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50 years of finite-gap integration
September 17, 2024 12:50–13:30, Moscow, Steklov Mathematical Institute of RAS
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Global KP integrability
M. E. Kazarianab a National Research University Higher School of Economics, Moscow
b Skolkovo Institute of Science and Technology
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Abstract:
We say that a (formal) solution of KP hierarchy posses a (rational)
spectral curve if its associated $n$-point functions extend as global
rational functions after a suitable change of variables, one and the
same for all $n$. We show that the KP integrability is an internal
property of a system of $n$-point functions: the corresponding potential
associated with their power expansion at some point in some local
coordinate satisfies KP hierarchy if and only if the same holds for any
other expansion point and any other local coordinate. As a consequence,
we show that potentials govern by the procedure of topological recursion
of Chekhov-Eynard-Orantin on a rational spectral curve posses KP
integrability property.
The talk is based on a series of joint papers with A.Alexandrov,
B.Bychkov, P.Dunin-Barkowsky, and S.Shadrin.
Language: English
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