119048Moscow, Usacheva str., 6
phone/fax: +7 (495) 624-26-16
phone: +7 (495) 916-89-05
Deputy Dean for Academic Progress
Deputy Dean for Research
The famous Witten's conjecture, proposed in 1991, claims that the generating series of intersection numbers on the moduli space of stable algebraic curves gives a solution of the Korteweg - de Vries hierarchy. Since that time, a lot of results, showing a close relation of the topology of the moduli space of curves with the theory of partial differential equations, possessing an infinitesimal number of symmetries, were obtained. In my talk, I will recall some of these results and will present a general construction that, given a system of cohomology classes on the moduli spaces of curves, satisfying a collection of simple properties, associates to it a system of partial differential equations with a rich algebraic structure. This construction gives a new information about generalizations of Witten's conjecture and also, unexpectedly, predicts new relations in the cohomology of the moduli space of curves.