Abstract:
I will describe an ongoing research project which aims to
encode the DT invariants of a CY3 triangulated category in a
geometric structure on its space of stability conditions. More
specifically we expect to find a complex hyperkahler structure on
the total space of the tangent bundle. These ideas are closely
related to the work of Gaiotto, Moore and Neitzke from a decade
ago. The main analytic input is a class of Riemann-Hilbert problems
involving maps from the complex plane to an algebraic torus with
prescribed discontinuities along a collection of rays.