KP integrability of triple Hodge integrals -- Alexander Alexandrov, PHK seminar 02 Dec 2020

Speaker: Alexander Alexandrov (IBS, Center for Geometry and Physics, Pohang)
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.


Talk given at the Prague-Hradec Králové seminar on Cohomology in algebra, geometry, physics and statistics:
https://calendar.math.cas.cz/cohomology-in-algebra,-geometry,-physicsand-statistics-actual
https://researchseminars.org/talk/PHK-cohomology-seminar/21/


Slides:
https://users.math.cas.cz/~hvle/PHK/Alexandrov2020.pdf