Open Collections

Open intersection numbers, integrability and Virasoro constraints

Banff International Research Station for Mathematical Innovation and Discovery

Abstract: From the seminal papers of Witten and Kontsevich we know that the intersection theory on the moduli spaces of complex curves is described by a tau-function of the KdV integrable hierarchy. Moreover, this tau-function is given by a matrix integral and satisfies the Virasoro constraints. Recently, an open version of this intersection theory was introduced. I will show that this open version can also be naturally described by a tau-function of the integrable hierarchy (MKP in this case), and the matrix integral, Virasoro and W constraints for the open case are also simple deformations of the closed ones. However, it is not clear how to deform the first Painleve hierarchy, satisfied by the Kontsevich-Witten tau-function.

Mathematics; Ordinary differential equations; Dynamical systems and ergodic theory; Dynamical systems

video/mp4

Author affiliation: Université de Montréal

2017-04-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61140

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/