# Events for January 18, 2017 from General and Seminar calendars

## Colloquium - Tian Yang

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Tian Yang, Stanford University

**Description:**

Title: Mapping class group action on character varieties and the ergodicity

Abstract:

Character varieties of a surface are central objects in several beaches of math- ematics, such as low dimensional topology, algebraic geometry, differential geom- etry and mathematical physics. On the character varieties, there is a tautological action of the mapping class group - the group of symmetries of the surface, which is expected to be ergodic in certain cases. In this talk, I will review related results toward proving the ergodicity and introduce two long standing and related conjec- tures: Goldman’s Conjecture and Bowditch’s Conjecture. It is shown by Marche and Wolff that the two conjectures are equivalent for closed surfaces. For punc- tured surfaces, we disprove Bowditch’s Conjecture by giving counterexamples, yet prove that Goldman’s Conjecture is still true in this case.