The DR-DZ equivalence

par Xavier Blot

mardi 9 déc. 2025, 11:15 → 12:15 Europe/Paris

1R2-207

A central problem in enumerative geometry, motivated by string theory, is the computation of the Gromov–Witten invariants of a target variety X. In 1990, Witten’s conjecture, proved by Kontsevich one year later, stated that the Gromov–Witten invariants for a target variety reduced to a point are governed by the KdV hierarchy. The aim of this talk is to explain how the DR–DZ conjecture, which we have recently established, makes it possible to generalize this result by constructing an integrable hierarchy that governs the Gromov–Witten invariants of any smooth projective variety X (and, more generally, the potential of any cohomological field theory).

This talk will be introductory: we shall recall Witten’s conjecture before presenting the general problem that we have resolved.

This is based on joint works with Danilo Lewanski, Adrien Sauvaget and Sergey Shadrin.