Corso D. Lewanski: "Spin Hurwitz theory and Topological Recursion"

Danilo  Lewanski (Università di Trieste) terrà un corso dal titolo "A spin on Hurwitz theory and Topological Recursion". Le lezioni si svolgeranno dalle 17 alle 19 in aula 3014 del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca (edificio U5) nei seguenti giorni:  28 settembre, 4-5 ottobre, 11-12 ottobre 2023. 

 

Abstract: Hurwitz numbers enumerate branched coverings of Riemann surfaces and provide a rich sandbox of examples for enumerative geometry and neighbouring areas. Surprisingly, there is a formula that connects them to the intersection theory of the moduli spaces of stable curves: the Ekedahl-Lando-Shapiro-Vainshtein formula (shortly ELSV formula). Furthermore, these numbers enjoy an integrability of type 2D-Toda, a result that has been later employed in the Gromov-Witten/Hurwitz correspondence. The topological recursion is a procedure originally arising from random matrix models that takes as input a spectral curve — a Riemann surface with some extra data on it — and returns the solution of some enumerative geometric problem. In fact topological recursion is under certain constraints equivalent to the Givental-Teleman reconstruction for semisimple cohomological field theories. A spin-off from the research on the mirror symmetry on Calaby-Yau 3-folds led to the generation of Hurwitz numbers via topological recursion. Over time this result has been generalised in different directions, including the Hurwitz count of Riemann surfaces with a spin structure, which are conjecturally determining Gromov-Witten invariants of surfaces with smooth canonical divisor.

 

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