Quantum intersection numbers and the Gromov-Witten invariants of the Riemann sphere.
Alexandr Buryak (National Research University Higher School of Economics, Skolkovo Institute of Science and Technology)
Abstract: Quantum intersection numbers were introduced through a natural quantization of the KdV hierarchy in a work of Buryak, Dubrovin, Guere, and Rossi. Because of the Kontsevich-Witten theorem, a part of the quantum intersection numbers coincides with the classical intersection numbers of psi-classes on the moduli spaces of stable algebraic curves. I will talk about our joint work in progress with Xavier Blot, where we relate the quantum intersection numbers to the stationary relative Gromov-Witten invariants of the Riemann sphere, with an insertion of a Hodge class. Using the Okounkov-Pandharipande approach to such invariants (with the trivial Hodge class) through the infinite wedge formalism, we then give a short proof of an explicit formula for the ``purely quantum'' part of the quantum intersection numbers, found before by Xavier, which in particular relates these numbers to the one-part double Hurwitz numbers.
mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry
Audience: general audience
BIMSA Integrable Systems Seminar
Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.
Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.
The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.
| Organizers: | NiŃolai Reshetikhin, Andrii Liashyk, Ivan Sechin, Andrey Tsiganov* |
| *contact for this listing |