Dynamical Systems, Linear Programming and the Monge-Kantorovich Problem

Explore the connections between mass transport problems, linear programming, and dynamical systems in this 17-minute conference talk by Anthony Bloch from the University of Michigan. Discover how solutions to the Monge-Kantorovich mass transport problem relate to two fundamental areas of mathematical research that were central to Steve Smale's work. Learn about the problem's applications in both finite-dimensional settings involving adjoint orbits and infinite-dimensional contexts involving semigroups of measure-preserving transformations of the annulus. Examine the geometric relationships with convex polytopes that emerge in both scenarios. Gain insights into collaborative research conducted with Tudor Ratiu that bridges optimal transport theory, optimization methods, and dynamical systems theory. This presentation was delivered at the Smale@95 conference honoring the contributions of mathematician Steve Smale.