Speaker: Dr. Arpan Kabiraj

Date: 13th March, 2019 (Wednesday)

Time: 12 Noon;

Venue: Committee Room, Department of Mathematics.

Title:Center of the Goldman Lie algebra

Abstract: In 1980s Goldman introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface. This Lie bracket is known as the Goldman bracket and the Lie algebra is known as the Goldman Lie algebra. In this talk I will define Goldman Lie algebra and discuss a conjecture of Chas and Sullivan about the center of the Goldman Lie algebra. I will explain the relation between Goldman Lie algebra and character varieties of surface groups. If time permits, I will also show how techniques from geometric group theory could be used to compute center of the Goldman Lie algebra. I will mention some open problems related to Goldman Lie algebra.