Donaldson-Thomas invariants and a non-perturbative topological string partition function

Abstract: I will introduce a class of Riemann-Hilbert problems which (I claim) arise naturally in Donaldson-Thomas theory. I will start with the simplest example (corresponding to the DT theory of the A1 quiver) which leads via undergraduate mathematics to the gamma function. Then I will explain how the same procedure applied to the DT theory of coherent sheaves on the resolved conifold leads to a non-perturbative version of the Gromov-Witten generating series, i.e. a particular choice of holomorphic function having this series as its asymptotic expansion (in fact the same result holds for any non-compact CY threefold having no compact divisors). If there is time left at the end (which there never is) I will discuss recent attempts to go beyond these results.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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