KTH/SU Mathematics
Colloquium
20 September
2006
Maxim Kazarian, Independent Univ.
of Moscow
Integrable hierarchies
and intersection theory on the moduli spaces of
curves.
ABSTRACT
Witten's conjecture
(1991) claims that the generating function for certain
intersection numbers on the modula spaces of curves satisfies a system
of PDEs known as the KdV hierarchy. Since the conjecture was
formulated, a number different of proofs has appeared: first by Kontsevich,
and then by other mathematitians. All available proofs exploit techniques
which seems to be not intrinsically related to the initial problem.
Recently, M.Kazarian and S.Lando found a new proof based on the
classical now Ekedahl-Lando-Shapiro-Vainshtein formula using purely
algebro-geometric techniques. As a byproduct, this proof
seems to be simpler than all the known ones. Formally, our proof
provides a new miraculous reduction of the KP equation to the KdV
equation that has no analog in other domains of mathematics.