Activities This Week

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 F. 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 discuss some basic properties of Goldman bracket and its relation with Teichmüller space. 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 bracket.

The Container Method, developed in 2015 by Balogh-Morris-Samotij and Saxton-Thomason, has produced numerous applications in combinatorics. We will discuss applications to triangle free graphs and an Erdos discrete geometry problem.

Examine a polynomial with random, independent coefficients, uniform between 1 and 210. We show that it is irreducible over the integers with probability going to one as the degree goes to infinity. Joint work with Lior Bary-Soroker.