**SMS scnews item created by Haotian Wu at Wed 16 Nov 2016 2140**

Type: Seminar

Distribution: World

Expiry: 11 Jan 2017

**Calendar1: 24 Nov 2016 1400-1500**

**CalLoc1: Carslaw 535A**

CalTitle1: Geometry & Topology: Integrability of the moduli stack of parahoric Higgs bundles

Auth: haotianw@como.maths.usyd.edu.au

### Geometry & Topology Seminar

# Integrability of the moduli stack of parahoric Higgs bundles

### David Baraglia (Adelaide)

**Thursday 24 November 2016, 14:00–15:00 in Carslaw 535A.**

**Please join us for lunch at 12:30! We will meet at level 2 of Carslaw. **

**Abstract:** The cotangent bundle of the stack of principal G-bundles on a curve was shown by Hitchin to be an algebraically integrable system. Motivated by the Langlands program we consider the following generalisation: take the cotangent bundle of the stack of torsors over a non-constant group scheme. Do we still get an integrable system? We show that this is the case for the so-called parahoric group schemes. A special cases of this is the cotangent bundle of the stack of parabolic G-bundles. Determining the base of the integrable system turns out to be deeply related to the Kazhdan-Lusztig map, which sends nilpotent orbits to conjugacy classes in the Weyl group. This is Joint work with Masoud Kamgarpour and Rohith Varma.