Rice University Department of Mathematics Colloquium

The Riemann-Hilbert correspondence and enumerative geometry

4:00 pm Friday, October 13, 2017
Andrew Neitzke (UT Austin)

Abstract: The classical Riemann-Hilbert correspondence takes an ordinary differential equation in one complex variable to its corresponding monodromy representation. It is a classical problem to describe, as concretely as we can, what this correspondence actually is. In the last few years it has been understood that this problem is intimately connected with a web of other topics in geometry and quantum field theory. One key new ingredient is the theory of “generalized Donaldson-Thomas invariants”; originally introduced by Kontsevich-Soibelman and Joyce-Song in the study of 3-dimensional Calabi-Yau manifolds, these objects have turned out to be the key to a new scheme for solving the Riemann-Hilbert problem much more explicitly than was previously possible. I will review these developments, and some recent applications.

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