# Dr. Peter Crooks, Universität Hannover: "Noncommutative integrable systems on a class of hyperkähler manifolds"

May 04, 2017 from 04:15 PM to 05:45 PM

LMS 4 - R. 526 - Übungsraum

Abstract:

Holomorphic integrable systems are fruitfully studied at the interface of differential geometry, algebraic geometry, and mathematical physics. A particularly notable example is the Hitchin system, whose total space is the moduli space of semistable Higgs bundles (of fixed rank and degree) on a compact Riemann surface. This moduli space is known to be hyperkähler, and the Hitchin system thereby gives an instance of interesting and well-studied connections between hyperkähler geometry and integrable systems.

At the same time, there is an emerging body of literature on noncommutative integrable (NCI) systems. Recent work includes Fernandes, Laurent-Gengoux, and Vanhaecke’s notion of an abstract noncommutative integrable (ANCI) system, which is essentially a foliation-theoretic description of an NCI system.

I will describe an attempt to create connections between hyperkähler geometry and NCI systems, building on existing relationships between the former and ordinary integrable systems. The main result will be a canonical ANCI system on a class of manifolds Bielawski has shown to be hyperkähler.

This represents joint work with Steven Rayan.

Einladender: H. Weiß