# Hausdorff School: “TQFTs and their connections to representation theory and mathematical physics”

Dates: June 19 - 23, 2023

Venue: Lipschitzsaal, Endenicher Allee 60 (Bonn)

Organizers: Thorsten Heidersdorf (Bonn), Ingo Runkel (Hamburg), Christoph Schweigert (Hamburg), Catharina Stroppel (Bonn)

TQFTs (Topological quantum field theories) are of central importance in several areas of mathematics and physics. From a mathematical point of view (going back to Atiyah), a TQFT is a symmetric monoidal functor from the cobordism category to some symmetric monoidal category. It can thus be seen as a representation of a fundamental geometric category on a target category and thereby organizes interesting algebraic structures, e.g. representations of mapping class groups, in terms of cobordism categories. In recent years, TQFTs have appeared in many more mathematical areas such as algebraic topology (the study of 4-manifolds) or algebraic geometry (the study of moduli spaces). In this Hausdorff school we would like to explore various facets of TQFTs related to representation theory and mathematical physics. The interplay of representation theory and TQFT is, at least, two-fold: on the one hand side, representation theory provides input data to construct TQFTs. The most famous example is given by the quantum groups *U _{q}*(sl(2)) from which a modular tensor category and thus a Chern-Simons type TQFT can be constructed. On the other hand, TQFTs explain and organize structures appearing in representation categories, for example character varieties and their quantizations.

The following speakers will give a lecture series:

- Adrien Brochier (Paris): Factorization homology and representation theory
- Alexej Davydov (Ohio): E_n algebras and deformations of tensor categories
- Tudor Dimofte (Edinburgh): VOA's and 3d TQFT's from supersymmetric QFT's
- Mikhail Kapranov (Kavli IPMU): Higher Segal spaces

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The University of Bonn and HSM are committed to diversity and equal opportunity. We aim to increase the proportion of women in areas where women are underrepresented and to facilitate their careers. We therefore strongly encourage women with relevant qualifications to apply.

**In case of scientific questions, please contact the organizers**, in case of questions concerning services and administration, please contact hsm(at)hcm.uni-bonn.de.

**The due date for registration has expired.**

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