Speaker
Anton Alekseev, University of Geneva
Abstract
Let G be a Lie group with an invariant scalar product on its Lie algebra, and S be a closed oriented 2-manifold. Then, by results of Atiyah-Bott and Goldman, the corresponding moduli space of flat connections M(S, G) carryies a Poisson structure (a symplectic structures if S has no boundary).
We will show that if G is a unimodular Lie supergroup with an invariant odd scalar product on its Lie super algebra, then the moduli pace of flat connections M(S, G) carries a Batalin-Vilkovisky (BV) structure. Our main tool is an odd counterpart of the Fock-Rosly formula which defines this canonical BV structure. It time permits, we will also outline some open problems.
The talk is based on a joint work with F. Naef, J. Pulmann, and P. Severa, see arXiv:2210.08944.