Applied Mathematics Colloquium: Anthony Bloch (Michigan)
renowned expert in control and related fields
Location
Sherman Hall : 150
Date & Time
April 25, 2025, 11:00 am – 12:00 pm
Description
Title: Geometry of Hamiltonian and gradient flows
and total positivityAbstract: 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 interactingparticles 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 the theory of matrices all of whose minors are positive. This has fascinating generalizations to representation theory and applications in combinatorics, small vibrations and high energy physics. The type of dynamics discussed here also turns out to be able to prove interesting geometric results in the general theory of total positivity. I will also discuss links to general dissipative dynamics and to deep learning.
We will have the Departmental Coffee and Tea from 10 to 10:45 in M&P 422.
Tags: