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Solitons and Many-Body Systems in Algebraic Geometry
Colloquium| Speaker: | David Ben-Zvi, University of Chicago |
| Location: | 693 Kerr |
| Start time: | Tue, Jan 14 2003, 4:10PM |
Description
One of the more puzzling discoveries in the theory of integrable
systems is that the motion of the poles of meromorphic solutions to
soliton equations (PDE such as the KP hierarchy) is often governed by
integrable many--body systems (ODE such as the Calogero-Moser system).
I will present an explanation of this phenomenon (joint work with
T. Nevins) using (noncommutative) algebraic geometry. We study the
space of "configurations of points on the quantum plane" and other
spaces of noncommutative vector bundles as a natural bridge between
solitons and particles. Namely, the soliton equations are realized as
flows on these configurations, and a geometric Fourier transform
converts the flows into the linear flows along tori (Jacobians of
spectral curves) which give the "integration" of the many--body
system.
3:45 Refreshments will be served before the talk in 551 Kerr Hall