PIRSA:24100118

Video URL

https://pirsa.org/24100118

The Moore-Tachikawa conjecture via shifted symplectic geometry

Mayrand, M. (2024). The Moore-Tachikawa conjecture via shifted symplectic geometry. Perimeter Institute for Theoretical Physics. https://pirsa.org/24100118

Mayrand, Maxence. The Moore-Tachikawa conjecture via shifted symplectic geometry. Perimeter Institute for Theoretical Physics, Oct. 24, 2024, https://pirsa.org/24100118 

          @misc{ scivideos_PIRSA:24100118,
            doi = {10.48660/24100118},
            url = {https://pirsa.org/24100118},
            author = {Mayrand, Maxence},
            keywords = {Mathematical physics},
            language = {en},
            title = {The Moore-Tachikawa conjecture via shifted symplectic geometry},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {oct},
            note = {PIRSA:24100118 see, \url{https://scivideos.org/index.php/pirsa/24100118}}
          }

Maxence Mayrand

Talk numberPIRSA:24100118
DOI10.48660/24100118
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

The Moore-Tachikawa conjecture posits the existence of certain 2-dimensional topological quantum field theories (TQFTs) valued in a category of complex Hamiltonian varieties. Previous work by Ginzburg-Kazhdan and Braverman-Nakajima-Finkelberg has made significant progress toward proving this conjecture. In this talk, I will introduce a new approach to constructing these TQFTs using the framework of shifted symplectic geometry. This higher version of symplectic geometry, initially developed in derived algebraic geometry, also admits a concrete differential-geometric interpretation via Lie groupoids and differential forms, which plays a central role in our results. It provides an algebraic explanation for the existence of these TQFTs, showing that their structure comes naturally from three ingredients: Morita equivalence, as well as multiplication and identity bisections in abelian symplectic groupoids. It also allows us to generalize the Moore-Tachikawa TQFTs in various directions, raising interesting questions in Lie theory and Poisson geometry. This is joint work with Peter Crooks.