Anton Alekseev | Moduli spaces, planar curves and the Baker-Campbell-Hausdorff series 2/4
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 17/11/2021

School "Moduli Spaces, Combinatorics and Integrable Systems", November 16, 2021
Anton Alekseev (University of Geneva)
Moduli spaces, planar curves and the Baker-Campbell-Hausdorff series (2/4)

In this mini-course, we will cover several inter-related topics:
- Goldman Lie brackets and Turaev cobrackets defined in terms of intersections and self-intersections of curves on 2-dimensional oriented manifolds;
- Symplectic, Poisson and Batalin–Vilkovisky (BV) structures on moduli spaces of flat connections;
- The Kashiwawra–Vergne problem on properties of the Baker–Campbell–Hausdorff (BCH) series and its higher genus analogues.
Among other things, we will explain the Fock–Rosly approach to Poisson structures on moduli spaces, and we will discuss the Knizhnik–Zamolodchikov (KZ) flat connection on configuration spaces of points on the complex plane.
The mini-course will be essentially self-contained: in order to follow it, no previous knowledge of the topics listed above is required!