UTA Department of Mathematics

Applied Mathematics Seminar

Date/Time/Room: Friday (11/01/2002) at 2:00pm in 304 Pickard Hall

Speaker: Barbara Shipman, Department of Mathematics, The University of Texas at Arlington

"The Geometry of the Toda Lattice"

Abstract: The Toda lattice is a Hamiltonian system of ordinary differential equations that can be written in a special matrix form. The solution evolves by conjugating the initial matrix so that the eigenvalues remain fixed. There are several types of singular behaviors, for example, the solution may become undefined in finite time. To see more of the geometry of the system, the solutions are completed by embedding them into a flag manifold (which will be introduced and explained in the talk). A nice feature of this is that in the flag manifold, the solutions generate a group action, where the form of the group depends on the multiplicities of the eigenvalues. One can now study the orbits of these group actions to understand the completed Toda flows. Another nice feature is that a lot of the geometry can be seen in the structure of the moment polytope of the flag manifold (which will also be introduced in the talk).