The wall-crossing behaviour of Donaldson-Thomas invariants in CY3 categories is controlled by a beautiful formula involving the group of automorphisms of a symplectic algebraic torus. This formula invites one to solve a certain Riemann-Hilbert problem. I will start by explaining how to solve this problem in the simplest possible case (this is undergraduate stuff!). I will then talk about a more general class of examples of the wall-crossing formula involving moduli spaces of quadratic differentials.
- Algebraic and Symplectic Geometry Seminar