A noncommutative generalization of Witten's conjecture

Abstract: The classical Witten conjecture says that the generating series of integrals over the moduli spaces of curves of monomials in the psi-classes is a solution of the Korteweg - de Vries (KdV) hierarchy. Together with Paolo Rossi, we present the following generalization of Witten's conjecture. On one side, let us deform Witten's generating series by inserting in the integrals certain naturally defined cohomology classes, the so-called double ramification cycles. It turns out that the resulting generating series is conjecturally a solution of a noncommutative KdV hierarchy, where one spatial variable is replaced by two spatial variables and the usual multiplication of functions is replaced by the noncommutative Moyal multiplication in the space of functions of two variables.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration