The Witten-Kontsevich theorem relates intersection products of certain cohomology classes in the tautological ring of the moduli space of stable curves, to the KdV hierarchy of partial differential equations. In this thesis, a recent proof of this theorem is presented. Firstly, the ELSV formula relates such intersection products to simple Hurwitz numbers, which count branched covers of algebraic curves. Subsequently, the link between Hurwitz theory and integrable systems is made via the Sato Grassmannian construction for the KP hierarchy.

The Witten-Kontsevich theorem relates intersection products of certain cohomology classes in the tautological ring of the moduli space of stable curves, to the KdV hierarchy of partial differential equations. In this thesis, a recent proof of this theorem is presented. Firstly, the ELSV formula relates such intersection products to simple Hurwitz numbers, which count branched covers of algebraic curves. Subsequently, the link between Hurwitz theory and integrable systems is made via the Sato Grassmannian construction for the KP hierarchy.

The Witten-Kontsevich Theorem

KLOMPENHOUWER, DAVID
2022/2023

Abstract

The Witten-Kontsevich theorem relates intersection products of certain cohomology classes in the tautological ring of the moduli space of stable curves, to the KdV hierarchy of partial differential equations. In this thesis, a recent proof of this theorem is presented. Firstly, the ELSV formula relates such intersection products to simple Hurwitz numbers, which count branched covers of algebraic curves. Subsequently, the link between Hurwitz theory and integrable systems is made via the Sato Grassmannian construction for the KP hierarchy.
2022
The Witten-Kontsevich Theorem
The Witten-Kontsevich theorem relates intersection products of certain cohomology classes in the tautological ring of the moduli space of stable curves, to the KdV hierarchy of partial differential equations. In this thesis, a recent proof of this theorem is presented. Firstly, the ELSV formula relates such intersection products to simple Hurwitz numbers, which count branched covers of algebraic curves. Subsequently, the link between Hurwitz theory and integrable systems is made via the Sato Grassmannian construction for the KP hierarchy.
moduli space
tautological ring
Hurwitz theory
integrable hierarchy
Sato Grassmannian
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/52243