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Institute for the Physics and Mathematics of the UniverseWPI

IPMU seminar

Date: October 27, 2008, 13:30 - 15:00
Place: Seminar Room at IPMU Prefab. B, Kashiwa Campus of the University of Tokyo
Speaker: Michael Semenov-Tian-Shansky (University of Bourgogne)
Title: Poisson groups and differential Galois theory of Schroedinger equation on the circle.
Abstract: The projective geometry approach to Schroedinger equations on the circle and the differential Galois theory are combined with the theory of Poisson Lie groups to construct a natural Poisson structure on the space of wave functions of the Schroedinger equation on the circle (at the zero energy level). Applications to KdV-like nonlinear equations are discussed. The same approach may be applied to second order difference operators on a one-dimensional lattice, yielding an extension of the lattice Poisson Virasoro algebra.