BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christian Blohmann (MPIM Bonn) DTSTART:20230207T213000Z DTEND:20230207T230000Z DTSTAMP:20260314T090948Z UID:tandg/1 DESCRIPTION:Title: El astic diffeological spaces\nby Christian Blohmann (MPIM Bonn) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nI will in troduce a class of diffeological spaces\, called elastic\, on which the le ft Kan extension of the tangent functor of smooth manifolds defines an abs tract tangent functor in the sense of Rosický. On elastic spaces there is a natural Cartan calculus\, consisting of vector fields and differential forms\, together with the Lie bracket\, de Rham differential\, inner deriv ative\, and Lie derivative\, satisfying the usual graded commutation relat ions. Elastic spaces are closed under arbitrary coproducts\, finite produc ts\, and retracts. Examples include manifolds with corners and cusps\, dif feological groups and diffeological vector spaces with a mild extra condit ion\, mapping spaces between smooth manifolds\, and spaces of sections of smooth fiber bundles.\n LOCATION:https://researchseminars.org/talk/tandg/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Mazel-Gee (Caltech) DTSTART:20230221T213000Z DTEND:20230221T230000Z DTSTAMP:20260314T090948Z UID:tandg/2 DESCRIPTION:Title: To wards knot homology for 3-manifolds\nby Aaron Mazel-Gee (Caltech) as p art of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe J ones polynomial is an invariant of knots in R^3. Following a proposal of W itten\, it was extended to knots in 3-manifolds by Reshetikhin–Turaev us ing quantum groups. Khovanov homology is a categorification of the Jones p olynomial of a knot in R^3\, analogously to how ordinary homology is a cat egorification of the Euler characteristic of a space. It is a major open p roblem to extend Khovanov homology to knots in 3-manifolds. In this talk\, I will explain forthcoming work towards solving this problem\, joint with Leon Liu\, David Reutter\, Catharina Stroppel\, and Paul Wedrich. Roughly speaking\, our contribution amounts to the first instance of a braiding o n 2-representations of a categorified quantum group. More precisely\, we c onstruct a braided (∞\,2)-category that simultaneously incorporates all of Rouquier's braid group actions on Hecke categories in type A\, articula ting a novel compatibility among them.\n LOCATION:https://researchseminars.org/talk/tandg/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Domenico Fiorenza (Sapienza University of Rome) DTSTART:20230307T213000Z DTEND:20230307T230000Z DTSTAMP:20260314T090948Z UID:tandg/3 DESCRIPTION:Title: St ring bordism invariants in dimension 3 from U(1)-valued TQFTs\nby Dome nico Fiorenza (Sapienza University of Rome) as part of Topology and Geomet ry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe third string bordism group is known to be $\\mathbb{Z}/24\\mathbb{Z}$. Using Waldorf's notion of a ge ometric string structure on a manifold\, Bunke–Naumann and Redden have e xhibited integral formulas involving the Chern–Weil form representative of the first Pontryagin class and the canonical 3-form of a geometric stri ng structure that realize the isomorphism ${\\rm Bord}_3^{\\rm String} \\t o \\mathbb{Z}/24\\mathbb{Z}$ (these formulas have been recently rediscover ed by Gaiotto–Johnson-Freyd–Witten). In the talk I will show how these formulas naturally emerge when one considers the U(1)-valued 3d TQFTs ass ociated with the classifying stacks of Spin bundles with connection and of String bundles with geometric structure. Joint work with Eugenio Landi (< a href="https://arxiv.org/abs/2209.12933v2">arXiv:2209.12933).\n LOCATION:https://researchseminars.org/talk/tandg/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Emilio Minichiello (CUNY GC) DTSTART:20230404T203000Z DTEND:20230404T220000Z DTSTAMP:20260314T090948Z UID:tandg/4 DESCRIPTION:Title: Di ffeological Principal Bundles\, Čech Cohomology and Principal Infinity Bu ndles\nby Emilio Minichiello (CUNY GC) as part of Topology and Geometr y Seminar (Texas\, Kansas)\n\n\nAbstract\nThanks to a result of Baez and H offnung\, the category of diffeological spaces is equivalent to the catego ry of concrete sheaves on the site of cartesian spaces. By thinking of di ffeological spaces as kinds of sheaves\, we can therefore think of diffeol ogical spaces as kinds of infinity sheaves. We do this by using a model c ategory presentation of the infinity category of infinity sheaves on carte sian spaces\, and cofibrantly replacing a diffeological space within it. By doing this\, we obtain a new generalized cocycle construction for diffe ological principal bundles\, a new version of Čech cohomology for diffeol ogical spaces that can be compared very directly with two other versions a ppearing in the literature\, which is precisely infinity sheaf cohomology\ , and we show that the nerve of the category of diffeological principal G- bundles over a diffeological space X for a diffeological group G is weak e quivalent to the nerve of the category of G-principal infinity bundles ove r X.\n LOCATION:https://researchseminars.org/talk/tandg/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Fraser (Wichita State University) DTSTART:20230411T203000Z DTEND:20230411T220000Z DTSTAMP:20260314T090948Z UID:tandg/5 DESCRIPTION:Title: Fo urier analysis in Diophantine approximation\nby Robert Fraser (Wichita State University) as part of Topology and Geometry Seminar (Texas\, Kansa s)\n\n\nAbstract\nA real number $x$ is said to be normal if the s equence $a^n x$ is uniformly distributed modulo 1 for every integer $a≥2 $.\nAlthough Lebesgue-almost all numbers are normal\, the problem determin ing whether specific irrational numbers such as $e$ and $π$ are normal is extremely difficult.\nHowever\, techniques from Fourier analysis and geom etric measure theory can be used to show that certain “thin” subsets o f $\\mathbb{R}$ must contain normal numbers.\n LOCATION:https://researchseminars.org/talk/tandg/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Till Heine (Hamburg) DTSTART:20230418T203000Z DTEND:20230418T220000Z DTSTAMP:20260314T090948Z UID:tandg/6 DESCRIPTION:Title: Th e Dwyer Kan-correspondence and its categorification\nby Till Heine (Ha mburg) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbst ract\nExtensions of the Dold-Kan correspondence for the duplicial and (par a)cyclic index categories were introduced by Dwyer and Kan.\nBuilding on t he categorification of the Dold-Kan correspondence by Dyckerhoff\, we cate gorify the duplicial case by establishing an equivalence between the $\\in fty$-category of $2$-duplicial stable $\\infty$-categories and the $\\inft y$-category of connective chain complexes of stable $\\infty$-categories w ith right adjoints. \nI will further explain the current progress to wards a conjectured correspondence between $2$-paracyclic stable $\\infty$ -categories and connective spherical complexes.\nExamples of the latter na turally arise from the study of perverse schobers. \narXiv:2303.03653.\n LOCATION:https://researchseminars.org/talk/tandg/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Felix Wierstra (Korteweg-de Vries Institute for Mathematics\, Univ ersity of Amsterdam) DTSTART:20230425T203000Z DTEND:20230425T220000Z DTSTAMP:20260314T090948Z UID:tandg/7 DESCRIPTION:Title: A recognition principle for iterated suspensions as coalgebras over the litt le cubes operad\nby Felix Wierstra (Korteweg-de Vries Institute for Ma thematics\, University of Amsterdam) as part of Topology and Geometry Semi nar (Texas\, Kansas)\n\n\nAbstract\nIn this talk I will discus a recogniti on principle for iterated suspensions as coalgebras over the little cubes operad.\nThis is joint work with Oisín Flynn-Connolly and José Moreno-Fe rnádez.\n LOCATION:https://researchseminars.org/talk/tandg/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Kinard DTSTART:20231003T180000Z DTEND:20231003T195000Z DTSTAMP:20260314T090948Z UID:tandg/8 DESCRIPTION:Title: Sh eaves as a Data Structure\nby Rachel Kinard as part of Topology and Ge ometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe word “Topology”\, b est known for its association to the study of invariants of an abstract sp ace\, is a branch of Pure Mathematics whose best known applications are fo und in Physics (Quantum Mechanics\, Quantum Field Theory). Very rarely doe s a Pure Math Field find such as Topology find relevance in a world of Big Data and computer automation. Data Science utilizes these powerful topolo gical invariants to quickly gather information about complex data spaces i n a brave new area of study called “Topological Data Analysis” or TDA. Given a set of data points\, the nerve construction produces a simplicial complex that can be analyzed to understand important characteristics of t he data. I will provide an introduction to TDA and a few examples of surpr ising Data Science applications.\n LOCATION:https://researchseminars.org/talk/tandg/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Kinard DTSTART:20231005T190000Z DTEND:20231005T195000Z DTSTAMP:20260314T090948Z UID:tandg/9 DESCRIPTION:Title: Sh eaves as a Data Structure (Part 2)\nby Rachel Kinard as part of Topolo gy and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nWe continue our di scussion with an example of “Path-Optimization Sheaves” (https://arxiv .org/abs/2012.05974)\;\nan alternative approach to classical Dijkstra’s Algorithm\, paths from a source vertex to sink vertex in a graph are revea led as Sections of the Path-finding Sheaf.\n\nTables\, Arrays\, and Matric es are useful in data storage and manipulation\, employing operations and methods from Numerical Linear Algebra for computer algorithm development.\ nRecent advances in computer hardware and high performance computing invit e us to explore more advanced data structures\,\nsuch as sheaves and the u se of sheaf operations for more sophisticated computations.\nAbstractly\, Mathematical Sheaves can be used to track data associated to the open sets of a topological space\;\npractically\, sheaves as an advanced data struc ture provide a framework for the manipulation and optimization of complex systems of interrelated information.\nDo we ever really get to see a concr ete example?\nI will point to several recent examples of (1) the use of sh eaves as a tool for data organization\, and (2) the use of sheaves to gain additional information about a system.\n\nNotice the nonstandard day (Thu rsday) and the nonstandard time slot (2 pm Central Time).\n\nContinuation of the talk given on October 3 (https://researchseminars.org/talk/tandg/8/ ).\n\nRecording of Part I is available here: https://dmitripavlov.org/2023 -10-03.mp4\n LOCATION:https://researchseminars.org/talk/tandg/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Arun Debray (Purdue University) DTSTART:20231024T180000Z DTEND:20231024T195000Z DTSTAMP:20260314T090948Z UID:tandg/10 DESCRIPTION:Title: C onstructing the Virasoro groups using differential cohomology\nby Arun Debray (Purdue University) as part of Topology and Geometry Seminar (Texa s\, Kansas)\n\n\nAbstract\nAbstract: The Virasoro groups are a family of c entral extensions of ${\\rm Diff}^+(S^1)$ by the circle group $\\bf T$.\nI n this talk I will discuss recent work\, joint with Yu Leon Liu and Christ oph Weis\,\nconstructing these groups by beginning with a lift of the firs t Pontrjagin class to "off-diagonal" differential cohomology\,\nthen trans gressing it to obtain a central extension.\nAlong the way\, I will discuss what the Virasoro extensions are and how to recognize them\;\na brief int roduction to differential cohomology\; and lifts of characteristic classes to differential cohomology.\n LOCATION:https://researchseminars.org/talk/tandg/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Severin Bunk (University of Oxford) DTSTART:20231107T190000Z DTEND:20231107T205000Z DTSTAMP:20260314T090948Z UID:tandg/11 DESCRIPTION:Title: S mooth higher symmetries groups and the geometry of Deligne cohomology\ nby Severin Bunk (University of Oxford) as part of Topology and Geometry S eminar (Texas\, Kansas)\n\n\nAbstract\nWe construct the smooth higher grou p of symmetries of any higher geometric structure on manifolds. Via a univ ersal property\, this classifies equivariant structures on the geometry. W e present a general construction of moduli stacks of solutions in higher-g eometric field theories and provide a criterion for when two such moduli s tacks are equivalent. We then apply this to the study of generalised Ricci solitons\, or NSNS supergravity: this theory has two different formulatio ns\, originating in higher geometry and generalised geometry\, respectivel y. These formulations produce inequivalent field configurations and inequi valent symmetries. We resolve this discrepancy by showing that their modul i stacks are equivalent. This is joint work with C. Shahbazi.\n LOCATION:https://researchseminars.org/talk/tandg/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Araminta Amabel (Northwestern University) DTSTART:20231114T190000Z DTEND:20231114T205000Z DTSTAMP:20260314T090948Z UID:tandg/12 DESCRIPTION:Title: A factorization homology approach to line operators\nby Araminta Amabel (Northwestern University) as part of Topology and Geometry Seminar (Texas \, Kansas)\n\n\nAbstract\nThere are several mathematical models for field theories\, including the functorial approach of Atiyah–Segal and the fac torization algebra approach of Costello–Gwilliam.\nI'll discuss how to t hink about line operators in these contexts\, and the different strengths of each method.\nMotivated by work of Freed–Moore–Teleman\, I'll expla in how to exploit both models to say something about certain gauge theorie s.\nThis is based on joint work with Owen Gwilliam.\n LOCATION:https://researchseminars.org/talk/tandg/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Tooby-Smith (Cornell University) DTSTART:20231121T190000Z DTEND:20231121T205000Z DTSTAMP:20260314T090948Z UID:tandg/13 DESCRIPTION:Title: S mooth generalized symmetries of quantum field theories\nby Joseph Toob y-Smith (Cornell University) as part of Topology and Geometry Seminar (Tex as\, Kansas)\n\n\nAbstract\nIn this talk\, based on joint work with Ben Gr ipaios and Oscar Randal-Williams (arXiv:2209.13524 and 2310.16090)\, we wi ll\, with help from the geometric cobordism hypothesis\, define and study invertible smooth generalized symmetries of field theories within the fram ework of higher category theory. We will show the existence of a new type of anomaly that afflicts global symmetries even before trying to gauge\, w e call these anomalies “smoothness anomalies”. In addition\, we will s ee that d-dimensional QFTs when considered collectively can have d-form sy mmetries\, which goes beyond the (d-1)-form symmetries known to physicists for individual QFTs. We will also touch on aspects of gauging global symm etries in the case of topological quantum field theories.\n LOCATION:https://researchseminars.org/talk/tandg/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Berwick-Evans (University of Illinois Urbana-Champaign) DTSTART:20231128T190000Z DTEND:20231128T205000Z DTSTAMP:20260314T090948Z UID:tandg/14 DESCRIPTION:Title: T wisted equivariant Thom classes in topology and physics\nby Daniel Ber wick-Evans (University of Illinois Urbana-Champaign) as part of Topology a nd Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn their seminal work\ , Mathai and Quillen explained how free fermion theories can be used to co nstruct cocycle representatives of Thom classes in de Rham cohomology. Aft er reviewing this idea\, I will describe several avenues of generalization that lead to cocycle representatives of Thom classes in twisted equivaria nt KR-theory and (conjecturally) in equivariant elliptic cohomology. I wil l further describe nice properties enjoyed by these cocycle representative s\, e.g.\, compatibility with (twisted) power operations. This is joint wo rk with combinations of Tobi Barthel\, Millie Deaton\, Meng Guo\, Yigal Ka mel\, Hui Langwen\, Kiran Luecke\, Alex Pacun\, and Nat Stapleton.\n LOCATION:https://researchseminars.org/talk/tandg/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Grigorios Giotopoulos (NYU Abu Dhabi) DTSTART:20240213T160000Z DTEND:20240213T173000Z DTSTAMP:20260314T090948Z UID:tandg/15 DESCRIPTION:Title: S mooth sets as a convenient setting for Lagrangian field theory\nby Gri gorios Giotopoulos (NYU Abu Dhabi) as part of Topology and Geometry Semina r (Texas\, Kansas)\n\n\nAbstract\nIn this talk\, I will indicate how the s heaf topos of smooth sets serves as a sufficiently powerful and convenient context to host classical (bosonic) Lagrangian field theory. As motivatio n\, I will recall the textbook description of variational Lagrangian field theory\, and list desiderata for an ambient category in which this can ri gorously be phrased. I will then explain how sheaves over Cartesian spaces naturally satisfy all the desiderata\, and furthermore allow to rigorousl y formalize several more field theoretic concepts. Time permitting\, I wil l indicate how the setting naturally generalizes to include the descriptio n of (perturbative) infinitesimal structure\, fermionic fields\, and (gaug e) fields with internal symmetries. This is based on joint work with Hisha m Sati.\n LOCATION:https://researchseminars.org/talk/tandg/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Luigi Alfonsi (University of Hertfordshire) DTSTART:20240319T203000Z DTEND:20240319T220000Z DTSTAMP:20260314T090948Z UID:tandg/16 DESCRIPTION:Title: B atalin–Vilkovisky formalism beyond perturbation theory via derived geome try\nby Luigi Alfonsi (University of Hertfordshire) as part of Topolog y and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn this talk I will discuss applications of derived differential geometry to study a non-pert urbative generalisation of classical Batalin–Vilkovisky (BV-)formalism. First\, I will describe the current state of the art of the geometry of pe rturbative BV-theory. Then\, I will introduce a simple model of derived di fferential geometry\, whose geometric objects are formal derived smooth st acks (i.e. stacks on formal derived smooth manifolds)\, and which is obtai ned by applying Töen-Vezzosi’s homotopical algebraic geometry to the th eory of derived manifolds of Spivak and Carchedi-Steffens. I will show how derived differential geometry is able to capture aspects of non-perturbat ive BV-theory by means of examples in the cases of scalar field theory and Yang-Mills theory.\n LOCATION:https://researchseminars.org/talk/tandg/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Pelle Steffens (Technische Universität München) DTSTART:20240326T203000Z DTEND:20240326T220000Z DTSTAMP:20260314T090948Z UID:tandg/17 DESCRIPTION:Title: D ifferential geometric PDE moduli spaces: derived enhancements\, ellipticit y and representability\nby Pelle Steffens (Technische Universität Mü nchen) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbst ract\nAll sorts of algebro-geometric moduli spaces (of stable curves\, sta ble sheaves on a CY 3-folds\, flat bundles\, Higgs bundles...) are best un derstood as objects in derived geometry. Derived enhancements of classical moduli spaces give transparent intrinsic meaning to previously ad-hoc str uctures pertaining to\, for instance\, enumerative geometry and are indisp ensable for more advanced constructions\, such as categorification of enum erative invariants and (algebraic) deformation quantization of derived sym plectic structures. I will outline how to construct such enhancements for moduli spaces in global analysis and mathematical physics\, that is\, solu tion spaces of PDEs in the framework of derived ${\\rm C}^\\infty$ geometr y and discuss the elliptic representability theorem\, which guarantees tha t\, for elliptic equations\, these derived moduli stacks are bona fide geo metric objects (Artin stacks at worst). If time permits some applications to enumerative geometry (symplectic Gromov-Witten and Floer theory) and de rived symplectic geometry (the global BV formalism).\n LOCATION:https://researchseminars.org/talk/tandg/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Clough (NYU Abu Dhabi) DTSTART:20240416T150000Z DTEND:20240416T163000Z DTSTAMP:20260314T090948Z UID:tandg/18 DESCRIPTION:Title: H omotopical calculi and the smooth Oka principle\nby Adrian Clough (NYU Abu Dhabi) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\ nAbstract\nI will present a new proof of Berwick-Evans\, Boavida de Brito\ , and Pavlov’s theorem that for any smooth manifold A\, and any sheaf X on the site of smooth manifolds\, the mapping sheaf Hom(A\,X) has the corr ect homotopy type. The talk will focus on the main innovation of this proo f\, namely the use of test categories to construct homotopical calculi on locally contractible ∞-toposes. With this tool in hand I will explain ho w a suitable homotopical calculus may be constructed on the ∞-topos of s heaves on the site of smooth manifolds using a new diffeology on the stand ard simplices due to Kihara. The main theorem follows using a similar argu ment that for any CW-complex A\, and any topological space X the set of co ntinuous maps Hom(A\,X) equipped with compact-open topology models the map ping-homotopy-type map(A\,X).\n LOCATION:https://researchseminars.org/talk/tandg/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Darrick Lee (University of Oxford) DTSTART:20240423T150000Z DTEND:20240423T163000Z DTSTAMP:20260314T090948Z UID:tandg/19 DESCRIPTION:Title: C haracterizing paths and surfaces via (higher) holonomy\nby Darrick Lee (University of Oxford) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nClassical vector valued paths are widespread across pure and applied mathematics: from stochastic processes in probability to time series data in machine learning. Parallel transport of such paths in principal G-bundles have provided an effective method to characterise suc h paths. In this talk\, we provide a brief overview of these results and t heir applications. We will then discuss recent work on extending this fram ework to characterizing random and possibly nonsmooth surfaces using surfa ce holonomy. This is based on joint work with Harald Oberhauser.\n LOCATION:https://researchseminars.org/talk/tandg/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Lebovic (University of Oregon) DTSTART:20240430T203000Z DTEND:20240430T220000Z DTSTAMP:20260314T090948Z UID:tandg/20 DESCRIPTION:Title: I terated K-theory and Functorial Field Theory\nby Jacob Lebovic (Univer sity of Oregon) as part of Topology and Geometry Seminar (Texas\, Kansas)\ n\n\nAbstract\nUsing previous work by Bass\, Dundas\, and Rognes giving a geometric model of the iterated K-theory spectrum K(ku) in terms of bundle s of Kapranov-Voevodsky 2-vector spaces\, and recent work by Grady and Pav lov providing a rigorous foundation for fully-extended functorial field th eories\, we construct a model of K(ku) in terms of 2-dimensional functoria l field theories valued in KV 2-vector spaces.\n LOCATION:https://researchseminars.org/talk/tandg/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Grady (Wichita State University) DTSTART:20240910T200000Z DTEND:20240910T210000Z DTSTAMP:20260314T090948Z UID:tandg/21 DESCRIPTION:Title: D eformation classes of invertible field theories and the Freed–Hopkins co njecture\nby Dan Grady (Wichita State University) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn their seminal work \, Freed and Hopkins studied the moduli space of topological\, reflection positive\, invertible\, Euclidean field theories\, providing a complete cl assification in terms of certain objects arising in stable homotopy theory . In this work\, it was also conjectured that a similar classification ho lds in the case of nontopological field theories\, and this conjecture is already being used in a variety of applications to condensed matter physic s. In this talk\, I will discuss a recent result which provides an affirm ative answer to this conjecture. I will begin by reviewing motivation and background on reflection positive theories. Then I will state the conjec ture and sketch of the proof.\n LOCATION:https://researchseminars.org/talk/tandg/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jiaqi Fu (Université Paul Sabatier\, Toulouse\, France) DTSTART:20241106T160000Z DTEND:20241106T173000Z DTSTAMP:20260314T090948Z UID:tandg/22 DESCRIPTION:Title: A filtered Koszul duality of partition Lie algebras(-oids)\nby Jiaqi Fu (Université Paul Sabatier\, Toulouse\, France) as part of Topology and G eometry Seminar (Texas\, Kansas)\n\n\nAbstract\nPartition Lie algebras are sophisticated algebraic objects introduced by Brantner–Mathew to contro l infinitesimal deformations in positive characteristics. This talk will p resent a Koszul duality between partition Lie algebras and specific comple te filtered derived rings. This duality helps to understand the homotopy o perations on partition Lie algebras. Additionally\, a “many-object” ve rsion of this duality connects partition Lie algebroids with infinitesimal derived foliations in the sense of Toën–Vezzosi.\n LOCATION:https://researchseminars.org/talk/tandg/22/ END:VEVENT BEGIN:VEVENT SUMMARY:David Kern (KTH) DTSTART:20241119T213000Z DTEND:20241119T230000Z DTSTAMP:20260314T090948Z UID:tandg/23 DESCRIPTION:Title: C ategorical spectra and ℤ-categories\nby David Kern (KTH) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nCategorical spectra\, developed by Stefanich\, are a directed version of\nspectra wher e the suspension of pointed ∞-groupoids is replaced by that\nof pointed ω-categories. They are very useful for capturing stability\nphenomena in iterated categorifications\, or for defining “∞-vector\nspaces”. In this talk\, I will explain that they can be understood as a\nweak version of Lessard's ℤ-categories\, a kind of category with arrows\nin all negat ive as well as positive dimensions\, which allows for a more\ndirect study of their structure.\n LOCATION:https://researchseminars.org/talk/tandg/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Luuk Stehouwer (Dalhousie University) DTSTART:20250212T160000Z DTEND:20250212T173000Z DTSTAMP:20260314T090948Z UID:tandg/24 DESCRIPTION:Title: T he Unitary Cobordism Hypothesis\nby Luuk Stehouwer (Dalhousie Universi ty) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstrac t\nThe cobordism hypothesis classifies extended topological quantum\nfield theories (TQFTs) in terms of algebraic information in the target\ncategor y. One of the core principles in quantum field theory - unitarity -\nsays that state spaces are not just vector spaces\, but Hilbert spaces.\nRecent ly in joint work with many others\, we have defined unitarity for\nextende d TQFTs\, inspired by Freed and Hopkins. Our main technical tool is a\nhig her-categorical version of dagger categories\; categories $C$ equipped\nwi th a strict anti-involution $\\dagger: C \\to C^{op}$ which is the identit y\non objects. I explain joint work in progress with Theo Johnson-Freyd\,\ nCameron Krulewski and Lukas Müller in which we prove a version of the\nc obordism hypothesis for unitary TQFTs. The main observation is that the\n< em>stably framed bordism $n$-category is freely generated as a symmet ric\nmonoidal dagger $n$-category with unitary duals by a single object: t he point.\n LOCATION:https://researchseminars.org/talk/tandg/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukas Müller (Perimeter Institute for Theoretical Physics) DTSTART:20250305T160000Z DTEND:20250305T173000Z DTSTAMP:20260314T090948Z UID:tandg/25 DESCRIPTION:Title: A Higher Spin Statistics Theorem for Invertible Quantum Field Theories\ nby Lukas Müller (Perimeter Institute for Theoretical Physics) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe spin-st atistics theorem asserts that in a unitary quantum field theory\, the spin of a particle—characterized by its transformation under the central ele ment of the spin group\, which corresponds to a 360-degree rotation—dete rmines whether it obeys bosonic or fermionic statistics. This relationship can be formalized mathematically as equivariance for a geometric and alge braic action of the 2-group ${\\rm B}{\\bf Z}_2$. In my talk\, I will pres ent a refinement of these actions\, extending from ${\\rm B}{\\bf Z}_2$ to appropriate actions of the stable orthogonal group ${\\rm O}$\, and demon strate that every unitary invertible quantum field theory intertwines thes e ${\\rm O}$-actions.\n LOCATION:https://researchseminars.org/talk/tandg/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Rot (Vrije Universiteit Amsterdam) DTSTART:20250312T150000Z DTEND:20250312T163000Z DTSTAMP:20260314T090948Z UID:tandg/26 DESCRIPTION:Title: T he topology of infinite dimensional spaces and nonlinear proper Fredholm m appings\nby Thomas Rot (Vrije Universiteit Amsterdam) as part of Topol ogy and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn this talk I wi ll discuss the differential topology of non-linear proper Fredholm mapping s. In applications these mappings arise as non-linear PDE problems (of el liptic type). I will discuss work with Lauran Toussaint that relates these mappings to the stable homotopy groups of spheres\, and if time permits\, I will discuss an ongoing project on defining a new homology theory of si ngular type for infinite dimensional spaces. This is joint work with Alber to Abbondandolo\, Michael Jung and Lauran Toussaint.\n LOCATION:https://researchseminars.org/talk/tandg/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Urs Schreiber (NYU Abu Dhabi) DTSTART:20250326T150000Z DTEND:20250326T163000Z DTSTAMP:20260314T090948Z UID:tandg/27 DESCRIPTION:Title: N on-Lagrangian construction of abelian CS/FQH-theory via flux quantization in 2-Cohomotopy\nby Urs Schreiber (NYU Abu Dhabi) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nAfter briefly recalli ng how the analog of Dirac charge quantization in exotic (effective\, high er) gauge theories\, providing their global topological completion\, is en coded in a choice of classifying space $𝒜$ whose rationalization reflec ts the flux Bianchi identities\, I explain how the choice $𝒜 ≔ S^2$ ( “flux quantization in 2-Cohomotopy”) implements effective corrections to ordinary Dirac flux quantization\, which over surfaces yields exactly t he topological quantum observables of fractional quantum Hall systems\, tr aditionally described by abelian Chern-Simons theory. I close by briefly i ndicating how this situation is geometrically engineered on probe M5-brane s if the M-theory C-field is flux-quantized in 4-Cohomotopy (“Hypothesis H”).\nThis is joint work with Hisham Sati\; for more pointers see ncatlab.org/schreiber/show/ ISQS25.\n LOCATION:https://researchseminars.org/talk/tandg/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Lory Aintablian (MPIM Bonn) DTSTART:20250402T150000Z DTEND:20250402T163000Z DTSTAMP:20260314T090948Z UID:tandg/28 DESCRIPTION:Title: D ifferentiation of groupoid objects in tangent categories\nby Lory Aint ablian (MPIM Bonn) as part of Topology and Geometry Seminar (Texas\, Kansa s)\n\n\nAbstract\nThe infinitesimal counterpart of a Lie group(oid) is its Lie algebra(oid). I will show that the differentiation procedure works in any category with an abstract tangent structure in the sense of Rosicky\, which was later rediscovered by Cockett and Cruttwell. Mainly\, I will co nstruct the abstract Lie algebroid of a differentiable groupoid in a carte sian tangent category $C$ with a scalar $R$-multiplication\, where $R$ is a ring object of $C$. Examples include differentiation of infinite-dimensi onal Lie groups\, elastic diffeological groupoids\, etc. This is joint wor k with Christian Blohmann.\n LOCATION:https://researchseminars.org/talk/tandg/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Mayuko Yamashita (Perimeter Institute) DTSTART:20250430T150000Z DTEND:20250430T163000Z DTSTAMP:20260314T090948Z UID:tandg/29 DESCRIPTION:Title: T opological elliptic genera\nby Mayuko Yamashita (Perimeter Institute) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nT here is a classical notion of elliptic genera\, which assigns Jacobi forms to SU-manifolds. In this talk\, I explain my work with Ying-Hsuan Lin (< a href="https://arxiv.org/abs/2412.02298">arXiv:2412.02298) to give it s homotopy-theoretical refinements and variants\, which we call “topolog ical elliptic genera”. The codomain becomes genuinely equivariant twist ed Topological Modular Forms. In this talk\, I explain the construction a nd physical idea behind\, and discuss an application where we derive an in teresting divisibility result of Euler numbers for Sp-manifolds. Also I e xplain a recent update with Tilman Bauer (in preparation) proving the surj ectivity results of topological elliptic genera.\n LOCATION:https://researchseminars.org/talk/tandg/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Sanford (Ohio State University) DTSTART:20250409T150000Z DTEND:20250409T163000Z DTSTAMP:20260314T090948Z UID:tandg/30 DESCRIPTION:Title: M anifestly unitary higher Hilbert spaces\nby Sean Sanford (Ohio State U niversity) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\n Abstract\nA key aspect of quantum theory its insistence that states evolve via unitary transformations. In order to understand the symmetries of hig her dimensional quantum field theory\, we need to develop higher dimension al analogues of unitarity. The language and theory of higher categories ha s greatly clarified the way we express these higher symmetries\, but unfor tunately this language imposes a certain dogma seems to be in conflict wit h various attempts at describing unitarity. In the nLab for example\, ther e is a great debate over whether or not unitary structures on a (higher) c ategory are `evil’\; at term which is both dogmatic and technically prec ise.\n\nVarious attempts have been made to force these structures to `play nice’ with one another\, to varying degrees of success. In this talk I will present our most recent contribution to these efforts: defining the n otion of a 3-Hilbert space. Our work aims to encode a kind of evaluation o n spheres of every dimension that plays nicely with duality structures tha t are imposed by the cobordism hypothesis. I will show how this compatibil ity is stronger than simply having daggers at all levels\, thus differenti ating our construction from previous attempts at higher unitarity. If time permits\, we will discuss a roadmap for unitarity in any dimension via a unitary version of condensation completion.\n LOCATION:https://researchseminars.org/talk/tandg/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Nivedita (University of Oxford) DTSTART:20250423T150000Z DTEND:20250423T163000Z DTSTAMP:20260314T090948Z UID:tandg/31 DESCRIPTION:Title: B icommutant categories from conformal nets\nby Nivedita (University of Oxford) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbs tract\nTwo-dimensional chiral conformal field theories (CFTs) admit three distinct mathematical formulations: vertex operator algebras (VOAs)\, conf ormal nets\, and Segal (functorial) chiral CFTs. With the broader aim to b uild fully extended Segal chiral CFTs\, we start with the input of a confo rmal net.\n\nIn this talk\, we focus on presenting three equivalent constr uctions of the category of solitons\, i.e. the category of solitonic repre sentations of the net\, which we propose is what theory (chiral CFT) assig ns to a point. Solitonic representations of the net are one of the primary class of examples of bicommutant categories (a categorified analogue of a von Neumann algebras). The Drinfel’d centre of solitonic representation s is the representation category of the conformal net which has been studi ed before\, particularly in the context of rational CFTs (finite-index net s). If time permits\, we will briefly outline ongoing work on bicommutant category modules (which are the structures assigned by the Segal Chiral CF T at the level of 1-manifolds)\, hinting towards a categorified analogue o f Connes fusion of von Neumann algebra modules.\n\n(Bicommutant categories act on W*-categories analogous to von Neumann algebras acting on Hilbert spaces.)\n LOCATION:https://researchseminars.org/talk/tandg/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Simon Pacaud Lemay (Macquarie University) DTSTART:20250923T220000Z DTEND:20250923T233000Z DTSTAMP:20260314T090948Z UID:tandg/32 DESCRIPTION:Title: T he world of differential categories\nby Jean-Simon Pacaud Lemay (Macqu arie University) as part of Topology and Geometry Seminar (Texas\, Kansas) \n\n\nAbstract\nDifferential categories use category theory to provide the foundations of differential calculus. In this talk\, I will give you gui ded tour of the world of differential categories. We will see (1) differen tial categories\, which give the algebraic foundations of differentiation\ ; Cartesian differential categories\, which give the foundations of multiv ariable differential calculus\; and (3) tangent categories\, which give th e foundations of differential geometry. In particular we will look at the map of differential categories and see how these three concepts relate to each other. Moreover\, the theory of differential categories has been succ essful in formalising various important concepts related to differentiatio n. In particular\, this talk will set the table for next week’s talk\, w here Chiara Sava will explain how differential categories capture differen tial graded algebras.\n LOCATION:https://researchseminars.org/talk/tandg/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Chiara Sava (Charles University\, Prague) DTSTART:20250930T150000Z DTEND:20250930T163000Z DTSTAMP:20260314T090948Z UID:tandg/33 DESCRIPTION:Title: D ifferential graded algebras in differential categories\nby Chiara Sava (Charles University\, Prague) as part of Topology and Geometry Seminar (T exas\, Kansas)\n\n\nAbstract\nDifferential categories\, introduced in last week's talk by Jean-Simon Pacaud Lemay\, provide a categorical framework for the algebraic foundations of differential calculus. Within this settin g we can capture familiar notions such as derivations\, Kähler differenti als\, differential algebras and de Rham cohomology. Along this line\, in t his talk\, we will show how to define differential graded algebras in a di fferential category. In the case of polynomial differentiation\, this cons truction recovers the classical commutative differential graded algebras\, while for smooth functions it yields differential graded $C^\\infty$-ring s in the sense of Dmitri Pavlov. To further justify our definition\, we wi ll explain how the monad of a differential category can be lifted to its c ategory of chain complexes and how the algebras of the lifted monad corres pond precisely to differential graded algebras of the base category\, with the free ones given by the de Rham complexes. Finally\, we will discuss h ow the category of chain complexes of a differential category is itself a differential category\, pointing towards the prospect of differential dg-c ategories. This is joint work with Jean-Simon Pacaud Lemay.\n LOCATION:https://researchseminars.org/talk/tandg/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Georg Lehner (University of Münster) DTSTART:20251021T150000Z DTEND:20251021T163000Z DTSTAMP:20260314T090948Z UID:tandg/34 DESCRIPTION:Title: M easure theory via locales\nby Georg Lehner (University of Münster) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe re are two oftentimes unspoken truths in measure theory. 1) Practically al l useful measures in practice are given by Radon measures. 2) One does not really care so much about the sigma-algebra of measurable sets\, but rath er about its quotient by the ideal of null sets.\n\nThe quotient of measur able sets by null sets is\, in the case of a given Radon measure\, an exam ple of what is called a measurable locale\, and can be treated like a (usu ally point-free) space. We argue that this measurable locale can be constr ucted directly from a Grothendieck topology on the poset of compact sets. This opens the door to a purely sheaf-theoretic perspective on measure the ory. As an application\, we show that the locale of sublocales of a given Hausdorff space X equipped with a Radon measure can be equipped with a nat ural extension of the measure\, invariant under measure preserving homeomo rphisms.\n LOCATION:https://researchseminars.org/talk/tandg/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Riva (CMSA\, Harvard University) DTSTART:20251111T160000Z DTEND:20251111T173000Z DTSTAMP:20260314T090948Z UID:tandg/35 DESCRIPTION:Title: Z igzags and free adjunctions\nby Lorenzo Riva (CMSA\, Harvard Universit y) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract \nThe cobordism hypothesis tells us that the process of freely adding adjo ints to the $k$-morphisms of a symmetric monoidal $(\\infty\,n)$-category can be roughly described as follows: treat one such $k$-morphism as an $n$ -framed $k$-dimensional cube and change the framing appropriately to obtai n its left/right adjoint. At the very least\, this description is correct if we start with the the commutative monoid generated by a single object. But what happens with more complicated examples? Motivated by work of Daws on-Paré-Pronk\, we explicitly construct the functor that freely adds righ t adjoints to the morphisms of an infinity-category\; we also extend the c onstruction to arbitrary dimensions and speculate on what its universal pr operty should be. This is based on joint work with Martina Rovelli.\n LOCATION:https://researchseminars.org/talk/tandg/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Fei Han (National University of Singapore) DTSTART:20260211T000000Z DTEND:20260211T013000Z DTSTAMP:20260314T090948Z UID:tandg/36 DESCRIPTION:Title: D ifferential Models for Anderson Dual to Twisted Spin(^c) Bordism and the T wisted Anomaly Map\nby Fei Han (National University of Singapore) as p art of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nSpin( ^c) bordism is an important bordism theory with many connections and appli cations in topology\, geometry\, and physics. In this talk\, we explain th e construction of models for twisted Spin(^c) bordism and its Anderson dua l\, in homotopy-theoretic\, geometric\, and differential settings. The tal k is based on joint work with Yuanchu Li.\n LOCATION:https://researchseminars.org/talk/tandg/36/ END:VEVENT END:VCALENDAR