PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact John Roe, Nigel Higson, Ping Xu, Mathieu Stienon.

Title:Lie algebra cohomology, inifinite-dimensional symplectic structures and Hamiltonian systems
Seminar:Noncommutative Geometry Seminar
Speaker:Claude Roger, Universite de Lyon 1
Abstract:
We shall describe some relations between parts of some kind of a trilogy: 1) Infinite dimensional Lie algebras and their cohomology(algebra), 2) Symplectic structures on the coadjoint orbits on their dual(geometry), 3) Partial differential equations as hamiltonian systems (hopefully integrable!) on those symplectic structures(dynamics). The basic and most well known example is : Virasoro cocycle (Gel’fand-Fuks cohomology)?Quadratic densities on the circle and Schwarzian derivative?Korteweg-De Vries equation and hierarchy. We shall discuss various generalizations of the above scheme: a) change of metrics modifies the hamiltonian( but not the geometry) and the associated equations (results by Misiolek and Khesin) b) some new Lie algebras appear naturally as symmetries, and their cohomological properties imply unexpected hamiltonian action (results by J.Unterberger and the author) c) adding loops in the scenario gives equations with one more variable (results by V. Ovsienko and the author) d) the Lie algebra of unimodular vector fields and its various extensions sheds light on Magne- tohydrodynamics (MHD), and Chromohydrodynamics(CHD) (results by F. Gay-Balmaz).

Room Reservation Information

Room Number:MB106
Date:09 / 17 / 2009
Time:02:30pm - 03:30pm