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Seminar of Laboratory 5 IITP RAS "Integrable structures in statistical and field models"
February 23, 2017 14:00, Moscow, The Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, room 304
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Deformations of complex structures on Riemann surfaces and integrable structures of Whitham type hierarchies
A. V. Odesskii Brock University
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Abstract:
We obtain variational formulas for holomorphic objects on
Riemann surfaces with respect to arbitrary local coordinates on the
moduli space of complex structures. These formulas are written in
terms of a canonical object on the moduli space which corresponds to
the pairing between the space of quadratic differentials and the
tangent space to the moduli space. This canonical object satisfies
certain commutation relations which appear to be the same as the ones
that emerged in the integrability theory of Whitham type hierarchies.
Driven by this observation, we develop the theory of Whitham type
hierarchies integrable by hydrodynamic reductions as a theory of
certain differential-geometric objects. As an application we prove
that the universal Whitham hierarchy is integrable by hydrodynamic
reductions.
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