein theory and discussing how it computes the relevant strati fied factorization homology.\n LOCATION:https://researchseminars.org/talk/TQFT/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Upmeier (University of Aberdeen) DTSTART:20230524T160000Z DTEND:20230524T170000Z DTSTAMP:20260422T225721Z UID:TQFT/87 DESCRIPTION:Title: In vertible TQFTs and Atiyah–Singer index theory\nby Markus Upmeier (Un iversity of Aberdeen) as part of Topological Quantum Field Theory Club (IS T\, Lisbon)\n\n\nAbstract\nI will discuss work in progress that constructs a categorification of Atiyah-Singer index theory. My main theorem shows t hat these new\, categorical indices can be organized into an invertible TQ FT\, which can algebraically be viewed as a categorical group representati on of a cobordism category. If time permits\, I will outline how to comput e the categorical index topologically.\n LOCATION:https://researchseminars.org/talk/TQFT/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Haïoun (University of Toulouse) DTSTART:20230517T160000Z DTEND:20230517T170000Z DTSTAMP:20260422T225721Z UID:TQFT/88 DESCRIPTION:Title: No n-semisimple WRT as non-compact fully extended relative TQFTs\nby Benj amin Haïoun (University of Toulouse) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will argue that the Witten– Reshetikhin–Turaev-type TQFTs obtained from non-semisimple modular categ ories can be obtained from the Cobordism Hypothesis. This is in apparent c ontradiction with known results\, but I will explain how one can work arou nd these problems using relative TQFTs\, following ideas of Walker\, Freed –Teleman and Jordan–Safronov. I will present my recent dualizability r esults showing that the Cobordism Hypothesis does give a TQFT from the des ired data\, and conjecture that these recover the known non-semisimple TQF Ts. Based on arXiv:2304.12167.\n LOCATION:https://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:20260422T225721Z UID:TQFT/89 DESCRIPTION:Title: Tw isted eleven-dimensional supergravity and infinite-dimensional exceptional simple super Lie algebras\nby Surya Raghavendran (Perimeter Institute for Theoretical Physics/University of Toronto) as part of Topological Qua ntum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI'll describe a pertu rbative BV theory defined on 11-manifolds with a rank 6 transversely holom orphic foliation and a transverse Calabi–Yau structure. The theory has a n infinite dimensional algebra of gauge symmetries preserving the trivial background\, which is $L_\\infty$ equivalent to a Lie 2-extension of the i nfinite dimensional exceptional simple super Lie algebra E(5|10). Conjectu rally\, this theory describes the minimal twist of eleven-dimensional supe rgravity. After describing this conjecture\, and evidence for it\, I'll de scribe twisted avatars of the AdS_4 x S^7 and AdS_7 x S^4 backgrounds\, an d how two other infinite dimensional exceptional simple super Lie algebras E(1|6) and E(3|6) appear as asymptotic symmetries. Enumerating gravitons on such backgrounds naturally leads to refinements of generating functions of representation-theoretic significance\, such as the MacMahon function. Time permitting\, I'll explain how our results combined with holographic techniques can be used to produce enhancements of familiar vertex algebras such as the Heisenberg and Virasoro algebras\, to holomorphic factorizati on algebras in three complex dimensions\, and furnish geometric constructi ons of representations thereof. This talk is based on joint work with Ingm ar Saberi and Brian Williams.\n LOCATION:https://researchseminars.org/talk/TQFT/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Etingof (Massachusetts Institute of Technology) DTSTART:20230712T160000Z DTEND:20230712T170000Z DTSTAMP:20260422T225721Z UID:TQFT/90 DESCRIPTION:Title: Li e theory in tensor categories (with applications to modular representation theory)\nby Pavel Etingof (Massachusetts Institute of Technology) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract \nLet $G$ be a group and $k$ an algebraically closed field of characterist ic $p$. If $V$ is a finite-dimensional representation of $G$ over $k$\, th en by the classical Krull–Schmidt theorem\, the $n$th tensor power of $V $ can be uniquely decomposed into a direct sum of indecomposable represent ations. But we know very little about this decomposition\, even for very s mall groups\, such as $G = (\\Bbb Z/2)^3$ for $p = 2$ or $G = (\\Bbb Z/3)^ 2$ 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 $d(V) := \\lim_{n \\to \\infty} d_n(V)^{1/n}$\, but what kind of number is this? Is it algebraic or transcendental? Until recently \, there were no techniques to solve such questions (and in particular the same question about the sum of dimensions of these summands is still wide open). Remarkably\, a new subject which may be called "Lie theory in tens or categories" gives methods to show that $d(V)$ is indeed an algebraic nu mber\, which moreover has the form\n\\[ d(V) = \\sum_{1 \\leq j \\leq p/2} n_j(V)[j]_q\, \\]\nwhere $n_j(V)$ is a natural number\, $q := \\exp(\\pi i/p)$ 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 ring 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 explain what Lie theory in tensor categories is and how it can be applied to such problems. This is joint work with K. Coulembier and V. Ostrik.\n LOCATION:https://researchseminars.org/talk/TQFT/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Kinnear (University of Edinburgh) DTSTART:20230628T160000Z DTEND:20230628T170000Z DTSTAMP:20260422T225721Z UID:TQFT/91 DESCRIPTION:Title: Va rying the non-semisimple Crane–Yetter theory over the character stack\nby Patrick Kinnear (University of Edinburgh) as part of Topological Qua ntum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nAssociated to a certa in subquotient of the category of representations of the small quantum gro up at a root of unity is an invertible 4d TQFT known as Crane–Yetter: it is the anomaly theory of the 3d theory called Witten–Reshetikhin–Tura ev. In fact\, the non-semisimplified representation category is invertible in the Morita theory of braided tensor categories: under the cobordism hy pothesis this defines a non-semisimple invertible TQFT. Such an invertible theory assigns to a closed 3-manifold a 1-dimensional vector space. In th is talk\, we define a relative TQFT which can be seen as varying non-semis imple Crane-Yetter over the character stack: it assigns to a closed 3-mani fold $M$ a line bundle on its character stack $\\mathrm{Ch}_G(M)$. We cons truct this theory by analysing invertibility of a 1-morphism in the Morita theory of symmetric tensor categories\, coming from representations of Lu sztig's quantum group at a root of unity regarded as a bimodule for $\\mat hrm{Rep}(G)$ using the quantum Frobenius map. In the talk we will describe this 1-morphism and analyse its invertibility and the consequences of thi s in detail.\n LOCATION:https://researchseminars.org/talk/TQFT/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Pachol (University of South-Eastern Norway) DTSTART:20230726T160000Z DTEND:20230726T170000Z DTSTAMP:20260422T225721Z UID:TQFT/92 DESCRIPTION:Title: Qu antum groups in the digital setting\nby Anna Pachol (University of Sou th-Eastern Norway) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe main idea behind noncommutative geometry is to “algebralize” geometric notions and then generalize them to noncommut ative algebras. This way noncommutative geometry offers a generalised noti on of the geometry. Quantum groups or Hopf algebras play the role of ‘gr oup objects’ in noncommutative geometry and they provide an approach to the development of the theory much as Lie groups do in differential geomet ry.\n\nI will give an introduction to the topic and briefly mention result s on classification of all bialgebras and Hopf algebras of dimension ≤ 4 over the field $F_2 = \\{0\, 1\\}$. These results can be summarized as a quiver\, where the vertices are the inequivalent algebras and there is an arrow for each inequivalent bialgebra or Hopf algebra built from the algeb ra at the source of the arrow and the dual of the algebra at the target of the arrow. There are 314 distinct bialgebras and\, among them\, 25 Hopf a lgebras\, 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 $U_q(\\mathfrak{ sl}_2)$.\n LOCATION:https://researchseminars.org/talk/TQFT/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabian Hahner (Heidelberg University) DTSTART:20230719T160000Z DTEND:20230719T170000Z DTSTAMP:20260422T225721Z UID:TQFT/93 DESCRIPTION:Title: Pu re spinor techniques in (twisted) supergravity\nby Fabian Hahner (Heid elberg University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe pure spinor superfield formalism gives a syste matic and geometric technique to construct supersymmetric field theories f rom algebro-geometric input data. Crucially\, this procedure provides supe rfield descriptions where the actions of the supersymmetries are strict an d ompatible with twisting. In this talk\, I will demonstrate the merits of the formalism using the example of eleven-dimensional supergravity. In pa rticular\, I present a uniform construction of the interacting theory and all its twists realizing them as generalizations of Poisson–Chern–Simo ns theory. In addition to simplifying the computation of twists immensely\ , this also sheds some new light on the supergeometric origin of the super gravity theory. The talk is based on joint work with Ingmar Saberi.\n LOCATION:https://researchseminars.org/talk/TQFT/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Walker (Microsoft Station Q) DTSTART:20230914T160000Z DTEND:20230914T170000Z DTSTAMP:20260422T225721Z UID:TQFT/94 DESCRIPTION:Title: Lo w-dimensional H-bordism and H-modular TQFTs\nby Kevin Walker (Microsof t Station Q) as part of Topological Quantum Field Theory Club (IST\, Lisbo n)\n\n\nAbstract\nLet H denote a class of manifolds (such as SO (oriented) \, O (unoriented)\, Spin\, Pin+\, Pin-\, manifolds with spin defects\, etc .). We define a 2+1-dimensional H-modular TQFT to be one which lives on th e boundary of a bordism-invariant 3+1-dimensional H-TQFT. Correspondingly\ , we define a H-modular tensor category to be a H-premodular category whic h leads to a bordism-invariant 3+1-dimensional TQFT. When H = SO\, this re produces the familiar Witten-Reshetikhin-Turaev TQFTs and corresponding mo dular tensor categories. For other examples of H\, non-zero H-bordism grou ps in dimensions 4 or lower lead to interesting complications (anomalies\, mapping class group extensions\, obstructions to defining the H-modular t heory on all H-manifolds).\n\nPlease note that this is an in-person semina r that we will broadcast online. We encourage local participants to join u s in room 3.10 of the mathematics building.\n LOCATION:https://researchseminars.org/talk/TQFT/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Mnev (University of Notre Dame) DTSTART:20230920T170000Z DTEND:20230920T180000Z DTSTAMP:20260422T225721Z UID:TQFT/95 DESCRIPTION:Title: Wh y BF theory is not an Atiyah’s TQFT\, and how the BV-BFV approach helps< /a>\nby Pavel Mnev (University of Notre Dame) as part of Topological Quant um Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nBF theory does not quit e fit into (strict) Atiyah’s axioms. The space of states it assigns to a boundary is typically infinite-dimensional (which implies that the partit ion function of $S^1 \\times X$ is infinite). This can be seen (a) as a co nsequence of noncompactness of the phase space of the theory or (b) as a m anifestation of the problem of zero-modes. The BV-BFV formalism is an appr oach to gauge theories (in particular\, topological ones) combining the At iyah-Segal functorial picture with the idea of Wilson’s effective action . In this talk I will sketch the construction of BF theory in the BV-BFV l anguage and will explain how it assigns meaningful partition functions (sa tisfying an appropriate gluing property) to all cobordisms.\n LOCATION:https://researchseminars.org/talk/TQFT/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Costantino (University of Toulouse) DTSTART:20231206T170000Z DTEND:20231206T180000Z DTSTAMP:20260422T225721Z UID:TQFT/96 DESCRIPTION:Title: St ated skein modules of 3-manifolds and TQFTs\nby Francesco Costantino ( University of Toulouse) as part of Topological Quantum Field Theory Club ( IST\, Lisbon)\n\n\nAbstract\nAfter reviewing the definition of stated skei n modules for surfaces and 3-manifolds\, I will detail how this recent not ion allows us to relate topological constructions (related to cut and past e techniques) to algebraic ones (for instance\, braided tensor products of algebra objects in braided categories). I will explain how the stated ske in algebra of some special surfaces provides a topological description for some notable algebras (e.g. the quantised function ring $O_q(\\mathfrak{s l}_2)$ 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 comp letely standard one. If time permits I will also discuss some unexpected n oninjectivity results in dimension 3. This is joint work with Thang Le.\n LOCATION:https://researchseminars.org/talk/TQFT/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedram Hekmati (University of Auckland) DTSTART:20231214T170000Z DTEND:20231214T180000Z DTSTAMP:20260422T225721Z UID:TQFT/97 DESCRIPTION:Title: Eq uivariant Floer homology and its applications\nby Pedram Hekmati (Univ ersity of Auckland) as part of Topological Quantum Field Theory Club (IST\ , Lisbon)\n\n\nAbstract\nFloer theory comes in various flavours and has de veloped into a primary tool in low-dimensional topology. In this talk\, I will discuss the construction of an equivariant Seiberg–Witten–Floer h omology associated to finite group actions on rational homology 3-spheres. This gives rise to a series of numerical invariants and I will survey som e of their applications in knot theory\, to equivariant embeddings and as obstructions to extending group actions to bounding 4-manifolds. This is j oint work with David Baraglia.\n LOCATION:https://researchseminars.org/talk/TQFT/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco De Renzi (University of Montpellier) DTSTART:20240110T170000Z DTEND:20240110T180000Z DTSTAMP:20260422T225721Z UID:TQFT/98 DESCRIPTION:Title: Al gebraic presentation of cobordisms and TQFTs\nby Marco De Renzi (Unive rsity of Montpellier) as part of Topological Quantum Field Theory Club (IS T\, Lisbon)\n\n\nAbstract\nIt has long been known that the category of 2-d imensional cobordisms is freely generated by a commutative Frobenius algeb ra\, the circle. This result allows for a complete classification of TQFTs (Topological Quantum Field Theories) in dimension 2. In this talk I will discuss similar algebraic presentations in dimension 3 and 4 due to Bobtch eva and Piergallini. In both cases\, the fundamental algebraic structures are provided by certain Hopf algebras called BPH algebras. I will also pre sent 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://researchseminars.org/talk/TQFT/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukas Woike (University of Burgundy) DTSTART:20240124T170000Z DTEND:20240124T180000Z DTSTAMP:20260422T225721Z UID:TQFT/99 DESCRIPTION:Title: An introduction to quantum representations of mapping class groups\nby L ukas Woike (University of Burgundy) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/TQFT/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Nadia Ott (University of Southern Denmark) DTSTART:20240131T170000Z DTEND:20240131T180000Z DTSTAMP:20260422T225721Z UID:TQFT/100 DESCRIPTION:Title: T he super period map and the projectedness of supermoduli space\nby Nad ia Ott (University of Southern Denmark) as part of Topological Quantum Fie ld Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn 2014\, Donagi and Witten p roved that supermoduli spaces $\\mathfrak{M}_g$ of genus $g$ super Riemann surfaces are not projected for genus $g \\geq 5$. In joint work with Ron Donagi\, we show that $\\mathfrak{M}_g$ is projected\, for all genus $g$\, away from the so-called bad divisor. In other words\, we show that the co mplement $U_g$ of $\\mathcal{B} \\subset \\mathfrak{M}_g$ is a projected o pen subscheme of $\\mathfrak{M}_g$. Furthermore\, at least in genus $g = 2 $ and $g = 3$\, we show that the super period map defines a projection $U_ g \\to U_{g\,\\mathrm{bos}}$.\n LOCATION:https://researchseminars.org/talk/TQFT/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukas Müller (Perimeter Institute) DTSTART:20240207T170000Z DTEND:20240207T180000Z DTSTAMP:20260422T225721Z UID:TQFT/101 DESCRIPTION:Title: T opological defects form higher dagger categories\nby Lukas Müller (Pe rimeter Institute) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nRecently\, the study of higher categories of topol ogical defects in quantum field theory has gained significant attention du e to their connection to categorical symmetries. These higher categories e xhibit noteworthy additional structures\, depending upon the specific theo ries and defects under consideration. For instance\, in oriented 2-dimensi onal field theories\, they organize into a pivotal bicategory. Currently\, we lack a comprehensive framework to systematically describe these intric ate structures. In my talk I will argue that the theory of higher dagger c ategories provides such a framework. I will focus on defects within fully extended topological field theories. Except in low dimensions the picture proposed here is highly conjectural. The talk is partially based on joint work in progress with Bruce Bartlett\, Gio Ferrer\, Brett Hungar\, Theo Jo hnson-Freyd\, Cameron Krulewski\, Nivedita\, Dave Penneys\, David Reutter\ , Claudia Scheimbauer\, Luuk Stehouwer\, and Chetan Vuppulury.\n LOCATION:https://researchseminars.org/talk/TQFT/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Gunningham (Montana State University) DTSTART:20240221T170000Z DTEND:20240221T180000Z DTSTAMP:20260422T225721Z UID:TQFT/102 DESCRIPTION:Title: S kein theory and the geometric Langlands program\nby Sam Gunningham (Mo ntana 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\, modulo cert ain local relations. They can be thought of both as an obstruction to defi ning a polynomial invariant of knots in M and as an invariant of the 3-man ifold M. In this talk\, I will survey some history\, recent results\, and work in progress on skein modules\, motivated by their role in the geometr ic Langlands program. I will discuss joint work with (some subsets of) Dav id Ben-Zvi\, David Jordan\, Pavel Safronov\, Monica Vazirani\, and Haiping Yang.\n LOCATION:https://researchseminars.org/talk/TQFT/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Luuk Stehouwer (Dalhousie University) DTSTART:20240306T170000Z DTEND:20240306T180000Z DTSTAMP:20260422T225721Z UID:TQFT/103 DESCRIPTION:Title: T he Categorical Spin-Statistics Theorem: A TQFT Perspective\nby Luuk St ehouwer (Dalhousie University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe spin-statistics theorem is a corne rstone of physics\, linking particle spin to its fermionic or bosonic natu re in unitary quantum field theory. This talk presents a novel proof of th is theorem within the framework of unitary TQFTs using so-called dagger ca tegories. Our method draws upon the perspective on dagger categories by an ti-involutions and Hermitian forms\, which I jointly developed with Jan St einebrunner. This approach not only provides a clearer understanding of th e spin-statistics theorem\, but also offers valuable insights into symmetr ic monoidal dagger categories.\n LOCATION:https://researchseminars.org/talk/TQFT/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Marko Stošić (Instituto Superior Técnico) DTSTART:20240320T170000Z DTEND:20240320T180000Z DTSTAMP:20260422T225721Z UID:TQFT/104 DESCRIPTION:Title: C ombinatorics in knot-quiver correspondences\nby Marko Stošić (Instit uto Superior Técnico) as part of Topological Quantum Field Theory Club (I ST\, Lisbon)\n\n\nAbstract\nI will present different versions of the knot- quiver correspondence related to various knot invariants\, with the empha sis on combinatorial implications. In particular\, we shall review differe nt enumerative results and integrality properties that are corollaries of the knot-quiver correspondence\, as well as recent advances regarding quiv ers with higher level nodes.\n LOCATION:https://researchseminars.org/talk/TQFT/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristina Anghel (University of Leeds) DTSTART:20240410T160000Z DTEND:20240410T170000Z DTSTAMP:20260422T225721Z UID:TQFT/105 DESCRIPTION:Title: A universal coloured Alexander invariant from configurations on ovals in th e disc\nby Cristina Anghel (University of Leeds) as part of Topologica l Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe coloured Jon es and Alexander polynomials are quantum invariants that come from represe ntation theory. There are important open problems in quantum topology rega rding their geometric information. Our goal is to describe these invariant s from a topological viewpoint\, as intersections between submanifolds in configuration spaces. We show that the Nth coloured Jones and Alexander po lynomials of a knot can be read off from Lagrangian intersections in a fix ed configuration space. At the asymptotic level\, we geometrically constru ct a universal ADO invariant for links as a limit of invariants given by i ntersections in configuration spaces. The parallel question of providing a n invariant unifying the coloured Jones invariants is the subject of the u niversal Habiro invariant for knots. The universal ADO invariant that we c onstruct recovers all of the coloured Alexander invariants (in particular\ , the Alexander polynomial in the first term).\n LOCATION:https://researchseminars.org/talk/TQFT/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Inbar Klang (Vrije University Amsterdam) DTSTART:20240502T160000Z DTEND:20240502T170000Z DTSTAMP:20260422T225721Z UID:TQFT/106 DESCRIPTION:Title: A n algebraic topology perspective on factorization homology\nby Inbar K lang (Vrije University Amsterdam) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nI will give an introduction to fact orization homology using configuration spaces\, and discuss the nonabelian Poincaré duality theorem of Segal\, Salvatore\, Lurie\, and Ayala–Fran cis​\, which relates factorization homology to mapping spaces. Time perm itting\, I will also talk about the Ayala–Francis axiomatic approach to factorization homology\, which positions factorization homology as a "homo logy theory for manifolds."\n LOCATION:https://researchseminars.org/talk/TQFT/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Schulz (Johns Hopkins University) DTSTART:20240424T160000Z DTEND:20240424T170000Z DTSTAMP:20260422T225721Z UID:TQFT/107 DESCRIPTION:Title: S pectral networks and G2\nby Sebastian Schulz (Johns Hopkins University ) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbs tract\nSpectral networks are a combinatorial tool consisting of labelled l ines on a Riemann surface. They have a surprising amount of applications a nd are intimately linked to non-Abelianization of flat connections\, Fock –Goncharov cluster coordinates\, exact WKB theory\, etc. After reviewing this story for the SL(2) and SL(3) case\, I will describe this is in deta il for the group G2. Time permitting\, I will give as an application a con crete parametrization of the nonabelian Hodge correspondence for the Hitch in component of the split real form of G2. This is joint work with Andy Ne itzke.\n LOCATION:https://researchseminars.org/talk/TQFT/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Carqueville (University of Vienna) DTSTART:20240605T160000Z DTEND:20240605T170000Z DTSTAMP:20260422T225721Z UID:TQFT/108 DESCRIPTION:Title: O rbifold completion of 3-categories\nby Nils Carqueville (University of Vienna) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n \n\nAbstract\nWe develop a general theory of 1-\, 2-\, and 3-dimensional " orbifold completion"\, to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. This can be viewed as the "oriented version" of condensation completion. We give a basic introd uction to TQFTs and their orbifolds\, and discuss applications which inclu de defect TQFTs for state sum models\, Reshethikin-Turaev and Crane-Yetter theory. This is joint work with Lukas Müller.\n LOCATION:https://researchseminars.org/talk/TQFT/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrien Brochier (Université Paris Cité) DTSTART:20240417T160000Z DTEND:20240417T170000Z DTSTAMP:20260422T225721Z UID:TQFT/109 DESCRIPTION:Title: A classification of modular functors from generalized skein theory\nby Adrien Brochier (Université Paris Cité) as part of Topological Quantum F ield Theory Club (IST\, Lisbon)\n\n\nAbstract\nModular functors are collec tions of projective representations of mapping class groups of surfaces\, compatible with cutting and gluing operations. They can be thought of as c ategorified\, anomalous 2d topological field theories (TFT) where the "ano maly" is responsible for the projectiveness of the représentations.\n\nA well-known folklore theorem states that ordinary 2d TFT are classified by (commutative) Frobenius algebras. In a similar way\, any modular functor y ields a "categorified Frobenius algebra"\, of which ribbon categories form a large class of examples. In this talk\, we'll explain a necessary and s ufficient condition for such a structure to extend to a modular functor\, formulated in terms of certain generalized skein modules attached to handl ebodies. A key observation is that this is\, indeed\, a condition\, not ex tra structure\, so that such an extension is essentially unique whenever i t exists.\n\nThis construction should be thought of as a far reaching gene ralization of the construction by Masbaum and Roberts of a modular functor from Kauffman skein modules. As a special case it also recovers\, in a pu rely topological way\, the construction of a modular functor from a (not n ecessarily semisimple) modular category by Lyubachenko\, and the uniquenes s result is new even in those cases. This is based on joint work with Luka s Woike.\n LOCATION:https://researchseminars.org/talk/TQFT/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan-Willem van Ittersum (University of Cologne) DTSTART:20240412T130000Z DTEND:20240412T140000Z DTSTAMP:20260422T225721Z UID:TQFT/110 DESCRIPTION:Title: S hifted symmetric functions\, quasimodular forms and Hamiltonian operators< /a>\nby Jan-Willem van Ittersum (University of Cologne) as part of Topolog ical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nStarting with a counting problem for elements of the symmetric group\, we introduce the so-called shifted symmetric functions. These functions\, which also occur naturally in enumerative geometry\, have the remarkable property that the corresponding generating series are quasimodular forms. We discuss anothe r family of functions on partitions with the same property. In particular\ , using certain Hamiltonian operators associated to cohomological field th eories\, we explain how this seemingly different family of functions turns out to be closely related to the shifted symmetric functions.\n LOCATION:https://researchseminars.org/talk/TQFT/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Pranav Prandit (Tata Institute of Fundamental Research) DTSTART:20240508T160000Z DTEND:20240508T170000Z DTSTAMP:20260422T225721Z UID:TQFT/111 DESCRIPTION:Title: D eformations of objects in higher categories\nby Pranav Prandit (Tata I nstitute of Fundamental Research) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nI will describe a map that associat es to every deformation of an object in a higher category a collection of generalized symmetries of the object. Building on work by Lurie\, we will see that the failure of this map to be an equivalence can be quantified. U nder favorable circumstances\, the map is an equivalence\, and this leads to an explicit description of the space of deformations in terms of soluti ons to certain equations. I will discuss applications of these results to topological field theory and holomorphic symplectic geometry. This talk is based on joint work with Bhanu Kiran.\n LOCATION:https://researchseminars.org/talk/TQFT/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Christoph Schweigert (University of Hamburg) DTSTART:20240522T160000Z DTEND:20240522T170000Z DTSTAMP:20260422T225721Z UID:TQFT/112 DESCRIPTION:Title: T races and higher structures\nby Christoph Schweigert (University of Ha mburg) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n \nAbstract\nQuantum topologists are used to thinking about traces in the f ramework of pivotal tensor categories and thus in a two-dimensional contex t to which a two-dimensional graphical calculus can be associated. We expl ain that traces are already naturally defined for twisted endomorphisms of linear categories\, i.e. in a one-dimensional context. The endomorphisms are twisted by the Nakayama functor which\, for a module category over a m onoidal category\, is a twisted module functor and hence an inherently thr ee-dimensional object. This naturally leads to a three-dimensional graphic al calculus. This calculus also has applications to Turaev–Viro topologi cal field theories with defects.\n LOCATION:https://researchseminars.org/talk/TQFT/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Wasserman (University of Oxford) DTSTART:20240529T160000Z DTEND:20240529T170000Z DTSTAMP:20260422T225721Z UID:TQFT/113 DESCRIPTION:Title: T he Landau-Ginzburg / conformal field theory correspondence\nby Thomas Wasserman (University of Oxford) as part of Topological Quantum Field Theo ry Club (IST\, Lisbon)\n\n\nAbstract\nThe Landau-Ginzburg (LG) / Conformal 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 origin in p hysics\, and comes from observations about 2-dimensional N=2 supersymmetri c quantum field theory. I will explain how this prediction is to be interp reted mathematically and what difficulties one encounters in doing this. A fter this I will discuss joint work with Ana Ros Camacho in which we reali se the LG/CFT correspondence for the potentials $x^d$. The main ingredient in this is an enriched category theoretic version of the classical Temper ley-Lieb/Jones-Wenzl construction of the representation category of quantu m su(2).\n LOCATION:https://researchseminars.org/talk/TQFT/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang Yang (Technical University of Munich) DTSTART:20240612T160000Z DTEND:20240612T170000Z DTSTAMP:20260422T225721Z UID:TQFT/114 DESCRIPTION:Title: R CFT correlators as equivalences of modular functors\nby Yang Yang (Tec hnical University of Munich) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nThe local information of a 2d rational c onformal field theory (RCFT) is encoded in a vertex operator algebra\, who se modules constitute a modular fusion category C. The collection of globa l observables of the theory is given by conformal blocks and carries actio ns of mapping class groups\, which is described mathematically by a modula r functor that assigns the Drinfeld center Z(C) to a circle. The string-ne t construction\, which first appeared in the study of topological phases o f matter\, not only provides such a modular functor but also supplies a gr aphical construction of correlators. A generalization of the string-net co nstruction takes a pivotal bicategory as input. When such a bicategory is taken to be C (considered as a bicategory with one object)\, it recovers t he modular functor of conformal blocks. On the other hand\, the modular fu nctor associated with the Morita bicategory of separable symmetric Frobeni us algebras internal to C classifies stratified worldsheets up to "categor ical symmetries". In this talk we explain\, using the framework of double categories\, that RCFT correlators exhibit an equivalence between these tw o modular functors. This is in fact a consequence of the functoriality of the string-net construction: the lax biadjunction between a pivotal bicate gory and its orbifold completion induces an equivalence between their stri ng-net modular functors.\n LOCATION:https://researchseminars.org/talk/TQFT/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Catherine Meusburger (University of Erlangen-Nuremberg) DTSTART:20240619T160000Z DTEND:20240619T170000Z DTSTAMP:20260422T225721Z UID:TQFT/115 DESCRIPTION:Title: Q uantum double models and Dijkgraaf-Witten TQFT with defects\nby Cather ine Meusburger (University of Erlangen-Nuremberg) as part of Topological Q uantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe use 3d defect TQ FTs and state sum models with defects to give a gauge theoretical formulat ion of Kitaev's quantum double model (for a finite group) and the (untwist ed) Dijkgraaf-Witten TQFT with defects. This leads to a simple description in terms of embedded quivers\, groupoids and their representations. Defec t Dijkgraaf-Witten TQFT is then formulated in terms of spans of groupoids and their representations.\n\nThis is work in progress with João Faría M artins (University of Leeds).\n LOCATION:https://researchseminars.org/talk/TQFT/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Agnès Beaudry (University of Colorado Boulder) DTSTART:20240626T160000Z DTEND:20240626T170000Z DTSTAMP:20260422T225721Z UID:TQFT/116 DESCRIPTION:Title: H omotopy theory of parametrized quantum systems\nby Agnès Beaudry (Uni versity of Colorado Boulder) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nIn recent years\, there has been a growi ng number of applications of stable homotopy theory to condensed matter ph ysics\, many of which stem from a conjecture of Kitaev that gapped inverti ble phases of matter should be classified by the homotopy groups of a spec trum. This gives rise to a mathematical modeling question: how do we model quantum systems in such a way that this result can be better understood\, perhaps even proved? In this talk\, I will discuss some aspects of this m odeling problem. This is based on joint work with Mike Hermele\, Juan More no\, Markus Pflaum\, Marvin Qi and Daniel Spiegel\, David Stephen\, Xueda Wen.\n LOCATION:https://researchseminars.org/talk/TQFT/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregor Schaumann (University of Würzburg) DTSTART:20240703T160000Z DTEND:20240703T170000Z DTSTAMP:20260422T225721Z UID:TQFT/117 DESCRIPTION:Title: S tate spaces in TFT: Quivers and infinite particle algebras\nby Gregor Schaumann (University of Würzburg) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nA topological field theory (TFT) with particles exhibits distinguished state spaces\, where the incoming an d outgoing particles match. These "endo-state spaces" occur naturally in p hysical applications and possess interesting mathematical structures: Ther e is a natural gauge action by conjugation and a natural stabilization map . We will show that the gauge action has a non-trivial orbit structure\, l eading to quiver moduli spaces\, and the stabilization map leads to a trea tment of infinite particle content and AF-algebras.\n\nThe talk will be ra ther introductory and assumes no knowledge of quivers or AF-algebras.\n LOCATION:https://researchseminars.org/talk/TQFT/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Minghao Wang (Boston University) DTSTART:20240710T140000Z DTEND:20240710T150000Z DTSTAMP:20260422T225721Z UID:TQFT/118 DESCRIPTION:Title: F eynman graph integrals from topological-holomorphic theories and their app lications\nby Minghao Wang (Boston University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nFeynman graph inte grals of topological field theories have been proved to be ultraviolet fin ite by Axelrod and Singer\, and Kontsevich independently. This result lead s to many applications including universal finite type knot invariants and the formality of $E_n$ operads. In this talk\, I will extend the finitene ss results (and some anomaly cancellation results) to Feynman graph integr als of topological-holomorphic theories on flat spaces. The main technique for the proof is compactification of the moduli space of metric graphs. A s a result\, we can construct many factorization algebras from quantum top ological-holomorphic theories. In the special case of 4d Chern–Simons th eory\, the factorization algebra structure encodes the Yang–Baxter equat ion. If time permits\, I will sketch how to extend these results to Feynma n graph integrals on Kähler manifolds. Part of this work is joint with Br ian Williams.\n\nReference: https://arxiv.org/abs/2401.08113\n\nPlease not e the unusual hour!\n LOCATION:https://researchseminars.org/talk/TQFT/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Kapustin (Caltech) DTSTART:20240724T160000Z DTEND:20240724T170000Z DTSTAMP:20260422T225721Z UID:TQFT/119 DESCRIPTION:Title: T opological invariants of gapped states and cosheaves on sites\nby Anto n Kapustin (Caltech) as part of Topological Quantum Field Theory Club (IST \, Lisbon)\n\n\nAbstract\nRecently\, an approach to constructing topologic al invariants of gapped ground-states of lattice systems has been develope d in our joint work with N. Sopenko. It applies to arbitrary gapped states of infinite-volume lattice spin systems with rapidly decaying interaction s and employs C*-algebraic techniques. In this talk\, I will explain an in terpretation of these invariants as obstructions to gauging\, i.e. to prom oting a symmetry to a local symmetry. The key observation is that locality on a lattice is an asymptotic notion sensitive only to the large-scale ge ometry of the support set. Following Kashiwara and Schapira\, one can enco de locality using a natural Grothendieck topology on a category of semilin ear subsets of Eucludean space. Infinitesimal symmetries of a gapped state form a cosheaf over the corresponding site\, and the topological invarian ts are encoded in its Cech complex.\n LOCATION:https://researchseminars.org/talk/TQFT/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Clark Barwick (University of Edinburgh) DTSTART:20240814T160000Z DTEND:20240814T170000Z DTSTAMP:20260422T225721Z UID:TQFT/120 DESCRIPTION:Title: F actorization algebras in quite a lot of generality\nby Clark Barwick ( University of Edinburgh) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nIn the last decade there has been a flurry o f interest in arithmetic quantum field theories​. Since the 1960s\, rese archers have identified an analogy between various objects of arithmetic g eometry and low-dimensional manifolds. For example\, Spec of a number ring “looks like” an open 3-manifold\, and primes therein “are” embedd ed knots. This story has become known as arithmetic topology​. The idea of arithmetic QFT is to enrich that analogy by importing tools from physic s\, just as with low-dimensional topology. One even dreams of using these tools to study number-theoretic questions (the behavior of L-functions\, L anglands dualities\, etc.).\n\nBut the objects of arithmetic geometry are not​ manifolds. The tools of topology and differential geometry do not w ork directly in arithmetic. So it’s unclear how to translate physical co ncepts to arithmetic settings.\n\nTo this end\, we introduce a minimalist framework for factorization algebras\, where the role of the spacetime man ifold can be played by a geometric object of a very general sort. In retro spect\, the main idea amounts to a categorification of Borcherds’ approa ch to vertex algebras.\n LOCATION:https://researchseminars.org/talk/TQFT/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Monica Vazirani (University of California\, Davis) DTSTART:20240717T160000Z DTEND:20240717T170000Z DTSTAMP:20260422T225721Z UID:TQFT/121 DESCRIPTION:Title: S keins on tori\nby Monica Vazirani (University of California\, Davis) a s part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstra ct\nWe study skeins on the 2-torus and 3-torus via the representation theo ry of the double affine Hecke algebra of type A and its connection to quan tum D-modules. As an application we can compute the dimension of the gener ic $SL_N$- 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://researchseminars.org/talk/TQFT/121/ END:VEVENT BEGIN:VEVENT SUMMARY:David Ayala (Montana State University) DTSTART:20240807T160000Z DTEND:20240807T170000Z DTSTAMP:20260422T225721Z UID:TQFT/122 DESCRIPTION:Title: F actorization homology of higher categories\nby David Ayala (Montana St ate University) as part of Topological Quantum Field Theory Club (IST\, Li sbon)\n\n\nAbstract\nThe “alpha” version of factorization homology pai rs framed n-manifolds with $E_n$-algebras. This construction generalizes the classical homology of a manifold\, yields novel results concerning con figuration spaces of points in a manifold\, and supplies a sort of state-s um model for sigma-models (i.e.\, mapping spaces) to (n-1)-connected targe ts. This “alpha” version of factorization homology novelly extends Po incaré duality\, shedding light on deformation theory and dualities among field theories. Being defined using homotopical mathematical foundations \, “alpha” factorization homology is manifestly functorial and continu ous in all arguments\, notably in moduli of manifolds and embeddings betwe en them\, and it satisfies a local-to-global expression that is inherently homotopical in nature. \n\nNow\, $E_n$-algebras can be characterized as $(\\infty\,n)$-categories equipped with an (n-1)-connected functor from a point. The (full) “beta” version of factorization homology pairs fram ed n-manifolds with pointed $(\\infty\,n)$-categories with adjoints. Appl ying 0th homology\, or $\\pi_0$\, recovers a version of the string net con struction on surfaces\, as well as skein modules of 3-manifolds. In some sense\, the inherently homotopical nature of (full) “beta” factorizati on homology affords otherwise unforeseen continuity in all arguments\, and local-to-global expressions. \n\nIn this talk\, I will outline a definit ion of “beta” factorization homology\, focusing on low-dimensions and on suitably reduced $(\\infty\,n)$-categories (specifically\, braided mono idal categories). I will outline some examples\, and demonstrate some fea tures of factorization homology. Some of this material is established in the literature\, some a work in progress\, and some conjectural — the st atus of each assertion will be made clear. I will be especially intereste d in targeting this talk to those present\, and so will welcome comments a nd questions.\n LOCATION:https://researchseminars.org/talk/TQFT/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Jackson Van Dyke (Technical University of Munich) DTSTART:20240731T160000Z DTEND:20240731T170000Z DTSTAMP:20260422T225721Z UID:TQFT/123 DESCRIPTION:Title: G eometric quantization\, fusion categories\, and Rozansky–Witten theory\nby Jackson Van Dyke (Technical University of Munich) as part of Topolo gical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will begin by reviewing geometric and deformation quantization of a symplectic vecto r space. The goal will be to explain an analogy between these objects and Rozansky–Witten theory (along with a certain four-dimensional TQFT). Thi s analogy will factor through an analogy concerning three-dimensional TQFT s generated by pointed fusion categories. Throughout\, there will be an em phasis on equivariance and anomalies.\n LOCATION:https://researchseminars.org/talk/TQFT/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Tashi Walde (Technical University of Munich) DTSTART:20240821T160000Z DTEND:20240821T170000Z DTSTAMP:20260422T225721Z UID:TQFT/124 DESCRIPTION:Title: A ssembly of constructible factorization algebras\nby Tashi Walde (Techn ical University of Munich) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\n\nAbstract\nThe theory of factorization algebras\, and particularly that of constructible factorization algebras\, is expected t o be very well behaved. For example\, it has long been “known” that th e assignment taking a stratified manifold to its category of constructible factorization algebras satisfies gluing\, i.e.\, is itself a sheaf. Unfor tunately\, this and other related facts about factorization algebras have long been “folklore knowledge”\, but with no proofs available.\n\nIn t his talk I will report on recent work with Eilind Karlsson and Claudia I. Scheimbauer\, where we close some of these gaps in the literature\, includ ing the aforementioned gluing result.\n LOCATION:https://researchseminars.org/talk/TQFT/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Colleen Delaney (Purdue University) DTSTART:20240828T160000Z DTEND:20240828T170000Z DTSTAMP:20260422T225721Z UID:TQFT/125 DESCRIPTION:Title: A n efficient* classical algorithm for some quantum invariants of 3-manifold s\nby Colleen Delaney (Purdue University) as part of Topological Quant um Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe will share some rece nt results that are instructive for approaching the classification of 3d T QFTs and topological order by computational complexity. We show that the T uraev-Viro-Barrett-Westbury state sum TQFT invariants of 3-manifolds that arise from Tambara-Yamagami fusion categories can actually be computed in polynomial time on a classical computer\, provided that there is a bound o n the first Betti number. On the other hand\, if we don’t insist on a bo und on the first Betti number\, then the invariants should be NP-hard to c ompute. This talk is based on joint work with Clément Maria and Eric Samp erton.\n\nPlease note that this session will not be recorded.\n LOCATION:https://researchseminars.org/talk/TQFT/125/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaël Rouquier (UCLA) DTSTART:20240904T160000Z DTEND:20240904T170000Z DTSTAMP:20260422T225721Z 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\nAbstract\n2- Representations of simple Lie algebras are expected to lead to 4-dimension al TQFTs\, as envisioned by Crane and Frenkel. The tensor product of 2-rep resentations introduces homotopical phenomena which disappear when conside ring instead the case of the super Lie algebra gl(1|1). I will discuss how to construct parts of the structure of a braided monoidal 2-category asso ciated to gl(1|1)\, and how this compares with the known 4-dimensional Hee gaard–Floer TQFT.\n LOCATION:https://researchseminars.org/talk/TQFT/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Elliott (Amherst College) DTSTART:20240911T150000Z DTEND:20240911T160000Z DTSTAMP:20260422T225721Z UID:TQFT/127 DESCRIPTION:Title: T opological twists of superconformal field theory\nby Chris Elliott (Am herst College) as part of Topological Quantum Field Theory Club (IST\, Lis bon)\n\n\nAbstract\nIn quantum field theory\, "twisting" is a procedure fo r producing new theories from old\, where the new theories have particular ly nice symmetry properties (for example\, topological quantum field theor ies). The twisting construction involves the choice of a nilpotent element of a super Lie algebra that acts on the theory. I will discuss joint work with Owen Gwilliam and Matteo Lotito on twisting for theories with an act ion of a superconformal algebra and the appearance of interesting algebrai c structures such as vertex algebras and $E_n$ algebras.\n LOCATION:https://researchseminars.org/talk/TQFT/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Thang Le (Georgia Institute of Technology) DTSTART:20240918T160000Z DTEND:20240918T170000Z DTSTAMP:20260422T225721Z UID:TQFT/128 DESCRIPTION:Title: A lgebraic structures of skein algebras\nby Thang Le (Georgia Institute of Technology) as part of Topological Quantum Field Theory Club (IST\, Lis bon)\n\n\nAbstract\nWe will survey some results of stated $SL_n$ skein alg ebras and show how to use them to study the ordinary skein algebras of sur faces. We will discuss the integrality of the skein algebra\, the injectiv ity of the cutting homomorphism\, and the structure of the skein algebras of the bigon and the triangle. The talk is based on joint work with F. Cos tantino\, J. Korinman\, A. Sikora\, and T. Yu.\n LOCATION:https://researchseminars.org/talk/TQFT/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Kristel (Hausdorff Center for Mathematics) DTSTART:20241009T090000Z DTEND:20241009T100000Z DTSTAMP:20260422T225721Z UID:TQFT/129 DESCRIPTION:Title: 2 -vector bundles\nby Peter Kristel (Hausdorff Center for Mathematics) a s part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstra ct\nI will introduce the notion of 2-vector bundles\, which are a categori fied version of vector bundles. This notion is based on the idea that the bicategory of 2-vector spaces is the bicategory of algebras\, bimodules\, and intertwiners. I will recall the definition of that bicategory\, which leads into the definition of 2-vector bundles. As time permits\, I will di scuss connections to string geometry\, and extended TQFT\, and classifying results. This is all based on work with Matthias Ludewig and Konrad Waldo rf.\n LOCATION:https://researchseminars.org/talk/TQFT/129/ END:VEVENT BEGIN:VEVENT SUMMARY:William Stewart (Technical University of Munich) DTSTART:20241016T090000Z DTEND:20241016T100000Z DTSTAMP:20260422T225721Z UID:TQFT/130 DESCRIPTION:Title: D omain walls and oplax natural transformations\nby William Stewart (Tec hnical University of Munich) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nI will review the notion of a topologica l (or gapped) domain wall between topological quantum field theories and i llustrate an equivalence between domain walls and oplax natural transforma tions. I will show how this provides a reformulation of Lurie's cobordism hypothesis with singularities.\n LOCATION:https://researchseminars.org/talk/TQFT/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Ödül Tetik (University of Vienna) DTSTART:20241030T100000Z DTEND:20241030T110000Z DTSTAMP:20260422T225721Z UID:TQFT/131 DESCRIPTION:Title: Y oga with twisted stratifications\nby Ödül Tetik (University of Vienn a) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAb stract\nLinked spaces\, originally motivated by applications to TQFTs\, si multaneously simplify and generalise stratified spaces. I will briefly int roduce the concept and the accompanying exit-path quasi-category construct ion. To exhibit the nontriviality of the generalisation\, I will then cons ider some fundamental categories (as in "fundamental groupoid") of linked spaces and realise\, from a "twist" of the complement of the trefoil knot with a point defect\, a two-object category where the hom-set is the modul ar group PSL(2\,Z) and argue that there is no stratified space with this f undamental category.\n LOCATION:https://researchseminars.org/talk/TQFT/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Hofer (University of Hamburg) DTSTART:20241120T100000Z DTEND:20241120T110000Z DTSTAMP:20260422T225721Z UID:TQFT/132 DESCRIPTION:Title: C FT/TFT correspondence beyond semisimplicity\nby Aaron Hofer (Universit y of Hamburg) as part of Topological Quantum Field Theory Club (IST\, Lisb on)\n\n\nAbstract\nSince the 1980s\, it has been well known that there is a close relationship between two-dimensional conformal field theories and three-dimensional topological field theories. This CFT/TFT correspondence provides a tractable example of holography as well as a first example of t he symmetry TFT framework.\n\nThe Fuchs-Runkel-Schweigert construction is a mathematically precise incarnation of this correspondence and provides a rigorous construction of correlators for rational CFTs using 3D TFTs of R eshetikhin-Turaev type. In this talk\, I will review the FRS construction and explain how it can be generalized to non-rational CFTs using the non-s emisimple 3D TFTs of De Renzi\, Gainutdinov\, Geer\, Patureau-Mirand\, and Runkel.\n LOCATION:https://researchseminars.org/talk/TQFT/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Theodoros Lagiotis (University of Edinburgh) DTSTART:20241218T100000Z DTEND:20241218T110000Z DTSTAMP:20260422T225721Z UID:TQFT/133 DESCRIPTION:Title: N oncompact 3d TQFTs from non-semisimple modular categories\nby Theodoro s Lagiotis (University of Edinburgh) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nPerhaps the most (mathematically ) well understood 3d TQFT is that of Reshetikhin–Turaev. Famously\, the input data for their construction is that of a semisimple modular tensor c ategory (MTC). Attempts at generalizing this construction to the non-semis imple case date back to the 90's with work of Hennings\, Lyubashenko and K erler–Lyubashenko. However\, only partial results were achieved. This wa s until De Renzi et al. defined a 3d TQFT from such non-semisimple modular categories. Importantly\, they had to impose an admissibility condition o n the cobordism categories they use. My work has been in the direction of defining a once-extended 3d TQFT from this data. However\, Bartlett et al. proved that such TQFTs are classified by semisimple modular categories. W e will investigate the most natural method of circumventing this. This wil l lead to the notion of noncompact TQFT. I will then proceed to talk about my work on constructing such a TQFT from the data of a (potentially) non- semisimple MTC\, with an emphasis on the key ingredients of this construct ion. Time permitting\, I will also discuss how to extract 3-manifold invar iants and a modified trace from such a noncompact TQFT.\n LOCATION:https://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:20260422T225721Z UID:TQFT/134 DESCRIPTION:Title: E quivariant Khovanov homotopy type\nby Maciej Borodzik (Institute of Ma thematics\, Polish Academy of Sciences) as part of Topological Quantum Fie ld Theory Club (IST\, Lisbon)\n\n\nAbstract\nGiven a periodic link L\, we construct a group action on the Khovanov homotopy type defined by Lipshitz and Sarkar. As a result\, we prove that the annular Khovanov homology of the quotient link has no larger rank than the Khovanov homology of the per iodic link. This is a joint work with Wojciech Politarczyk and Marithania Silvero.\n LOCATION:https://researchseminars.org/talk/TQFT/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthias Ludewig (University of Greifswald) DTSTART:20250205T100000Z DTEND:20250205T110000Z DTSTAMP:20260422T225721Z UID:TQFT/135 DESCRIPTION:Title: T he stringor bundle and the spinor bundle on loop space\nby Matthias Lu dewig (University of Greifswald) as part of Topological Quantum Field Theo ry Club (IST\, Lisbon)\n\n\nAbstract\nWe explain the construction of the s tringor bundle on a string manifold recently given in joint work with Pete r Kristel and Konrad Waldorf. We start by discussing the spinor bundle on the loop space of a string manifold\, together with its fusion product. Th en we explain how the stringor bundle on the manifold itself can be obtain ed using a regression procedure.\n LOCATION:https://researchseminars.org/talk/TQFT/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Clement Delcamp (IHES) DTSTART:20250402T090000Z DTEND:20250402T100000Z DTSTAMP:20260422T225721Z UID:TQFT/136 DESCRIPTION:Title: T opological symmetry and duality in quantum lattice models\nby Clement Delcamp (IHES) as part of Topological Quantum Field Theory Club (IST\, Lis bon)\n\n\nAbstract\nDefining internal symmetry in a quantum theory through the lens of topological defects opens the door to generalised notions of symmetry\, including some arising from non-invertible transformations\, an d enables a calculus that leverages well-established methods from topologi cal quantum field theory. In d spatial dimensions\, the framework of fusio n d-category theory is believed to offer an axiomatisation for finite non- invertible symmetries. Though seemingly exotic\, such non-invertible symme tries can be shown to naturally arise as dual symmetries upon gauging inve rtible symmetries. In this talk\, I will present a framework to systematic ally investigate these aspects in quantum lattice models.\n LOCATION:https://researchseminars.org/talk/TQFT/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Ingo Runkel (University of Hamburg) DTSTART:20250423T090000Z DTEND:20250423T100000Z DTSTAMP:20260422T225721Z UID:TQFT/137 DESCRIPTION:Title: T opological symmetries and their gaugings in 2d CFT and 3d TFT\nby Ingo Runkel (University of Hamburg) as part of Topological Quantum Field Theor y Club (IST\, Lisbon)\n\n\nAbstract\nThe study of topological defects in q uantum field theory has seen a wealth of activity recently leading to man y interesting insights\, for example the explicit realisation of non-inver tible topological defects in higher dimensional QFTs via the gauging of hi gher form symmetries\, or the description of the higher algebraic structur es inherent in these topological defects. In this talk\, I would like to f ocus on low-dimensional examples\, where such defects and their properties have been investigated for some time already. I would like to exhibit som e of the properties of topological defects in two-dimensional conformal field theory and in three-dimensional topological field theory\, and sho w 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-dimensional ca se might serve as a source of ideas and as a test case for higher dimensio nal constructions.\n LOCATION:https://researchseminars.org/talk/TQFT/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Bertrand Patureau-Mirand (Université de Bretagne-Sud) DTSTART:20250430T090000Z DTEND:20250430T100000Z DTSTAMP:20260422T225721Z UID:TQFT/138 DESCRIPTION:Title: W eaving 4-Dimensional TQFTs with Ribbon Categories\nby Bertrand Paturea u-Mirand (Université de Bretagne-Sud) as part of Topological Quantum Fiel d Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will describe some requireme nts 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://researchseminars.org/talk/TQFT/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Cris Negron (University of Southern California) DTSTART:20250716T160000Z DTEND:20250716T170000Z DTSTAMP:20260422T225721Z UID:TQFT/139 DESCRIPTION:Title: $ (3-\\epsilon)$-dimensional TQFTs from derived quantum group representation s\nby Cris Negron (University of Southern California) as part of Topol ogical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will disc uss joint work with Agustina Czenky. We introduce a $(3-\\epsilon)$-dimens ional TQFTs which is generated\, in some sense\, by the derived category o f quantum group representations. This TQFT is valued in the $\\infty$-cate gory of dg vector spaces\, and the value on a genus $g$ surface is a $g$-t h iterate of the Hochschild cohomology for the aforementioned category. I will explain how this TQFT arises as a derived variant of the usual Reshet ikhin–Turaev theory and\, if time allows\, I will discuss the possibilit y of introducing local systems into the theory. Our interest in local syst ems comes from proposed relationships with 4-dimensional non-topological Q FT.\n LOCATION:https://researchseminars.org/talk/TQFT/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Joshua Sussan (CUNY Medgar Evers) DTSTART:20250723T160000Z DTEND:20250723T170000Z DTSTAMP:20260422T225721Z UID:TQFT/140 DESCRIPTION:Title: S ymmetries of link homology\nby Joshua Sussan (CUNY Medgar Evers) as pa rt of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\n We construct an action of $\\mathfrak{sl}(2)$ on equivariant Khovanov–Ro zansky link homology. We will discuss some topological applications and s how how the construction simplifies in characteristic p. This is joint w ith You Qi\, Louis-Hadrien Robert\, and Emmanuel Wagner.\n LOCATION:https://researchseminars.org/talk/TQFT/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Rajan Mehta (Smith College) DTSTART:20250703T083000Z DTEND:20250703T093000Z DTSTAMP:20260422T225721Z UID:TQFT/141 DESCRIPTION:Title: 2 -Segal sets as combinatorial models for algebras\nby Rajan Mehta (Smit h College) as part of Topological Quantum Field Theory Club (IST\, Lisbon) \n\n\nAbstract\nRoughly\, 2-Segal sets are simplicial sets such that highe r-dimensional simplices can be uniquely described by triangulated polygons 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 me mber\, you might ask\, “Are there 2-Segal sets that correspond to (commu tative) Frobenius algebras?” The answer is yes\, commutativity and Frobe nius structures come from asking the simplicial set to possess additional compatible structure maps. I’ll give an overview of these correspondence s as well as some background as to how I arrived at this topic from the wo rld of Poisson geometry. This is based on joint works with Ivan Contreras \, Walker Stern\, and Sophia Marx.\n LOCATION:https://researchseminars.org/talk/TQFT/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Rhea Palak Bakshi (University of California\, Santa Barbara) DTSTART:20250730T160000Z DTEND:20250730T170000Z DTSTAMP:20260422T225721Z UID:TQFT/142 DESCRIPTION:Title: O n the structure of skein modules\nby Rhea Palak Bakshi (University of California\, Santa Barbara) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\nSkein modules were introduced by Józef H . Przytycki as generalisations of the Jones and HOMFLYPT polynomial link i nvariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket s kein module (KBSM) is the most extensively studied of all. However\, compu ting the KBSM of a 3-manifold is known to be notoriously hard\, especially over the ring of Laurent polynomials. With the goal of finding a definite structure of the KBSM over this ring\, several conjectures and theorems w ere stated over the years for KBSMs. We show that some of these conjecture s\, and even theorems\, are not true. In this talk I will briefly discuss a counterexample to Marche’s generalisation of Witten’s conjecture. 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 exa ct structure of the KBSM of the connected sum of two solid tori and show t hat it is isomorphic to the KBSM of a genus two handlebody modulo some spe cific handle sliding relations. Moreover\, these handle sliding relations can be written in terms of Chebyshev polynomials.\n LOCATION:https://researchseminars.org/talk/TQFT/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Harshit Yadav (University of Alberta) DTSTART:20250806T160000Z DTEND:20250806T170000Z DTSTAMP:20260422T225721Z UID:TQFT/143 DESCRIPTION:Title: M odular tensor categories via local modules\nby Harshit Yadav (Universi ty of Alberta) as part of Topological Quantum Field Theory Club (IST\, Lis bon)\n\n\nAbstract\nGiven a commutative algebra $A$ in a braided monoidal 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 studying vertex operator algebra extensions\, is a braided monoidal category under very general conditions. In this setting\, I will present a criterion for $C_A^\\mathrm{loc}$ to be a rigid monoidal category. When $C$ is pivotal/ 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 that when $C$ is a modular tensor category and $A$ is a commutative simple symmetri c Frobenius algebra in $C$\, then $C_A^\\mathrm{loc}$ is a modular tensor category. Furthermore\, I will discuss methods to construct such commutati ve algebras using simple currents and the Witt group of non-degenerate bra ided finite tensor categories. This presentation is based on joint work wi th Kenichi Shimizu.\n LOCATION:https://researchseminars.org/talk/TQFT/143/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Lauda (University of Southern California) DTSTART:20250813T160000Z DTEND:20250813T170000Z DTSTAMP:20260422T225721Z UID:TQFT/144 DESCRIPTION:Title: N onsemisimple Topological Quantum Computation\nby Aaron Lauda (Universi ty of Southern California) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\n\nAbstract\nSince the foundational work of Freedman\, Kitaev\, Larsen\, and Wang\, it has been understood that 3-dimensional top ological quantum field theories (TQFTs)\, described via modular tensor cat egories\, 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 categories— discarding objects with quantum trace zero. The resulting semisimple categ ories describe anyons whose braiding enables robust quantum computation.\n \nThis talk explores recent advances in low-dimensional topology\, focusin g on the use of nonsemisimple categories that retain quantum trace zero ob jects to construct new TQFTs. These nonsemisimple TQFTs surpass their semi simple counterparts\, distinguishing topological features inaccessible to the latter. For physical applications\, unitarity is essential\, ensuring Hom spaces form Hilbert spaces. We present joint work with Nathan Geer\, B ertrand Patureau-Mirand\, and Joshua Sussan\, where nonsemisimple TQFTs ar e equipped with a Hermitian structure. This framework introduces Hilbert s paces with possibly indefinite metrics\, presenting new challenges.\n\nWe further discuss collaborative work with Sung Kim\, Filippo Iulianelli\, an d Sussan\, demonstrating that nonsemisimple TQFTs enable universal quantum computation at roots of unity where semisimple theories fail. Specificall y\, we show how Ising anyons within this framework achieve universality th rough braiding alone. The resulting braiding operations are deeply connect ed to the Lawrence–Krammer–Bigelow representations\, with the Hermitia n structure providing a nondegenerate inner product grounded in quantum al gebra.\n LOCATION:https://researchseminars.org/talk/TQFT/144/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Plavnik (Indiana University) DTSTART:20250820T160000Z DTEND:20250820T170000Z DTSTAMP:20260422T225721Z UID:TQFT/145 DESCRIPTION:Title: T he homotopy coherent classification of fusion 2-categories\nby Julia P lavnik (Indiana University) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\nFusion 2-categories are a higher categori cal 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 physics. The classifiction of fusion (1-) categories is a very active research area and has provided new examples and led to the development of new invariants an d tools to understand these categories. \n\nIn this talk\, we will present a parametrization of multifusion 2-categories in terms of lower categoric al data\, involving braided fusion categories\, group theory\, and cohomol ogical data. If time allows\, we will also show some applications of this result. This is a joint work in with T. Décoppet\, T. Johnson-Freyd\, P. Huston\, D. Nikshych\, D. Penneys\, D. Reutter\, and M. Yu.\n LOCATION:https://researchseminars.org/talk/TQFT/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack Romö (University of Leeds) DTSTART:20250827T160000Z DTEND:20250827T170000Z DTSTAMP:20260422T225721Z UID:TQFT/146 DESCRIPTION:Title: H omotopy bicategories of $(\\infty\,2)$-categories\nby Jack Romö (Univ ersity of Leeds) as part of Topological Quantum Field Theory Club (IST\, L isbon)\n\n\nAbstract\nAcross the multitude of definitions for a higher cat egory\, a dividing line can be found between two major camps of model. On one side lives the ‘algebraic’ models\, like Bénabou’s bicategories \, tricategories following Gurski and the models of Batanin and Leinster\, Trimble and Penon. On the other end\, one finds the ‘non-algebraic’ m odels\, including more homotopy-theoretic ones like quasicategories\, Sega l n-categories\, complete n-fold Segal spaces and more. The bridges betwee n these models remain somewhat mysterious. Progress has been made in certa in instances\, as seen in the work of Tamsamani\, Leinster\, Lack and Paol i\, Cottrell\, Campbell\, Nikolaus and others. Developing comparisons betw een these forms of higher category has relevance to topological quantum fi eld theories in relating the work done on fully extended TQFTs using homot opy theoretic models of higher category\, such as Lurie's proof-sketch of the Cobordism Hypothesis conducted using n-fold Segal spaces\, and the lar ge body of work on extended TQFTs using algebraic models of higher categor y\, such as symmetric monoidal bicategories.\n\nNonetheless\, the correspo ndence remains incomplete\; indeed\, for instance\, there is no fully veri fied means in the literature to take an 'algebraic’ homotopy n-category of any known model of $(\\infty\, n)$-category for general n. One might se e 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 current wor k in the problem of taking homotopy bicategories of non-algebraic $(\\inft y\, 2)$-categories\, including a construction of my own. If time permits\, I will discuss the connections of this problem to topological quantum fie ld theories.\n LOCATION:https://researchseminars.org/talk/TQFT/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Voronov (University of Minnesota) DTSTART:20250910T150000Z DTEND:20250910T160000Z DTSTAMP:20260422T225721Z UID:TQFT/147 DESCRIPTION:Title: T he superstring measure on the moduli spaces of genus-zero super Riemann su rfaces\nby Alexander Voronov (University of Minnesota) as part of Topo logical Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nI will pre sent 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 using fi rst principles\, i.e.\, exclusively complex algebraic supergeometry and\, in particular\, the super Mumford isomorphism. The answer in the Ramond ca se 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-progress i n the Ramond case.\n LOCATION:https://researchseminars.org/talk/TQFT/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Jones (North Carolina State University) DTSTART:20250903T160000Z DTEND:20250903T170000Z DTSTAMP:20260422T225721Z UID:TQFT/148 DESCRIPTION:Title: L evin–Wen models: a mathematician's perspective from the boundary\nby Corey Jones (North Carolina State University) as part of Topological Quan tum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nTopological quantum ma ny-body systems on the lattice are characterized by having the property th at their low energy effective theories are TQFTs. Levin–Wen models are c lasses of spin systems on the 2D lattice whose low energy effective theori es are Turaev–Viro TQFTs. The problem (from a mathematician's perspectiv e) is that low energy effective theories are not at all well-defined! This leads to the question: for systems that (supposedly) exhibit topological order\, how can we see the emergent TQFT directly on the lattice in the in finite volume limit? We will discuss our recently proposed approach to mat hematically formalize the ideas of topological holography in terms of boun dary algebras\, and explain how this provides a solution for systems with local topological order.\n LOCATION:https://researchseminars.org/talk/TQFT/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Dionne Ibarra (Monash University) DTSTART:20250917T090000Z DTEND:20250917T100000Z DTSTAMP:20260422T225721Z UID:TQFT/149 DESCRIPTION:Title: O ctahedral fully augmented links and the TV volume conjecture\nby Dionn e Ibarra (Monash University) as part of Topological Quantum Field Theory C lub (IST\, Lisbon)\n\n\nAbstract\nTuraev–Viro (TV) invariants are 3-mani fold invariants\, defined for a given fixed integer $r$ and $2r$-th root o f unity. Chen and Yang extended the definition of TV-invariants to pseudo 3-manifolds and introduced a volume conjecture for TV-invariants which sta tes 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 determine th e volume of $M$.\n\nThe Witten–Reshetikhin–Turaev (WRT) 3-manifold inv ariants (also known as the Chern–Simons 3-manifold invariants)\, are def ined for a given fixed integer $r$\, and a $2r$-th root of unity. The exis tence of such invariants were predicted by Witten in his work on Chern–S imons gauge theory and topological quantum field theory. They were constru cted by Reshetikhin and Turaev by using representation theory and Kirby ca lculus. Later\, Lickorish gave a skein theoretic definition. These invaria nts were also originally defined for closed orientable 3-manifolds\, but w ere recently extended to link complements. Furthermore\, Belletti\, Detche rry\, Kalfagianni\, and Yang provided an explicit formula relating the TV invariant to the WRT invariant of link complements in a closed orientable 3-manifold and used this formula to prove the TV volume conjecture for oct ahedral link complements in the connected sums of $S^2 \\times S^1$ called fundamental shadow links.\n\nIn contrast\, fully augmented links are link s in $S^3$ whose complements have nice geometric properties. For instance\ , Agol and Thurston showed that fully augmented links can be decomposed in to totally geodesic\, right-angled ideal polyhedra. In this talk\, we will present a geometric description of the relationship between octahedral fu lly augmented links and fundamental shadow links and we will outline an al ternative proof\, using the colored Jones polynomial\, to prove the TV vol ume conjecture for octahedral fully augmented links with no half-twists. T his is joint work with Emma McQuire and Jessica Purcell.\n LOCATION:https://researchseminars.org/talk/TQFT/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Norbury (University of Melbourne) DTSTART:20251001T090000Z DTEND:20251001T100000Z DTSTAMP:20260422T225721Z UID:TQFT/151 DESCRIPTION:Title: S uper volumes of the moduli space of super Riemann surfaces\nby Paul No rbury (University of Melbourne) as part of Topological Quantum Field Theor y Club (IST\, Lisbon)\n\n\nAbstract\nI will present the super volumes of t he moduli space of super Riemann surfaces. They will be defined using a fa mily of finite measures on the moduli space of genus $g$ curves. These mea sures are in turn given by a construction analogous to the classical const ruction of the Weil–Petersson metric\, using the extra data of a spin st ructure. The total measure gives the volume of the moduli space of super c urves and can be calculated via a deep relationship with the KdV equation. \n LOCATION:https://researchseminars.org/talk/TQFT/151/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiro Lee Tanaka (Texas State University) DTSTART:20251126T100000Z DTEND:20251126T110000Z DTSTAMP:20260422T225721Z UID:TQFT/152 DESCRIPTION:Title: B roken\nby Hiro Lee Tanaka (Texas State University) as part of Topologi cal Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe'll talk abo ut joint work with Jacob Lurie regarding moduli stacks of geometric object s developing natural breaks. If time allows\, I'll end with some speculati on regarding a 3-D TFT arising from various G2 manifolds.\n LOCATION:https://researchseminars.org/talk/TQFT/152/ END:VEVENT BEGIN:VEVENT SUMMARY:César Galindo (Universidad de los Andes) DTSTART:20251029T170000Z DTEND:20251029T180000Z DTSTAMP:20260422T225721Z UID:TQFT/153 DESCRIPTION:Title: A manifestly Morita-invariant construction of Turaev–Viro invariants\ nby César Galindo (Universidad de los Andes) as part of Topological Quant um Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nWe present a bicategori cal state sum construction for 3-manifold invariants. Using the pivotal bi category of spherical module categories over a spherical fusion category\, we construct invariants that manifestly preserve Morita equivalence. Our main result shows that this bicategorical invariant recovers the standard Turaev–Viro invariant\, thereby proving Morita invariance of Turaev–Vi ro invariants without appealing to the Reshetikhin–Turaev construction.\ n\nThis is joint work with Jürgen Fuchs\, David Jaklitsch\, and Christoph Schweigert.\n LOCATION:https://researchseminars.org/talk/TQFT/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne-Laure Thiel (Université de Bourgogne) DTSTART:20251203T100000Z DTEND:20251203T110000Z DTSTAMP:20260422T225721Z UID:TQFT/154 DESCRIPTION:Title: O n faithful representations of the braid group\nby Anne-Laure Thiel (Un iversité 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 strands. In the early 2000s\, two constructions were provided to fix faithfulness: the first being the Lawrence–Krammer–Bigelow linear representation\, henc e proving linearity of braid groups\, and the second being the Khovanov– Seidel categorical representation. In this talk\, based on joint work in p rogress with Licata\, Queffelec\, and Wagner\, I will investigate the inte rplay between these two representations.\n LOCATION:https://researchseminars.org/talk/TQFT/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Huston (University of Leeds) DTSTART:20251022T160000Z DTEND:20251022T170000Z DTSTAMP:20260422T225721Z UID:TQFT/155 DESCRIPTION:Title: A lgebraic techniques in 3-cateories of (2+1)D topological defects\nby P eter Huston (University of Leeds) as part of Topological Quantum Field The ory Club (IST\, Lisbon)\n\n\nAbstract\nTopological phases of matter in (2+ 1)D should naturally form a 3-category\, in which k-morphisms represent de fects of codimension k. By the cobordism hypothesis\, the 3-categories of (2+1)D topological order with a fixed anomaly are each equivalent to the 3 -category of fusion categories enriched over a corresponding UMTC. In ongo ing work with Fiona Burnell\, we introduce algebraic techniques for concre te computations in 3-categories of (2+1)D topological order\, including a tunneling approach to the classification of point defects which generalize s the use of braiding to identify anyon types. We then apply these techniq ues to compute ground state degeneracy and classify low energy excitations in a class of fracton-like (2+1)D topological defect networks.\n LOCATION:https://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:20260422T225721Z UID:TQFT/157 DESCRIPTION:Title: A relationship between gauge theories with finite and continuous gauge grou ps.\nby Pavel Putrov (The Abdus Salam International Centre for Theoret ical Physics) as part of Topological Quantum Field Theory Club (IST\, Lisb on)\n\n\nAbstract\nI will discuss certain relations between 3-dimensional topological gauge theories with continuous and finite gauge groups\, commo nly known as Chern–Simons and Dijkgraaf–Witten theories respectively. The relations of this form appear when the continuous and finite gauge gro ups are the same algebraic group considered over the complex/real numbers and a finite field\, respectively. In this talk\, I will focus on the SU(2 ) example and consider the relationship on the level of the corresponding invariants of closed 3-manifolds: Witten–Reshetikhin–Turaev and Dijkgr aaf–Witten invariants.\n LOCATION:https://researchseminars.org/talk/TQFT/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincentas Mulevicius (University of Vienna) DTSTART:20260128T170000Z DTEND:20260128T180000Z DTSTAMP:20260422T225721Z UID:TQFT/158 DESCRIPTION:Title: C ategorical 4-manifold invariants from trisection diagrams\nby Vincenta s Mulevicius (University of Vienna) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nTrisections give a diagrammatic d escription of smooth 4-manifolds\, similar to Heegaard splittings in dimen sion three. In this talk\, I will describe new 4-manifold invariants defin ed from trisection diagrams using categorical data. The input consists of three spherical fusion categories\, a semisimple bimodule category with a bimodule trace\, and a pivotal functor into the category of bimodule endof unctors.\n\nThe construction works by labelling the trisection diagrams wi th the categorical data and evaluating them using a diagrammatic calculus for bimodule categories. The details of this procedure ensures that the re sult is invariant under moves on trisections yielding the same 4-manifold. This construction generalises existing Hopf algebraic trisection invarian ts due to Chaidez--Cotler--Cui and recovers the Crane--Yetter and Bärenz --Barrett invariants as special cases. I will outline the main ideas of th e construction and briefly discuss examples and connections to TQFTs.\n\nB ased on the work 2511.19384 with Catherine Meusburger (FAU) and Fiona Torz ewska (Bristol).\n LOCATION:https://researchseminars.org/talk/TQFT/158/ END:VEVENT BEGIN:VEVENT SUMMARY:Angela Tabiri (African Institute for Mathematical Sciences Ghana) DTSTART:20251210T170000Z DTEND:20251210T180000Z DTSTAMP:20260422T225721Z UID:TQFT/159 DESCRIPTION:Title: D ecomposable 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\nAbst ract\nDecomposable plane curves of degree up to 5 were shown to be quantum homogeneous spaces by Brown and Tabiri. It was conjectured that all decom posable plane curves of any degree are quantum homogeneous spaces. In this talk\, we will discuss recent results which show that decomposable surfac es and plane curves of any degree are quantum homogeneous spaces. Other al gebras such as the reduced algebra will be constructed and its properties discussed.\n LOCATION:https://researchseminars.org/talk/TQFT/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxine Calle (University of Pennsylvania) DTSTART:20260123T160000Z DTEND:20260123T170000Z DTSTAMP:20260422T225721Z UID:TQFT/160 DESCRIPTION:Title: N ested cobordisms and TQFTs\nby Maxine Calle (University of Pennsylvani a) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAb stract\nA well-known folklore theorem classifies 2-dimensional topological quantum field theories (TQFTs) in terms of Frobenius algebras\, providing a unifying link between topology\, algebra\, and physics. In this talk\, we explore what happens when the usual cobordism category is replaced by a category of nested cobordisms\, in which 2-dimensional surfaces are equip ped with embedded 1-dimensional submanifolds. We study symmetric monoidal functors out of this category and the resulting algebraic structures they encode. This talk is based on joint work with R. Hoekzema\, L. Murray\, N. Pacheco-Tallaj\, C. Rovi\, and S. Sridhar.\n\nPlease note the change of d ay and time!\n LOCATION:https://researchseminars.org/talk/TQFT/160/ END:VEVENT BEGIN:VEVENT SUMMARY:Constantin Teleman (University of California\, Berkeley) DTSTART:20260304T170000Z DTEND:20260304T180000Z DTSTAMP:20260422T225721Z UID:TQFT/161 DESCRIPTION:Title: R eshetikhin–Turaev theories are fully local\nby Constantin Teleman (U niversity of California\, Berkeley) as part of Topological Quantum Field T heory Club (IST\, Lisbon)\n\n\nAbstract\nI will review two results pertain ing to 3-dimensional Reshetikhin–Turaev TQFTs\, defined from modular ten sor categories M. These theories were not constructed as “fully local” TQFTs (in the framework of Lurie’s Cobordism Hypothesis): no algebraic structures were assigned to points. (The obstruction was the Witt class of M.) Kevin Walker solved the locality problem in the setting of anomalous theories. A ‘no-go’ theorem (joint with Dan Freed) showed that\, if lo calized as linear theories\, these RT theories did not admit local topolog ical boundary conditions\, and could therefore not be generated from a poi nt by this method. (The group-like case had been addressed by Kapustin and Saulina.) In recent work with Freed and Claudia Scheimbauer\, we displaye d a fully local realization of these theories\, by objects in a target 3-c ategory which enlarges that of fusion categories. This allowed us to settl e some conjectures relating orientations and spherical structures.\n LOCATION:https://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:20260422T225721Z UID:TQFT/162 DESCRIPTION:Title: D efect skein theory\, parabolic restriction and the Turaev coproduct\nb y Juan-Ramón Gómez-García (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as part of Topological Quantum Field Theory Club (IST\, Lisbo n)\n\n\nAbstract\nInspired by Jaeger’s composition formula for the HOMFL Y polynomial\, Turaev defined a coproduct on the HOMFLY skein algebra 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 represen tation from GL_m+n to GL_m x GL_n. The restriction functor\, however\, is not braided\, and therefore there is a priori no reason for the induced li near map between the corresponding skein algebras to be multiplicative. 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 talk\, I will introduce skein theory for 3-manifolds with both surface and line def ects. Local relations near the defects are produced from the algebraic dat a of a central algebra (codimension 1) and a centred bimodule (codimension 2). Examples of such structures are provided by the formalism of paraboli c restriction. In the second part of the talk\, I will explain how to cons truct a universal version of this formalism. Finally\, we will see how Tur aev’s coproduct extends to the entire skein category using the previous constructions.\n LOCATION:https://researchseminars.org/talk/TQFT/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Thiago Paiva (Beijing University) DTSTART:20260318T140000Z DTEND:20260318T150000Z DTSTAMP:20260422T225721Z UID:TQFT/163 DESCRIPTION:Title: A simpler braid description for all links in the 3-sphere\nby Thiago Pa iva (Beijing University) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nBy Alexander's theorem\, every link in the 3 -sphere can be represented as the closure of a braid. Lorenz links and twi sted torus links are two families that have been extensively studied and a re well-described in terms of braids. In this talk\, we will present a nat ural generalization of Lorenz links and twisted torus links that produces all links in the 3-sphere. This provides a simpler braid description for a ll links in the 3-sphere.\n\nJoint seminar with CEMS.UL.\n LOCATION:https://researchseminars.org/talk/TQFT/163/ END:VEVENT END:VCALENDAR