Zeros of isomonodromic tau functions, spectral problems, and holomorphic anomaly

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 arxiv.org/abs/2410.17868 and arxiv.org/abs/2105.00985.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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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.

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