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BIRS Workshop Lecture Videos

Open intersection numbers, integrability and Virasoro constraints Alexandrov, Alexander


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.

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