Title: Characters of representations and the topology of flag varieties

• Description: 

We will study representations of algebraic structures of Lie type (such as algebraic groups, Lie algebras, quantum groups, and Kac-Moody algebras). One guiding problem will be to determine the characters of simple representations. In various situations we have formulas for those characters (some proven and some still conjectural). These formulas arise from a common combinatorial framework and derive from the famous Kazhdan-Lustig conjecture. We will show how to prove these formulas in almost all cases by relating them to the topology of flag varieties using moment graph techniques.

• Prerequesites: 

Some familiarity with the representation theory of algebraic groups and with sheaf theory on topological spaces and derived categories.