KP integrability of triple Hodge integrals

Abstract: In my talk, I will describe a relation between the Givental group of rank one and the Heisenberg-Virasoro symmetry group of the KP integrable hierarchy. It appears 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 the 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 the case of linear Hodge integrals. I will also describe the relation of this family of tau-functions with the deformation of the Kontsevich matrix model. My talk is based on two papers, arXiv:2009.01615 and arXiv:2009.10961.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

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