Pavlo Gavrylenko (SISSA, Trieste, IT)

Title: Isomonodromic deformations on a torus, Fredholm determinant, and connection constant.

Abstract: We will see how isomonodromic tau functions on a torus with one puncture can be expressed as a matrix Fredholm determinant. This Fredholm determinant can be used to prove Kyiv formula in the toric case. We also use it to study the monodromy dependence of the tau functions, and then to find the connection constant for the modular transformation of these tau functions. This connection constant can also be easily turned into the fusion kernel for c=1 toric conformal blocks. The talk will be based on a joint work with Fabrizio Del Monte and Harini Desiraju.