Università degli Studi di Padova

“Frobenius manifolds, moduli spaces of curves, and enumerative geometry: the topological recursion”

Mercoledì 20 Ottobre 2021, ore 11:00 - Aula 2AB40 - Danilo Lewanski (IHES e IPhT - France)


Topological recursion (TR) is a recently developed method, which can be thought as an algorithm recursively generating solutions to enumerative geometric problems. For instance, TR generates interesting numbers involved in Gromov-Witten theory, Mirror Symmetry, String Theory, different graphs counting on surfaces, Hurwitz theory, Weil-Petersson and Masur-Veech volumes, WKB analysis, Painlevé equations, polynomial invariants of knots, Hitchin systems, BPS states, and more. On the other hand, it provides a system of cohomology classes on the moduli spaces of curves with good properties — often a cohomological field theory, therefore in correspondence under certain conditions with the Frobenius manifolds introduced by Dubrovin.

It is an exciting time for TR, many new results are being developed, and several conjectures await to be proved.