Monday 22 June 2026
15:00–16:30*

Filippos Sytilidis (Max Planck Institute for Mathematics, Bonn) — Towards a finite presentation of the 3-dimensional bordism bicategory

Topological quantum field theories (TQFTs) are symmetric monoidal functors from bordism categories to categories of vector spaces. Classifying low-dimensional TQFTs often relies on presenting bordism categories in terms of generators and relations. This talk introduces these ideas and outlines a general procedure, due to Juhász, for constructing such presentations using Morse-Cerf theory and surgery. We further discuss how this perspective can be extended to yield presentations of bordism bicategories and describe an explicit finite presentation of the invertible part of the 3-dimensional bordism bicategory, following joint work with Bruce Bartlett and Chris Douglas. Time permitting, we will end by discussing some applications and future directions regarding constructions and classification of 3-dimensional (partially defined) TQFTs.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.