Wednesday, July 24
In this presentation, the speaker will focus on ideas from dynamic and geometric ideas associated with the theory of integrable Hamiltonian systems and the application of these ideas to various problems in applied mathematics. In particular the speaker will describe the relationship between integrable Hamiltonian systems and gradient flows, the Toda lattice and related systems, the geometry of the momentum map and convexity, the flow of the generalized rigid body equations, and other geodesic flows. He will also discuss some extensions of these ideas to infinite-dimensional flows and describe the new phenomena that arise in this case. In addition, he will show how integrable systems shed light on problems of least squares theory, linear programming and other computational problems, and on optimal control theory.
Integrable Systems-Theory and Applications
Anthony M. Bloch
Department of Mathematics
The University of Michigan, Ann Arbor
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