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Seminar by Leonid Chekhov (Steklov Mathematical Institute)

Title: Quantum Riemann surfaces related to Shroedinger equation solutions

2013.11.01 | Christine Dilling

Date Wed 23 Feb
Time 16:15 17:15
Location Aud. D3


(based on joint work with B.Eynard and O.Marchal)
We introduce the notion of hyperelliptic quantum Riemann surfaces constructed on the base of solutions of Shroedinger equation related to $\beta$-ensemble integrals in the large N limit. We present analogues of Seiberg--Witten equations, Riemann bilinear identities, and recursion relations enabling us to construct solutions for correlation functions order by order in $1/N^2$. In the case of rational potentials, these correlation functions and free energies correspond to the nonperturbative limit of the Nekrasov functions.