Geometry and Integrability in Mathematical Physics GIMP'06
May 15 - 19, 2006, Moscow, Russia
Maxim Kazaryan
IUM, Moscow
An algebro-geometric proof of Witten's conjecture
Witten's conjecture (first proved by M.Kontsevich) predicts certain intersection numbers on moduli spaces of complex curves. Namely, it claims that the generating function for these numbers satisfies KdV hierarchy of PDE's. Since it was formulated, several independent proofs have been given. All these proofs use technique that do not seem to be related intrinsically to the original problem.
We present a new rather sort proof of the conjecture which is entirely fulfilled in the framework of algebraic geometry. Our approach is based on the classical now ELSV-formula that relates intersection numbers on moduli spaces to the Hurwitz numbers enumerating ramified coverings of the sphere by Riemann surfaces.
Go to the Laboratoire Poncelet home page.