|Location:||MSRI: Simons Auditorium, Online/Virtual|
Conformal Blocks On A Torus Via Fredholm Determinants
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Conformal blocks are fundamental building blocks of conformal field theories and appear in the theory of Painlevé equations through tau-functions, i.e the solutions of Painlevé equations can be expressed in terms of conformal blocks. Such a connection is established through Fredholm determinant techniques. In this talk I will show that the conformal block on a torus with one puncture arises as the tau-function of a special case of elliptic Painlevé VI equation, and can be written as a Fredholm determinant of an operator explicit in terms of hypergeometric functions. I will also explain how these results fit into the web of connections between integrable systems, conformal blocks, gauge theories and beta ensembles. This talk is based on joint work with F. Del Monte, P. Gavrylenko.