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This term we focus on "Inspiration from Physics to Mathematics." The speaker's abstract:

From the symmetric differentials calculated by the Chekhov-Eynard-Orantin topological recursion on a given spectral curve, one can naturally reconstruct an associated wave-function. Inspired by physics, the topological recursion/quantum curve correspondence asserts that this wave-function should be annihilated by a quantization of the original spectral curve. While this conjecture has been verified for a large class of genus zero spectral curves, all of those are algebraic, and do not include, for instance, the spectral curves that encapsulate the data of various types of Hurwitz numbers and Gromov-Witten invariants. (For some of those, one can verify the conjecture using other means, but not directly from the topological recursion.) In this work we prove the topological recursion/quantum curve correspondence for a class of spectral curves with essential singularities. Our method involves studying sequences of algebraic spectral curves, and whether topological recursion commutes with the limit of these sequences. Unexpectedly, we obtain in the process a generalization of topological recursion in which contributions from contour integrals around essential singularities must be incorporated.

This is based on joint work with my MSc student Quinten Weller.

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