# Witten's Conjecture

Witten's conjecture is a recursive constraint for top intersections of -classes on . More precisely, if one considers the generating function

Setting , Witten's conjecture is that is annihilated by a certain partial differential operator that also arises in studying the KdV equation in soliton theory. It can be restated as a specialization of the Virasoro conjecture for the case where is a point.

Multiple proofs of this conjecture now exist, due to Kontsevich, Okounkov-Pandharipande, and most recently Mirzakhani.

Jeffrey Herschel Giansiracusa 2005-06-27