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Graphs on surfaces and curves over number fields
November 3, 2021 18:30–21:00, Moscow, online
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Gaudin model and branched coverings of a sphere
I. Tolstukhin National Research University "Higher School of Economics", Moscow
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Abstract:
The Gaudin model is a physical system originally introduced for
descriptions of the interaction of several charged particles on a straight line. Her
the quantum version consists of n commuting operators (Hamiltonians),
depending on n pairwise different complex parameters and acting on
tensor product of n representations of the Lie algebra sl_2. One of the tasks
the Gaudin model - to diagonalize these operators and understand how they change
joint spectrum when changing parameters. It turns out that the mapping
the joint spectrum of Hamiltonians for a given set of parameters continues
to the ramified covering overline {M_ {0, n + 1}}, - the Deligne compactification
Mumford spaces of moduli of stable rational curves with n + 1
marked with a dot. The talk will tell you about the device of this cover.
in the case when n = 3 and the base of the covering is the Riemann sphere. Everything
the necessary definitions and information will be given in the course of the report.
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