## Video URL

https://pirsa.org/24100118# The Moore-Tachikawa conjecture via shifted symplectic geometry

### APA

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

### MLA

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

### BibTex

@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/pirsa/24100118}} }

**Source Repository**PIRSA

**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.