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Seminar Physique Math茅matique

Title:听Transalgebraic听Spectral Curves, Quantum Curves, and Atlantes Hurwitz Numbers.

础产蝉迟谤补肠迟:听Physics is a great source of ideas for pure mathematics. The topological recursion of Chekhov-Eynard-Orantin (CEO) is an example of this approach: it was originally developed to solve matrix models in physics, but was then abstracted away from its physics origins. The result is a mathematical formalism that has听found听numerous applications in various areas of mathematics, particularly in enumerative geometry.听

The Topological Recursion/Quantum Curve (TR/QC) correspondence, which also originated in the context of matrix models, states that the CEO topological recursion (and its higher analog), which associates a sequence of differentials to a spectral curve, can be used to reconstruct the WKB asymptotic solution of a differential equation that is a quantization of the spectral curve (known as a "quantum curve"). In this work we prove the TR/QC correspondence for a class of transalgebraic spectral curves; those are curves with听exponential singularities, which听can be obtained as limits of sequences of algebraic spectral curves. To this end, we construct a generalization of topological recursion that is consistent with limits of sequences of algebraic curves; it includes contributions from the exponential singularities. The prototypical example is the spectral curve which is known to give rise to r-spin Hurwitz numbers via the usual topological recursion; we show that, for the same spectral curve, our natural generalization of the topological recursion instead computes atlantes Hurwitz numbers, and reconstructs the WKB solution of the appropriate quantum curve. This is particularly interesting given that atlantes Hurwitz numbers had so far evaded topological recursion methods.This is joint work with Reinier Kramer and Quinten Weller.

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Zoom : Meeting ID: 957 6100 0966 / Passcode: 198672

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