Higher geometry

Texas Tech Topology and Geometry Seminar: May 5, 18:00 (Moscow time) Maxime Ramzi (University of Münster)— Rigid commutative algebras and a generalized 1D cobordism hypothesis Baez and Dolan's cobordism hypothesis, in dimension 1, describes the free symmetric monoidal infinity-category on a dualizable object as a certain cobordism category. It's only reasonable to try and guess what a generalization of this may look like, namely how one could describe free rigid categories on more complicated inputs. In this talk, I will explain how a generalization of the notion of "rigid category" to other settings leads to a proof of the natural guess by bootstrapping from the usual cobordism hypothesis. This generalization, namely the notion of rigid commutative algebra in a symmetric monoidal (∞,2)-category, has received growing attention following recent advances in algebraic K-theory, and I will spend some time discussing it. Associated preprint (April). Online announcement that displays the seminar time in your browser's time zone. The Zoom link is available here (message here to join the Higher Geometry Telegram forum)

Texas Tech Topology and Geometry Seminar: April 22, 02:00 (Moscow time, strictly night) Kensuke Arakawa (Kyoto University) — On the equivalence of two approaches to multiplicative homotopy theories Locally presentable (∞,1) categories admit two popular models: Presentable quasicategories and combinatorial model categories. Building on the foundational work of Dugger and Lurie, Pavlov proved that their associated (∞,1)-categories are equivalent, confirming a long-standing expectation. He then went on to conjecture that this should also hold multiplicatively, i.e., for presentably symmetric monoidal quasicategories and combinatorial symmetric monoidal model categories. In arXiv:2603.23018, I proved this conjecture. The main difficulty is that existing techniques to rigidify quasicategories often break down multiplicatively. If time permits, I will also explain applications to enriched infinity operads . The Zoom link is available here (message here to join the Higher Geometry Telegram forum)

Texas Tech Quantum Homotopy Seminar: April 15, 18:00 (Moscow time) Ignat Romanov (Qiuzhen College, Tsinghua University) — Connections on ordinary principal G-bundles. Atiyah algebroids. The Zoom link is available here (message here to join the Higher Geometry Telegram forum).

Texas Tech Topology and Geometry Seminar: April 14, 18:00 (Moscow time) Pablo Bustillo Vazquez (Northwestern University) — Fully-Dualizable and Invertible E_n-Algebras The easiest source of fully extended TQFTs is found in E_n-algebras: for any symmetric monoidal category V and E_n-algebra A in V, one automatically obtains an n-dimensional TQFT given by factorization homology. Sometimes, however, these TQFTs can be extended to (n+1)-dimensional ones. In this talk, I will explain how to characterize precisely when this extension is possible and when the resulting theory is invertible. Online announcement that displays the seminar time in your browser's time zone. The Zoom link is available here (message here to join the Higher Geometry Telegram forum)

Texas Tech Quantum Homotopy Seminar: 1 апреля, 18:00 (по Москве) Vasiliy Volkov — Derived manifolds Ссылка на Zoom доступна здесь (напишите сюда, чтобы присоединиться к телеграм-форуму Higher Geometry).

https://t.me/mipt_math/356

Texas Tech Quantum Homotopy Seminar: 25 марта, 18:00 (по Москве) Grisha Taroyan — ∞-sheaves / stacks on smooth manifolds Ссылка на Zoom доступна здесь (напишите сюда, чтобы присоединиться к телеграм-форуму Higher Geometry).

Texas Tech Quantum Homotopy Seminar: 11 марта, 18:00 по Москве This semester's topic is higher and derived differential geometry. We aim to cover sufficient background to understand the definition of a connection on a principal ∞-bundle in the paper "Symmetries and Higher-Form Connections in Derived Differential Geometry" (Feb 2026) by Bunk, Müller, Nuiten, Szabo. The first talk will be an introductory talk, discussing some fundamental ingredients of higher geometry: the duality between geometry and algebra; passing to derived spaces; passing to (higher) stacks. Here is a list of talks assigned so far, we still have more talks to be claimed: 1) Introductory talk. Duality between geometry and algebra. Higher geometry: sheaves, stacks, derived stacks. 2) ∞-sheaves / stacks on smooth manifolds. Examples: BG, B_∇ G, etc. 3) Derived manifolds, derived intersections, etc. 4) Connections on ordinary (nonderived) principal G-bundles. Atiyah algebroids. 5) Higher Lie theory. Lie ∞-algebras and their integration. 6) Deformation theory. Lie differentiation and infinitesimal symmetries. (Chapters 2, 3 in the paper) 7) Connections and curvature on principal ∞-bundles. (Chapters 4 in the paper) Ссылка на Zoom доступна здесь (напишите сюда, чтобы присоединиться к телеграм-форуму Higher Geometry).

Texas Tech Quantum Homotopy Seminar: сегодня (22 января) в 21:00 (по московскому времени) Dmitri Pavlov (TTU) -- Differential geometry of the Standard Model of Particle Physics I will give a very brief introduction to the topic and we will assign talks for…

Texas Tech Topology and Geometry Seminar: 30 апреля, 18:00 по Москве Mayuko Yamashita (Perimeter Institute) — Topological elliptic genera There 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 (arXiv:2412.02298) to give its homotopy-theoretical refinements and variants, which we call “topological elliptic genera”. The codomain becomes genuinely equivariant twisted Topological Modular Forms. In this talk, I explain the construction and physical idea behind, and discuss an application where we derive an interesting divisibility result of Euler numbers for Sp-manifolds. Also I explain a recent update with Tilman Bauer (in preparation) proving the surjectivity results of topological elliptic genera. Ссылка на Zoom доступна здесь (напишите сюда, чтобы присоединиться к телеграм-форуму Higher Geometry).

Texas Tech Topology and Geometry Seminar: 23 апреля, 18:00 по Москве Nivedita (University of Oxford) — Bicommutant categories from conformal nets Two-dimensional chiral conformal field theories (CFTs) admit three distinct mathematical formulations: vertex operator algebras (VOAs), conformal nets, and Segal (functorial) chiral CFTs. With the broader aim to build fully extended Segal chiral CFTs, we start with the input of a conformal net. In this talk, we focus on presenting three equivalent constructions of the category of solitons, i.e., the category of solitonic representations of the net, which we propose is what theory (chiral CFT) assigns 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 representations is the representation category of the conformal net which has been studied before, particularly in the context of rational CFTs (finite-index nets). If time permits, we will briefly outline ongoing work on bicommutant category modules (which are the structures assigned by the Segal Chiral CFT at the level of 1-manifolds), hinting towards a categorified analogue of Connes fusion of von Neumann algebra modules. Ссылка на Zoom доступна здесь (напишите сюда, чтобы присоединиться к телеграм-форуму Higher Geometry).

Texas Tech Topology and Geometry Seminar: 9 апреля, 18:00 по Москве Sean Sanford (OSU) — Manifestly unitary higher Hilbert spaces A key aspect of quantum theory its insistence that states evolve via unitary transformations. In order to understand the symmetries of higher dimensional quantum field theory, we need to develop higher dimensional analogues of unitarity. The language and theory of higher categories has greatly clarified the way we express these higher symmetries, but unfortunately this language imposes a certain dogma seems to be in conflict with various attempts at describing unitarity. In the nLab for example, there is a great debate over whether or not unitary structures on a (higher) category are 'evil'. I will present our recent contribution to these efforts: the notion of a 3-Hilbert space. If time permits, we will discuss a roadmap for unitarity in any dimension via a unitary version of condensation completion. Ссылка на Zoom доступна здесь (напишите сюда, чтобы присоединиться к форуму).

Texas Tech Topology and Geometry Seminar: сегодня (2 апреля) в 18:00 по московскому времени Lory Aintablian (MPIM Bonn) — Differentiation of groupoid objects in tangent categories The 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 Rosický, which was later rediscovered by Cockett and Cruttwell. Mainly, I will construct the abstract Lie algebroid of a differentiable groupoid in a cartesian tangent category C with a scalar R-multiplication, where R is a ring object of C. Examples include differentiation of infinite-dimensional Lie groups, elastic diffeological groupoids, etc. This is joint work with Christian Blohmann. Ссылка на Zoom доступна здесь (это сообщение на телеграм-форуме Higher Geometry, напишите сюда, чтобы присоединиться).

Texas Tech Topology and Geometry Seminar: в среду (26 марта) в 18:00 по московскому времени Urs Schreiber (NYU Abu Dhabi) — Non-Lagrangian construction of abelian CS/FQH-theory via flux quantization in 2-Cohomotopy. After briefly recalling how the analog of Dirac charge quantization in exotic (effective, higher) gauge theories, providing their global topological completion, is encoded in a choice of classifying space 𝒜 whose rationalization reflects 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 the topological quantum observables of fractional quantum Hall systems, traditionally described by abelian Chern-Simons theory. I close by briefly indicating how this situation is geometrically engineered on probe M5-branes if the M-theory C-field is flux-quantized in 4-Cohomotopy (“Hypothesis H”). This is joint work with Hisham Sati; for more pointers see on nlab Урс Шрайбер — это человек, который — создал nlab и рекордное количество страниц на нём, — написал 1000-страничную книгу Differential cohomology in a cohesive infinity-topos (2013, 2017), — разработал программу исследования гипотезы H, о математической формулировке M-теории (гипотетической 11-мерной теории бран, предложенной Виттеном в 1995 году, объединяющий все предыдущие теории струн и оказавшей революционное влияние на дальнейшей развитие теоретической физики и математики) Один из самых ключевых и известных исследователей в высшей геометрии. См. его работы на личной странице и см. по теме доклада flux quantization. Ссылка на Zoom доступна здесь (это сообщение на форуме сообщества -- напишите сюда, чтобы присоединиться).

На картинке выше Денис Гайцгори и Сэм Раскин, возглавлявшие команду из девяти человек, которая доказала геометрическую гипотезу Ленглендса в мае 2024. https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/