# 30th Annual Owens Lecture: Geometry of Integrable Hamiltonian & Gradient Flows and Total Positivity

This event is in the past.

**Date:**April 18, 2023

**Time:**2:30 p.m. to 3:30 p.m.

**Category:**Lecture

**RSVP is closed.**

Title:The Geometry of Integrable Hamiltonian and Gradient Flows and Total Positivity

Speaker: Anthony M. Bloch, University of Michigan

Abstract:

In this talk I will discuss various connections between the dynamics of integrable (solvable) Hamiltonian flows, gradient flows, and geometry. A key example will be the Toda lattice flow which describes the dynamics of interacting particles on the line. I will show how versions of this can also be viewed as gradient flows and relate the flow to the geometry of convex polytopes as well as to the theory of total positivity. The latter theory has its origins in linear algebra and matrices, all of whose minors are positive. This simple concept has fascinating generalizations to representation theory and applications in combinatorics, small vibrations and high energy physics. The type of dynamics discussed here turns out to be able to prove interesting results in the general theory of total positivity. The talk will be accessible to a general scientific audience.

About the speaker:

Anthony M. Bloch is the Alexander Ziwet Collegiate Professor of Mathematics at the University of Michigan where he is currently department chair. He received a B.Sc.(Hons) from the University of the Witwatersrand, Johannesburg, in 1978, an M. S. from the California Institute of Technology in 1979, an M. Phil. from Cambridge University in 1981 and a Ph. D from Harvard University in 1985. He has received various awards including a Presidential Young Investigator Award, a Guggenheim Fellowship and a Simons Fellowship and is a Fellow of the IEEE, SIAM and the AMS. He has served on the editorial boards of various journals, was Editor-in-Chief of the SIAM Journal of Control and Optimization and is currently co-Editor-in-Chief of the Journal of Nonlinear Science.

About the Owens Lecture:

The Owens Lecture is named for the late Owen G. Owens, a former Professor of Mathematics at Wayne State University. The Lecture is supported by the Owens Fund, which was established by the family of Professor Owens.