BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:John Baez (University of California Riverside) DTSTART:20201007T180000Z DTEND:20201007T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/1 DESCRIPTION:Title: Fock space techniques for stochastic physics\nby John Baez (University of California Riverside) as part of Categories seminar UN AM\n\n\nAbstract\nSome ideas from quantum theory are beginning to percolat e back to classical probability theory. For example\, the master equation for a chemical reaction network - also known as a stochastic Petri net - d escribes particle interactions in a stochastic rather than quantum way. If we look at this equation from the perspective of quantum theory\, this fo rmalism turns out to involve creation and annihilation operators\, coheren t states and other well-known ideas — but with a few big differences.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Joe Moeller (University of California\, Riverside) DTSTART:20201014T180000Z DTEND:20201014T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/2 DESCRIPTION:Title: Network models\nby Joe Moeller (University of Californ ia\, Riverside) as part of Categories seminar UNAM\n\n\nAbstract\nNetworks can be combined in various ways\, such as overlaying one on top of anothe r or setting two side by side. We introduce `network models' to encode the se ways of combining networks. Different network models describe different kinds of networks. We show that each network model gives rise to an opera d\, whose operations are ways of assembling a network of the given kind fr om smaller parts. Such operads\, and their algebras\, can serve as tools f or designing networks. Technically\, a network model is a lax symmetric mo noidal functor from the free symmetric monoidal category on some set to Ca t\, and the construction of the corresponding operad proceeds via a symmet ric monoidal version of the Grothendieck construction.\n\nLivestream: http s://www.youtube.com/watch?v=Pa96YVgazQk\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jade Master (University of California Riverside) DTSTART:20201021T180000Z DTEND:20201021T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/3 DESCRIPTION:Title: Open Petri nets and their Categories of Processes\nby Jade Master (University of California Riverside) as part of Categories sem inar UNAM\n\n\nAbstract\nIn this talk we will discuss Petri nets from a ca tegorical perspective. A Petri net freely generates a symmetric monoidal c ategory whose morphisms represent its executions. We will discuss how to m ake Petri nets "open" i.e. equip them with input and output boundaries whe re resources can flow in and out. Open Petri nets freely generate open sym metric monoidal categories: symmetric monoidal categories which can be glu ed together along a shared boundary. The mapping from open Petri nets to t heir open symmetric monoidal categories is functorial and this gives a com positional framework for reasoning about the executions of Petri nets.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Camilo Arias (Universidad de Chile) DTSTART:20201028T190000Z DTEND:20201028T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/4 DESCRIPTION:Title: Grupos cuánticos\, categorías derivadas y anillos de fus ión\nby Juan Camilo Arias (Universidad de Chile) as part of Categorie s seminar UNAM\n\n\nAbstract\nSea C una categoría esférica abeliana. Den ote por N_C la subcategoría plena consistente de objetos despreciables\, es decir\, objetos tales que la traza de cualquiera de sus endomorfismos s e anula. En esta charla\, propondremos una definición en nivel derivado d e categoría y anillo de fusión para la categoría C. Como ejemplo\, most raremos que esta definición produce los mismos anillos de fusión que se obtienen de las categorías de representaciones de los grupos cuánticos g rande y pequeño.\n\nLanguage: Spanish\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrique Becerra (IPN) DTSTART:20201104T190000Z DTEND:20201104T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/5 DESCRIPTION:Title: Algunas ideas sobre la entropia de entrelazamiento\nby Enrique Becerra (IPN) as part of Categories seminar UNAM\n\nAbstract: TBA \n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Tobias Fritz (University of Innsbruck) DTSTART:20201111T190000Z DTEND:20201111T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/6 DESCRIPTION:Title: Markov categories: Probability and Statistics as a Theory of Information Flow\nby Tobias Fritz (University of Innsbruck) as part of Categories seminar UNAM\n\n\nAbstract\nMarkov categories have recently gained prominence as a categorical approach to probability and statistics . In this talk\, I will argue that Markov categories provide a very genera l theory of information flow\, and that this theory generalizes probabilit y theory in a manner analogous to how topos theory generalizes set theory. \n\nIn the first part\, I will sketch some theorems of probability and sta tistics which have already been developed synthetically in terms of Markov categories\, including a version of the Blackwell-Sherman-Stein theorem w hich seems to be new even when instantiated in the traditional measure-the oretic framework. In the second part\, I will sketch the vast and largely unexplored landscape of Markov categories on which these synthetic results can be instantiated. Some basic knowledge of monoidal categories and disc rete probability should be enough to follow the talk.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alcides Buss (UFSC) DTSTART:20201118T190000Z DTEND:20201118T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/7 DESCRIPTION:Title: Noncommutative Symmetries -a higher category approach- \nby Alcides Buss (UFSC) as part of Categories seminar UNAM\n\n\nAbstract\ nMany operator algebras describe "noncommutative spaces" admitting intrins ic symmetries that cannot be described in a classical way\, through a grou p action. However\, many of these "noncommutative symmetries" can be under stood in a broader spectrum via the use of 2-groups or even 2-groupoids. W hile a groupoid can be seen as a category where all morphisms are invertib le\, a 2-groupoid is nothing but a 2-category (or bicategory) where all mo rphisms and 2-morphisms are invertible. A 2-group is just a 2-groupoid wit h a single object. To understand how these act on objects of other bicateg ories\, like C*-algebras\, we use the theory of bicategories and look at w eak functors from a 2-groupoid to certain bicategories of C*-algebras. Thi s gives us a good flexibility and allows to understand several sort of new symmetries and also rediscover known ones from a different point of view. \n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophie Libkind (Stanford) DTSTART:20201125T190000Z DTEND:20201125T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/8 DESCRIPTION:by Sophie Libkind (Stanford) as part of Categories seminar UNA M\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Joachim Kock (UAB) DTSTART:20201202T190000Z DTEND:20201202T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/9 DESCRIPTION:Title: Whole-grain Petri nets and processes\nby Joachim Kock (UAB) as part of Categories seminar UNAM\n\n\nAbstract\nI will present a n ew formalism for Petri nets based on polynomial-style finite-set configura tions and etale maps. The processes of a Petri net P are etale maps G -> P from graphs. The main feature of the formalism is that Petri nets have elements --- they are the elements you see in the pictures. This makes th e definition more representable (in the categorical sense of the word) tha n previous definitions. The main result I want to arrive at is that P-pro cesses form a symmetric monoidal Segal space\, which is the free prop-in-g roupoids on P\, but most of the time will be spent just explaining Petri n ets\, their markings and firings\, the token game\, processes\, and the ba sic idea of concurrency and causality --and how these notions look in the new formalism.\n\n\n\nReference: "Elements of Petri nets and processes" [A rXiv:2005.05108]\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yasuyuki Kawahigashi (The University of Tokyo) DTSTART:20201209T230000Z DTEND:20201210T000000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/10 DESCRIPTION:Title: Topological order\, operator algebras and topological qua ntum field theory\nby Yasuyuki Kawahigashi (The University of Tokyo) a s part of Categories seminar UNAM\n\n\nAbstract\nWe will explain studies o f 2-dimensional topological order in terms of tensor networks and subfacto rs arising from commuting squares. Appearance of braiding strucuture from 3-dimensional topological quantum field theory is demonstrated from a vie wpoint of tensor categories. We will give higher relative commutants of a subfactor as spaces on which Hamiltonian acts.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Paré (Dalhousie University) DTSTART:20210210T230000Z DTEND:20210211T000000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/11 DESCRIPTION:Title: A case study in double categories\nby Robert Paré (D alhousie University) as part of Categories seminar UNAM\n\n\nAbstract\nWe give an elementary introduction to some ideas in double category\ntheory b y concentrating on one particular example\, the double category of rings\n with homomorphisms\, and bimodules. Along the way we discover a number of\ n“new” morphisms of rings\, interesting in their own right. We also lo ok at interesting\ndouble adjunctions in this context.\n\nNo previous know ledge of double categories is assumed\, just some familiarity\nwith catego ries\, rings and modules.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/11/ END:VEVENT BEGIN:VEVENT SUMMARY:David Spivak (Topos Institute) DTSTART:20210217T230000Z DTEND:20210218T000000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/12 DESCRIPTION:Title: Polynomials and the dynamics of data\nby David Spivak (Topos Institute) as part of Categories seminar UNAM\n\n\nAbstract\nOne c an imagine a database schema as a category and an instance or state of tha t database as a functor I: C-->Set\; the category of these is denoted C-Se t. One can think of a data-migration functor\, a way of moving data betwee n schemas C and D\, as a parametric right adjoint C-Set --> D-Set. In data base speak\, these are D-indexed "unions of conjunctive queries".\n\nScene change. The usual semiring of polynomials in one variable with cardinal c oefficients\, polynomials such as p = y^3 + 3y + 2\, can be categorified t o Poly\, the category of polynomial functors\, where + and x are the categ orical coproduct and product. Composition of polynomials (p o q) gives a m onoidal operation on this category for which the identity polynomial\, y\, is the unit. Ahman and Uustalu showed in 2016 that\, up to isomorphism\, the comonoids in (Poly\, o\, y) are precisely categories (!)\, and Garner sketched a proof in a recent video that bimodules between polynomial comon oids are parametric right adjoints between copresheaf categories. Recall t hat these are precisely the data-migration functors described above. In th e talk\, I will describe this circle of ideas.\n\nI propose that in 2021 a great transition is upon us\; distances that were measured in days are no w measured in zoom-hiccups. The speed of data migration—if that's indeed a valid way to model it—is much faster than ever\, driving dominance in to the hands of those who move data: roughly speaking\, computerized proce sses. Researchers use biomimicry to formalize as many aspects of human int elligence as they can\, much of which is then installed as automated softw are systems that run constantly. I call the automated speed-up of bio-insp ired intellectual processes AI\, and I'm not judging it as good or bad\, b ut I do consider it immensely important. I propose that we as mathematicia ns have the ability to shape the course of AI. Mathematics becomes technol ogy\, and I believe we'll fare better if that technology is based on elega nt principles rather than made ad-hoc. Polynomial functors are my entry po int\, and this talk can serve as an invitation to others to join in whatev er capacity appeals to them. To respect the standards of academic talks\, I will mainly restrict my discussion to mathematics and its applications\, rather than to speculation.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Paolo Perrone (Oxford) DTSTART:20210224T230000Z DTEND:20210225T000000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/13 DESCRIPTION:Title: Partial evaluations: the results so far\nby Paolo Per rone (Oxford) as part of Categories seminar UNAM\n\n\nAbstract\nPartial ev aluations are a way to encode\, in terms of monads\, operations which have been computed only partially. For example\, the sum "1+2+3+4" can be eval uated to "10"\, but also partially evaluated to "3+7"\, or to "6+4".\nSuch structures can be defined for arbitrary algebras over arbitrary monads\, and even 2-monads\, and can be considered the 1-skeleton of a simplicial o bject called the bar construction. The higher simplices of the bar constru ction can be interpreted as ways to compose partial evaluations. Recent re search has shown that\, while for cartesian monads partial evaluations for m a category\, for weakly cartesian monads the compositional structure is more complex\, and in particular it does not in general form any of the st andard higher-categorical structures.\nMoreover\, partial evaluations retu rn known concepts of "partially evaluated operations" in the following con texts:\n- For the free cocompletion monad\, where the operation is taking the colimit\, partial evaluations correspond to left Kan extensions\;\n- F or probability monads\, where the operation is taking the expected value\, partial evaluations correspond to conditional expectations.\n\nThe resear ch presented in this talk has been carried out jointly with Carmen Constan tin\, Tobias Fritz\, Brandon Shapiro\, and Walter Tholen.\n\nThe talk will be in English\, but you are welcome to ask questions in Spanish if anythi ng is not clear.\n\nThe following are references for the topics discussed in the talk:\n\nhttps://arxiv.org/abs/1810.06037\n\nhttps://arxiv.org/abs/ 2009.07302\n\nhttps://arxiv.org/abs/2101.04531\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Arthur Parzygnat (IHÉS) DTSTART:20210303T190000Z DTEND:20210303T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/14 DESCRIPTION:Title: String diagrams for C*-algebras and Bayesian inversion\nby Arthur Parzygnat (IHÉS) as part of Categories seminar UNAM\n\n\nAbs tract\nAbstract: The foundations of probability\, statistics\, and informa tion theory are slowly undergoing a potentially dramatic change of perspec tive through the language of category theory via string diagrams [3]. This point of view has been abstracted to finite-dimensional C*-algebras via a stochastic variant of the Gelfand—Naimark theorem and quantum Markov ca tegories. Through this abstraction\, one can immediately analyze concepts such as Bayesian inversion in non-classical settings\, which in fact has r ecently been done in finite dimensions [2]. What can be said for more gene ral (possibly infinite dimensional) C*-algebras? In this talk\, I will rev iew some background on Markov categories\, provide some motivation for the ir study\, introduce our main quantum example\, and then I'll provide a sm all refresher on C*-tensor products. Then\, I'll explain why all C*-algebr as do not form a quantum Markov category\, and I will provide some suggest ions for an alternative framework [1].\n \n\nMain reference:\n\n[1] https: //arxiv.org/abs/2001.08375 (especially Remark 3.12 and Question 3.25).\n\n Additional references of potential interest:\n\n[2] https://arxiv.org/abs/ 2005.03886 (on Bayesian inversion in quantum mechanics)\n\n[3] https://arx iv.org/abs/1908.07021 (on classical Markov categories)\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Shulman (University of San Diego) DTSTART:20210310T190000Z DTEND:20210310T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/15 DESCRIPTION:Title: Double categories\, multivariable mates\, and Chu constru ctions\nby Michael Shulman (University of San Diego) as part of Catego ries seminar UNAM\n\n\nAbstract\nIt is an old observation of Kelly and Str eet that the\n"calculus of mates" for adjunctions is naturally expressed u sing a\ndouble category of functors and adjunctions. This was generalized by\nCheng\, Gurski\, and Riehl to mates for multivariable adjunctions\, s uch\nas the tensor-hom adjunction of a closed monoidal category or the\nte nsor-hom-cotensor adjunction of an enriched category\, using a cyclic\nmul ti double category. I will explain how the latter is more\nnaturally view ed as a poly double category (that is\, an internal\ncategory in polycateg ories)\, and how it arises as a special case of a\n"double Chu constructio n".\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Brendan Fong (Topos Institute) DTSTART:20210331T190000Z DTEND:20210331T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/16 DESCRIPTION:Title: Cospans as a tool for composition\nby Brendan Fong (T opos Institute) as part of Categories seminar UNAM\n\n\nAbstract\nWe often understand our world piece by piece\, weaving local models and perspectiv es into a bigger picture. In any category\, amalgamating parts into a sing le object can be captured through the notion of colimit. Cospans provide a convenient syntax for performing this weaving\, building colimits piece b y piece. Through the use of decorated and structured cospans\, this approa ch can extend to categories where colimits may be complicated to compute\, or may not even exist at all. In this talk\, I'll provide a perspective o n both the power and limits of cospans as a tool for composition\, meditat ing on why\, how\, and when cospans can contribute.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Martín Szyld (Dalhousie University) DTSTART:20210407T180000Z DTEND:20210407T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/17 DESCRIPTION:Title: The three F's in bicategory theory (joint work with P. Bu stillo and D. Pronk)\nby Martín Szyld (Dalhousie University) as part of Categories seminar UNAM\n\n\nAbstract\nWe consider the notions of Fibra tion of categories\, (pseudo)Filtered category\, and the axioms for a cate gory of Fractions. A basic fact involving them is: given a Fibration\, if the arrows of the base category are (pseudo)coFiltered\, then the cartesia n arrows satisfy Fractions. This is a Proposition in SGA 4 (Exp. VI\, Prop . 6.4) whose proof is left to the reader as an exercise\, and I want to st art this talk by solving this exercise. Let me tell you why.\n\nEach of th e three "F" notions above has been considered for bicategories\, or at lea st for 2-categories. I will start with what may be the easiest one to unde rstand\, that of Filtered: in a Filtered bicategory\, in addition to askin g for cones for two objects and for two parallel arrows\, we add a third a xiom asking for cones for parallel 2-cells. I will present the definitions of Filtered and pseudoFiltered bicategory\, a set of axioms for a bicateg ory of Fractions\, and some properties of Fibrations of bicategories that all fit this same pattern. We arrived at these notions when proving a "bic ategory version" of the Proposition in SGA 4\, in fact a small generalizat ion that I will present.\n\nThis result is part of an ongoing collaboratio n with P. Bustillo and D. Pronk\, we're working on showing some basic prop erties of the bicategorical localization by fractions which are known in d imension 1. If time permits\, I hope to mention how we ended up here withi n our current work and how this result can be applied here.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Roberto Hernández (Ohio State University) DTSTART:20210317T190000Z DTEND:20210317T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/18 DESCRIPTION:Title: Actions of unitary tensor categories on C*-algebras\n by Roberto Hernández (Ohio State University) as part of Categories semina r UNAM\n\n\nAbstract\nA subfactor is a unital inclusion of simple von Neum ann algebras/factors $A\\subset B\,$ and we study it via its standard inva riant $\\cC\,$ which corresponds to a unitary tensor category (UTC). We wi ll review some subfactor reconstruction techniques by Popa\, and Guionnet- Jones-Shlyakhtenko (GJS)\, highlighting that subfactors have quantum symme tries which are encoded by UTC-actions. Namely\, we reinterpret the inclus ion $A\\subset B$ as encoding an action of its standard invariant $\\cC$ o n $A\,$ and reconstruct the overfactor $B$ as a generalized crossed-produc t by this UTC-action.\n\nLarge scale work of many researchers worldwide ha s recently culminated in the classification of C*-algebras\, which is now at the level of Connes' classification of injective factors. Nowadays\, C* -algebras is at a similar state to that of von Neumann algebras after Jone s introduced the index for subfactors in the early 80s. Thereafter\, great interest has arisen in constructing and classifying UTC-actions on C*-alg ebras\, aiming to understand their structure from the viewpoint of quantum symmetries.\n\nWe will see that every UTC $\\cC$ acts on some simple\, un ital separable and monotracial C*-algebra constructed only from $\\cC$ by adapting diagrammatic and free probabilistic techniques from GJS. Using a 'Hilbertification' technique\, we recover the UTC-action constructed by B rothier-Harglass-Penneys of $\\cC$ on the free group factor $L\\mathbb{F}_ \\infty.$ This is joint work with Hartglass. Finally\, we will review some recent developments and obstructions to the existence of UTC actions on ( classifiable) C*-algebras.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Nadia Romero (Universidad de Guanajuato) DTSTART:20210414T180000Z DTEND:20210414T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/19 DESCRIPTION:Title: La completación aditiva de la categoría de biconjuntos< /a>\nby Nadia Romero (Universidad de Guanajuato) as part of Categories sem inar UNAM\n\n\nAbstract\nEn los últimos años\, la teoría de funtores en biconjuntos ha\ndemostrado ser una herramienta muy útil para abordar pro blemas\nrelacionados con grupos finitos y sus representaciones. En esta\np lática comenzaré por la definición de funtor en biconjuntos y la\nmotiv ación que llevó a esta definición. Después\, presentaré la\ncompletac ión aditiva de la categoría de biconjuntos\, veremos que los\nobjetos en esta categoría pueden escribirse como fracciones y que\, de\nhecho\, en muchos sentidos se comportan como tales. Veremos también que\nesta catego ría es aditiva\, monoidal simétrica\, autodual y con una\ndescomposició n de tipo Krull-Schmidt para los objetos. Si el tiempo lo\npermite\, verem os su relación con la categoría de Burnside\, introducida\npor Lindner e n 1976.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Maru Sarazola (Cornell) DTSTART:20210428T180000Z DTEND:20210428T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/20 DESCRIPTION:Title: The stable homotopy hypothesis\nby Maru Sarazola (Cor nell) as part of Categories seminar UNAM\n\n\nAbstract\nThe homotopy hypot hesis is a well-known bridge between topology and category theory. Its mos t general formulation\, due to Grothendieck\, asserts that topological spa ces should be "the same" as infinity-groupoids. In the stable version of t he homotopy hypothesis\, topological spaces are replaced with spectra. \n\ nIn this talk we will review the classical homotopy hypothesis\, and then focus on the stable version. After discussing what the stable homotopy hyp othesis should look like on the categorical side\, we will use the Tamsama ni model of higher categories to provide a proof. This is based on joint w ork with Moser\, Ozornova\, Paoli and Verdugo.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamie Vicary (Cambridge) DTSTART:20210421T180000Z DTEND:20210421T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/21 DESCRIPTION:Title: Infinity categories with strict units\nby Jamie Vicar y (Cambridge) as part of Categories seminar UNAM\n\n\nAbstract\nCompositio n in ordinary 1-categories is strictly unital\, and it's known that every weak 2-category is equivalent to a 2-category with strict units\, a useful theorem that makes 2-categories easier to work with. But what does it mea n for an n-category\, or even an infinity-category\, to have strict units? In this talk I give an accessible introduction to infinity categories\, a nd use lots of examples to illustrate the theory of strict units for infin ity-categories. This is joint work with Eric Finster and David Reutter (ar Xiv:2007.08307).\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Makoto Yamashita (The University of Oslo) DTSTART:20210325T000000Z DTEND:20210325T010000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/22 DESCRIPTION:Title: Reflection equation and quantization of symmetric spaces< /a>\nby Makoto Yamashita (The University of Oslo) as part of Categories se minar UNAM\n\n\nAbstract\nThe reflection equation\, an analogue of the Yan g-Baxter equation\, appeared from the boundary quantum field theory due to Cherednik in the 80's. It came to known to have strong connection to quan tization of homogeneous spaces\, and in particular symmetric spaces throug h Tannaka-Krein type duality. In this talk I will review the basic categor ical paradigm behind this correspondence\, and an analogue of Kohno-Drinfe ld rigidity theorem that gives a classification of monoidal categorical st ructure (ribbon braided module category) quantizing compact symmetric spac es in terms of eigenvalues of solution to reflection equation. Based on jo int works with Kenny De Commer\, Sergey Neshveyev\, and Lars Tuset.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernardo Uribe (Universidad del Norte) DTSTART:20210505T180000Z DTEND:20210505T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/23 DESCRIPTION:Title: Pontrjagin duality on multiplicative gerbes\nby Berna rdo Uribe (Universidad del Norte) as part of Categories seminar UNAM\n\n\n Abstract\nMultiplicative gerbes can be understood as monoid objects on the 2-category of gerbes. We take this point of\nview on the 2-category of to pological gerbes in order to define appropriate representations of these m ultiplicative gerbes. \nWe take an explicit model for topological gerbes u sing Graeme Segal's cohomology of topological groups and we show that with this model\nwe may replicate several constructions done over multiplicati ve gerbes over finite groups.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Ross Street (Macquarie University) DTSTART:20210513T000000Z DTEND:20210513T010000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/24 DESCRIPTION:Title: Views of centers\nby Ross Street (Macquarie Universit y) as part of Categories seminar UNAM\n\n\nAbstract\nInitially\, the centr e of a monoidal category was used independently by V. Drinfeld\nin connect ion with Hopf algebras and by A. Joyal and the speaker to study the\ncateg ory of framed tangles. We were influenced by lectures of Yu. Manin in Mont réal\nand the work of D. Yetter and V. Turaev. In this talk I will give a gentle introduction to\nhow the construction can be viewed in various way s. In particular\, it is a limit construction\nwhich can be performed in o ther places besides the cartesian monoidal 2-category of\ncategories. Some examples from different fields will be provided.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Dorette Pronk (Dalhousie University) DTSTART:20210526T190000Z DTEND:20210526T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/25 DESCRIPTION:Title: Orbispace Mapping Objects: Exponentials and Enrichment!\nby Dorette Pronk (Dalhousie University) as part of Categories seminar UNAM\n\n\nAbstract\nOrbifolds are defined like manifolds\, by local charts . Where manifold charts are open subsets of Euclidean space\, orbifold cha rts consist of an open subset of Euclidean space with an action by a finit e group (thus allowing for local singularities). This affects the way that transitions between charts need to be described\, and it is generally rat her cumbersome to work with atlases. It has been shown in [Moerdijk-P] tha t one can represent orbifolds by groupoids internal to the category of man ifolds\, with etale structure maps and a proper diagonal\, I.e.\, combined source-target map (s\,t): G_1 -> G_0 x G_0. We have since generalized thi s notion further to orbispaces\, represented by proper etale groupoids in the category of Hausdorff spaces. Two of these groupoids represent the sam e orbispace if they are Morita equivalent. However\, Morita equivalences are generally not pseudo-invertible in this 2-category\, so we consider th e bicategory of fractions with respect to Morita equivalences.\n\n \n\nFor a pair of paracompact locally compact orbigroupoids G and H\, with G orbi t-compact\, we want to study the mapping groupoid [G\, H] of arrows and 2- cells in the bicategory of fractions. The question we want to address is h ow to define a topology on these mapping groupoids to obtain mapping objec ts for the bicategory of orbispaces. This question was addressed in [Chen] \, but not in terms of orbigroupoids\, and with only partial answers.\n\n\ nWe will present the following results:\n\n\n1. When the orbifold G is com pact\, we define a topology on [G\,H] to obtain a topological groupoid OMa p(G\, H)\, which is Morita equivalent to an orbigroupoid. To obtain a Mori ta equivalent orbigroupoid\, we need to restrict ourselves to so-called ad missible maps to form AMap(G\,H)\, and\n\n\nOrbispaces(K × G\, H) is equi valent to Orbispaces(K\, AMap(G\, H)).\n\n\nSo AMap(G\,H) is an exponentia l object in the bicategory of orbispaces.\n\n\n2. We will also show that A Map(G\,H) thus defined provides the bicategory of orbit-compact orbispaces with bicategorical enrichment over the bicategory of orbispaces: composit ion can be given as a generalized map (an arrow in the bicategory of fract ions) of orbispaces.\n\nIn this talk I will discuss how this work extends the work done by Chen and I will show several examples. This is joint work with Laura Scull.\n\n\n[Chen] Weimin Chen\, On a notion of maps between o rbifolds I: function spaces\, Communications in Contemporary Mathematics 8 (2006)\, pp. 569-620.\n\n\n[Moerdijk-P] I. Moerdijk\, D.A. Pronk\, Orbifo lds\, sheaves and groupoids\, K-Theory 12 (1997)\, pp. 3-21.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Ingo Runkel (Hamburg University) DTSTART:20210519T180000Z DTEND:20210519T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/26 DESCRIPTION:Title: Area dependent 2d QFT\nby Ingo Runkel (Hamburg Univer sity) as part of Categories seminar UNAM\n\n\nAbstract\nOne beautiful resu lt one learns early when studying the functorial approach to TQFTs is that in two dimensions\, such theories are the same as commutative Frobenius a lgebras. One furthermore learns that in functorial TQFTs\, state spaces ar e necessarily finite-dimensional. There are several ways to overcome this restriction\, and in two dimensions\, one possibility is to equip the surf aces with an area. The most famous example of such a QFT is 2d Yang Mills theory for a compact gauge group. Surprisingly\, one finds that a very sim ilar classification to the 2d TQFT still holds. Time permitting\, I will a lso discuss defects in 2d area dependent QFTs\, of which Wilson line obser vables in 2d Yang Mills are an example. This is joint work with Lorant Sze gedy.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Gurski (Case Western Reserve University) DTSTART:20211006T180000Z DTEND:20211006T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/27 DESCRIPTION:Title: The truncated sphere spectrum in homological algebra\ nby Nick Gurski (Case Western Reserve University) as part of Categories se minar UNAM\n\n\nAbstract\nThe stable homotopy hypothesis predicts that "st able" n-groupoids should model stable homotopy n-types. Stability on the c ategorical side is usually interpreted as a symmetric monoidal structure w ith invertible objects\, while on the topological side these are spectra ( instead of spaces) with homotopy groups concentrated between dimensions 0 and n. Proving this hypothesis is the first step in comparing spectra and higher categories rather than the goal. I will discuss a very special case of going further than the hypothesis when n=1 and 2 (the dimensions in wh ich the stable homotopy hypothesis is a theorem rather than just conjectur e)\, namely what categorical objects correspond to the truncated sphere sp ectrum. We will recover some classical algebra for n=1\, and a complicated generalization of that algebra for n=2 that I don't think we really under stand yet.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleks Kissinger (Oxford) DTSTART:20211013T180000Z DTEND:20211013T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/28 DESCRIPTION:Title: A categorical logic of consistency for causal processes\nby Aleks Kissinger (Oxford) as part of Categories seminar UNAM\n\n\nAb stract\nI will talk about some recent developments in the framework of "bl ack box causal reasoning". In this minimal setting\, we assume access to s ome abstract process and attempt to describe\, quantify\, or prove propert ies about the causal relationships between its inputs and outputs. This wo rks both for first-order processes\, which can capture e.g. a device share d by multiple agents\, or higher-order processes\, which can capture the u niverse in which those agents live. This higher-order picture leads natura lly to the structure of a *-autonomous category. Whereas first order proce sses (e.g. quantum gates) only have two natural notions of composition (in series and in parallel)\, higher-order processes have a rich and nuanced notion of composition that must avoid inconsistency in the composition of causal paths. I will show how provability in the internal logic of a *-aut onomous category gives sufficient conditions for causal consistency\, then discuss several avenues of extension toward a complete characterisation.\ n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Toby St. Clere Smithe (Oxford/Topos Institute) DTSTART:20211020T180000Z DTEND:20211020T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/29 DESCRIPTION:Title: The changing shapes of cybercats\nby Toby St. Clere S mithe (Oxford/Topos Institute) as part of Categories seminar UNAM\n\n\nAbs tract\nThe ménagerie of categorical models of dynamical systems is becomi ng a veritable zoo\, but what makes all these animals tick? In this talk\, I will introduce a new specimen: a symmetric monoidal category of continu ous-time open Markov processes with general state spaces. I will explain h ow this category is obtained from a category of "continuous-time coalgebra s" opindexed by polynomials\, and describe how this recipe also gives cate gories of nondeterministic systems in arbitrary (continuous) time. These n ew specimens are motivated by the cybernetic question of how to model syst ems that are continuously performing approximate Bayesian inference. I wil l therefore sketch why their better-known cousins weren't quite up to the job\, and show that our new SMC admits Bayesian inversion. Finally\, I wil l attempt to make contact with the the "open games" branch of categorical cybernetics\, asking what makes the shapes of our structures seem so simil ar-but-different\, and how we might begin to understand systems nested wit hin systems.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Akif Mehmet Erdal (Yeditepe University) DTSTART:20211027T180000Z DTEND:20211027T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/30 DESCRIPTION:Title: Actions of monoidal categories and (co)stabilization\ nby Akif Mehmet Erdal (Yeditepe University) as part of Categories seminar UNAM\n\n\nAbstract\nSuppose that we are given a collection of endofunctors (e.g.\, loop space functors) on a pointed homotopy theory $A$. We will c all such a homotopy theory stable if it is stable under these functors\; t hat is\, each functor is an auto-equivaence. Alternatively\, one can consi der this as an action of a monoidal category\, and in this case stable mea ns the monoidal category acts by auto-equivalences. In this talk\, we disc uss actions of monoidal categories on relative categories\, and applicatio ns in stable homotopy theory. Given a monoidal category $I$ and an $I$-rel ative category $A$ (that is\, a relative category with an $I$-action)\, th e (co)stabilization of $A$ is an $I$-relative category that is universal with respect to the property that every object of $I$ acts by auto-equival ences (on homotopy category). We introduce a notion of $I$-equivariance fo r functors between $I$-relative categories and give constructions of stabi lization and costabilization in terms of (weak) ends and coends in a $2$-c ategory of $I$-relative categories and $I$-equivariant relative functors. Several examples existing in the literature\, including various categories of spectra and cohomology theories with exotic gradings\, can be seen as particular instances of this setting after fixing $A$ and the $I$-action o n it. In particular\, categories of sequential spectra\, coordinate free s pectra\, genuine equivariant spectra\, genuine parameterized spectra (inde xed by vector bundles)\, and cohomology theories with various exotic gradi ngs can be obtained in terms of weak ends. On the other hand\, the costabi lization of a relative category with respect to an action gives a stable r elative category akin to a version of the Spanier-Whitehead category. This is a joint work with Özgün Ünlü.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Gogioso (Oxord) DTSTART:20211103T190000Z DTEND:20211103T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/31 DESCRIPTION:by Stefano Gogioso (Oxord) as part of Categories seminar UNAM\ n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Leinster (University of Edimburgh) DTSTART:20211117T190000Z DTEND:20211117T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/33 DESCRIPTION:Title: Large sets\nby Tom Leinster (University of Edimburgh) as part of Categories seminar UNAM\n\n\nAbstract\nLawvere's Elementary Th eory of the Category of Sets (ETCS) was conceived as an alternative to ZFC that represents more accurately how mathematicians actually do mathematic s. But can ETCS do everything that ZFC can? I will present some evidence t hat yes\, it can. Specifically\, I will sketch how the beginning of the th eory of large cardinals looks in ETCS\, describing both the similarities a nd the differences between the two approaches. No prior familiarity with E TCS will be assumed.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexei Davydov (Ohio University) DTSTART:20211201T190000Z DTEND:20211201T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/34 DESCRIPTION:Title: Autoequivalences of tensor categories and Bogomolov multi plier\nby Alexei Davydov (Ohio University) as part of Categories semin ar UNAM\n\n\nAbstract\nThe Bogomolov multiplier of a group is the subgroup of its Schur multiplier\, of classes with vanishing restrictions to all a belian subgroups. Bogomolov multiplier plays an important role in biration al algebraic geometry (Noether problem) and in topology (groups of singula r submanifolds).\n\n\nIn the talk explain how Bogomolov multiplier appears in the study of soft symmetries of modular tensor categories. Here soft m eans that a symmetry does not move objects. More precisely\, I will interp ret Bogomolov multiplier as a normal subgroup of the group of soft autoequ ivalences of the Drinfeld double.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Riehl (Johns Hopkins University) DTSTART:20220330T190000Z DTEND:20220330T200000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/35 DESCRIPTION:Title: Elements of ∞-Category Theory\nby Emily Riehl (John s Hopkins University) as part of Categories seminar UNAM\n\n\nAbstract\nCo nfusingly for the uninitiated\, experts in weak infinite-dimensional categ ory theory make use of different definitions of an ∞-category\, and theo rems in the ∞-categorical literature are often proven "analytically"\, i n reference to the combinatorial specifications of a particular model. In this talk\, we present a new point of view on the foundations of ∞-categ ory theory\, which allows us to develop the basic theory of ∞-categories --- adjunctions\, limits and colimits\, co/cartesian fibrations\, and poi ntwise Kan extensions --- "synthetically" starting from axioms that descri be an ∞-cosmos\, the infinite-dimensional category in which ∞-categori es live as objects. We demonstrate that the theorems proven in this manner are "model-independent"\, i.e.\, invariant under change of model. Moreove r\, there is a formal language with the feature that any statement about ∞-categories that is expressible in that language is also invariant unde r change of model\, regardless of whether it is proven through synthetic o r analytic techniques. This is joint work with Dominic Verity.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/35/ END:VEVENT BEGIN:VEVENT SUMMARY:David Roberts DTSTART:20220406T230000Z DTEND:20220407T000000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/37 DESCRIPTION:Title: Geometric string structures on homogeneous spaces\nby David Roberts as part of Categories seminar UNAM\n\n\nAbstract\nThe notio n of string structure on a space X goes back to work in the 1980s\, partic ularly of Killingback\, starting as an analogue of a spin structure on the loop space LX. In the decades since\, increasingly refined versions of st ring structures have been defined. Ultimately\, one wants to have a full-f ledged String 2-bundle with connection\, a structure from higher geometry\ , which combines differential geometry and category-theoretic structures. A half-way step\, due to Waldorf\, is known as a "geometric string structu re". Giving examples of such structures\, despite existence being know\, h as been an outstanding problem for some time. In this talk\, I will descri be joint work with Raymond Vozzo on our framework for working with the str ucture that obstruct the existence of a geometric string structure\, which is a 2-gerbe with connection\, as well as give a general construction of geometric string structures on reductive homogeneous spaces.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Urs Schreiber (NYU Abu Dhabi and Czech Academy of Siences) DTSTART:20220413T170000Z DTEND:20220413T180000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/38 DESCRIPTION:Title: Anyonic Defect Branes in Twisted Equivariant Differential K-Theory\nby Urs Schreiber (NYU Abu Dhabi and Czech Academy of Sience s) as part of Categories seminar UNAM\n\n\nAbstract\nI'll start with an ex position of higher equivariant principal bundle\ntheory\, using a convenie nt category/homotopy-theoretic approach\,\nfollowing the notes here:\nncat lab.org/schreiber/show/Higher+and+Equivariant+Bundles . By way of\nexample and application\, I'll then show how this provides a pleasantly\ntranspar ent way to understand:\n 1. the CPT-twisting of equivariant K-theory\, whi ch has come to be\nknown as the "10-fold way"\,\n 2. the neglected twistin g of equivariant K-theory by "inner local\nsystems" appearing inside orbi- singularities.\nI'll close by briefly indicating how\, under the interpret ation of\nK-cohomology as D-brane charge\, these two facts have remarkable \nconsequences for the physics of exotic "defect branes" in string\ntheory (arxiv.org/abs/2203.11838).\nThis is joint work with H. Sati. Slides will become available at:\nncatlab.org/schreiber/show/Anyonic+defect+branes+in +TED-K-theory .\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Rowell (Texas A&M) DTSTART:20220518T180000Z DTEND:20220518T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/39 DESCRIPTION:Title: Classification of Modular Fusion Categories\nby Eric Rowell (Texas A&M) as part of Categories seminar UNAM\n\n\nAbstract\nThe c lassification of modular fusion categories has been pursued from various p erspectives over the last 20 years\, and provides a hands-on introduction to the intricacies of applied category theory. In this lecture we will rev iew what is known\, some open problems\, and a few of the successful techn iques from category theory\, algebraic geometry\, number theory and repres entation theory.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Plavnik (How to zest your modular categories) DTSTART:20220601T180000Z DTEND:20220601T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/40 DESCRIPTION:Title: Modular categories arise naturally in many areas of mathe matics\, such as conformal field theory\, representations of braid groups\ , quantum groups\, and Hopf algebras\, and low dimensional topology\, and they have important applications in condensed matter phys\nby Julia Pl avnik (How to zest your modular categories) as part of Categories seminar UNAM\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/40/ END:VEVENT BEGIN:VEVENT SUMMARY:César Galindo (University of Hamburg/Universidad de los Andes) DTSTART:20220615T180000Z DTEND:20220615T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/41 DESCRIPTION:Title: Equivariant fusion categories\nby César Galindo (Uni versity of Hamburg/Universidad de los Andes) as part of Categories seminar UNAM\n\n\nAbstract\nIn this talk\, I will report results from joint work with Corey Jones\, https://arxiv.org/abs/2111.09116. We describe all fusio n subcategories of the equivariantization of group action on a fusion cate gory. As applications\, we classify the Hopf subalgebras of Kac-Paljutkin type and recover the Naidu-Nikshych-Witherspoon classification of the fusi on subcategories of the representation category of a twisted quantum doubl e of a finite group.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Samperton (Purdue) DTSTART:20220622T180000Z DTEND:20220622T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/42 DESCRIPTION:Title: Anyons\, defects\, and computational complexity\nby E ric Samperton (Purdue) as part of Categories seminar UNAM\n\n\nAbstract\nT opological invariants of objects like knots and 3-manifolds are only pract ically useful insofar as one is able to efficiently compute them. So\, for any given invariant\, it is interesting to try to quantify its computatio nal complexity. \nBeyond just being an interesting "theoretical" problem\, such complexity-theoretic issues are foundational to topological quantum computation. I'll spend most of the talk introducing these ideas. Time per mitting\, I'll report on work-in-progress with Colleen Delaney that says\, roughly: coupling a finite group gauge symmetry to a topological quantum computer can not create a more powerful computer.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Colleen Delaney (University of Indiana Bloomington) DTSTART:20220629T180000Z DTEND:20220629T190000Z DTSTAMP:20260404T094546Z UID:CategoriesatUNAM/43 DESCRIPTION:Title: Zesting\, modular isotopes\, and Reshetikhin-Turaev invar iants\nby Colleen Delaney (University of Indiana Bloomington) as part of Categories seminar UNAM\n\n\nAbstract\nI'll give an overview of the zes ting construction on ribbon fusion categories through the lens of topologi cal phases of matter and topological quantum computation. In particular\, we'll see that Reshetekhin-Turaev invariants of knots and links transform in a nice way under zesting. As an application I will explain how zesting gives a new way to understand Mignard and Schauenburg's ``modular isotopes " -- examples of different modular categories with the same modular data.\ n \nThis talk is based on joint work with Parsa Bonderson\, Cesar Galindo\ , Sung Kim\, Julia Plavnik\, Eric Rowell\, Alan Tran\, Zhenghan Wang\, and Qing Zhang.\n LOCATION:https://stable.researchseminars.org/talk/CategoriesatUNAM/43/ END:VEVENT END:VCALENDAR