Timothy Moy (University of Cambridge) – Joyce structures from quadratic differentials on the sphere

Let M be a moduli space of quadratic differentials on the sphere with poles of fixed odd orders. Such a space has a concrete realisation as a space of rational functions. In this talk, I will explain an elementary construction that gives rise to a meromorphic hyper-Kähler metric on the algebraic torus bundle that is the quotient of TM by the natural period lattice. We will meet the theory of isomonodromic deformations, the geometry of Riemann surfaces and, crucially, twistor theory. All of this is motivated by the wall-crossing behaviour of Donaldson-Thomas invariants under the variation of Bridgeland stability conditions but the technical prerequisites to understand this particular construction should be minimal. This talk is partly based on joint work with Maciej Dunajski.