**Prof. Vladimir Turaev**

**Indiana University**

Title: *Brackets and cobrackets in topology of surfaces*

Abstract: We discuss Lie-type algebraic operations – brackets, cobrackets, and double brackets – in the module generated by free homotopy classes of loops in a surface. This subject was initially inspired by the study of the Atiyah-Bott Poisson brackets on the moduli spaces of surfaces. Recently, the algebraic operations on loops were related to the Kashiwara-Vergne equations on automorphisms of free Lie algebras.

Lecture 1: Monday, March 25, 2019 at 15:30

Lecture 2: Wednesday, March 27, 2019 at 15:30

Lecture 3: Thursday, March 28, 2019 at 15:30

Light refreshments will be given before the talks in the faculty lounge on the 8th floor.