Geometry Colloquium An algebro-geometric proof of Witten's conjecture

Date
2006-12-08 16:30 - 2006-12-08 18:00
Place
8-302
Speaker/Organizer
Maxim Kazarian (Steklov Math. Institute, Moscow)
 
(joint with S. Lando)Witten's conjecture (proved first by Kontsevich) predicts certainintersection numbers on the moduli space of complex curves withmarked points. We present a new relatively simple proof based onthe analysis of the relationship between intersection indices onmoduli spaces and Hurwitz numbers enumerating ramified coveringsof the $2$-sphere. Our computations lead to a new previouslyunknown miraculous relationship between KP and KdV integrablehierarchies.