BIMSA > BIMSA Integrable Systems Seminar Zeros of isomonodromic tau functions, spectral problems, and holomorphic anomaly
Zeros of isomonodromic tau functions, spectral problems, and holomorphic anomaly
Organizers
Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Pavlo Gavrylenko
Time
Tuesday, November 5, 2024 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711 (BIMSA)
Abstract
Isomonodromic tau functions have explicit expressions as sums of conformal blocks (or Nekrasov functions), so-called Kyiv formulas, found by Gamayun, Iorgov, Lisovyy. Zeros of these tau functions correspond to the situation when 2*2 isomonodromic problem becomes the quantum mechanical problem, e.g., with potential cosh x. This way we get exact quantization conditions for the latter. Expansion around zero of the tau function is also worth studying, since its modular properties are well-defined and imply the so-called holomorphic anomaly equation for E_2 dependence of conformal block. The talk will be partially based on the papers https://arxiv.org/abs/2410.17868 and https://arxiv.org/abs/2105.00985.