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