### Ritsumeikan University Geometry Seminar (09/December/2019)

2019.12.04 Wed up

<<Ritsumeikan University Geometry Seminar>>

Date: 09/December/2019, Monday, 16:30-17:30

Title: BV structures on moduli spaces of flat connections

Speaker: Pavol Severa （University of Geneva）

Abstract:

Loops (or rather their homotopy classes) on an oriented surface form a Lie algebra, originally discovered by Goldman.The Lie bracket is given by a simple formula involving intersection points of two loops. This Lie algebra can be interpreted as the Poisson bracket on a moduli space of flat connections (given by the famous Atiyah-Bott symplectic form), if to each loop we assign the trace of the holonomy along the loop. Loops come also with another operation, a Lie cobracket discovered by Turaev, given by a very similar formula. I will explain what is the corresponding geometric structure on the moduli space. I will also try to explain why this structure is interesting and how it relates to the Kashiwara-Vergne problem in Lie theory. Based on a joint work in progress with Anton Alekseev, Florian Naef, and Jan Pulmann.

Room: Ritsumeikan University, Biwako-Kusatsu Campus, Westwing 6th floor, Colloquium Room.