** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2018.11.27, 15:00–17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Character varieties."

**Speaker:** Anton
Mellit (Universität
Wien)

**Abstract:**
Character varieties are classical objects. They parametrize representations of the fundamental group of a given Riemann surface (possibly with punctures).
I am going to give a basic introduction to the subject, in particular to define the symplectic form and explain the non-abelian Hodge correspondence, which connects
character varieties to Hitchin's integrable systems. Then I will explain recent developments, such as P=W conjecture, and the curious hard Lefschetz property.