VIRTUAL SEMINAR SERIES -- INTEGRABLE SYSTEMS: The quantum Witten-Kontsevich series

Xavier Blot (Weizmann Institute of Science)

Wednesday 3rd March 13:30-14:30 Zoom seminar hosted by ICMS

Abstract

The Witten-Kontsevich series is a generating series of intersection numbers on the moduli space of curves. In 2016, Buryak, Dubrovin, Guéré and Rossi defined an extension of this series using a quantization of the KdV hierarchy based on the geometry of double ramification cycle. This series, the quantum Witten-Konstevich series, depends on a quantum parameter. When this quantum parameter vanishes, the quantum Witten-Kontsevich series restricts to the Witten-Kontsevich series. In this talk, we will first construct the quantum Witten-Kontsevich series and then present all the known results about its coefficients. Surprisingly, a part of these coefficients are expressed in terms of Hurwitz numbers.

 

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