Seminar talk, 8 June 2016

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Speaker: Vladimir Rubtsov

Title: On geometries of "paired" Monge-Ampère equations

Abstract:
I will talk about recently discovered interesting geometries related to pairs of operators of Monge-Ampère type. These "paired" operators are described by Monge-Ampère operators with coefficients that satisfy another Monge-Ampère equation. There will be shown Monge-Ampère pairs (initially appeared in geophysical hydrodynamics) that define a hypersymplectic structure in R^4 and an example related to generalized Hitchin complex structure. Hypothetically, all such pairs appear as two-dimensional reduction of a completely integrable system defined by a twistor "master-equation" related to Plebanski four-dimensional equation.