Wall-crossing and Riemann-Hilbert problems

Abstract:

I will start by introducing BPS structures and their variations. The point of this is to axiomatise the behaviour of Donaldson-Thomas invariants under changes in stability parameters, but it is not necessary to understand anything about that to understand the definitions. I will then introduce a natural Riemann-Hilbert problem associated to such structures, which involves holomorphic maps on the complex plane with prescribed discontinuities along a collection of rays. I will also explain how to solve this problem in the simplest example using the gamma function.