Cohomology in algebra, geometry, physicsand statistics

KP integrability of triple Hodge integrals

Speaker’s name:

Alexander Alexandrov

Speaker’s affiliation:

Center for Geometry and Physics, IBS Pohang, South Korea

Place:

ZOOM meeting

Date:

Wednesday, 2. December 2020 - 11:30 to 12:30

Abstract:

In my talk I will describe a relation between the Givental group of rank one and Heisenberg-Virasoro symmetry group of the KP integrable hierarchy. In particular I will show that only a two-parameter family of the Givental operators can be identified with elements of the Heisenberg-Virasoro symmetry group. This family describes triple Hodge integrals satisfying the Calabi-Yau condition. Using identification of the elements of two groups it is possible to prove that the generating function of triple Hodge integrals satisfying the Calabi-Yau condition and its $\Theta$-version are tau-functions of the KP hierarchy. This generalizes the result of Kazarian on KP integrability in case of linear Hodge integrals. I will also describe the relation of this family of tau-functions with the generalized Kontsevich matrix model. My talk is based on two papers, arXiv:2009.01615 and arXiv:2009.10961.

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Our ZOOM meeting shall be open at 11.15 at

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Our ZOOM meeting shall be open at 11.15 at

https://cesnet.zoom.us/j/99598413922?pwd=c2Y0TENuZHdDQ3hDWEkySFI3YWo3QT09

Meeting ID: 995 9841 3922

Passcode: cartan

and closed at 13.00