Time: 14:00-15:00, Monday, November 18 2024
Venue: E4-233, Yungu Campus
Host: Zhennan Zhou, ITS
Speaker: Jian-Guo Liu, Duke University
Biography: Jian-Guo Liu is a professor at Duke University specializing in applied mathematics, with a focus on kinetic theory, fluid dynamics, and numerical methods for partial differential equations. His research includes statistical, stochastic, and analytical methods in kinetic theory, particularly in the study of complex fluids, incompressible flows, and free-boundary problems. He is a Fellow of the American Mathematical Society. Liu received his B.S. and M.S. degrees from Fudan University in 1982 and 1985, respectively, and his Ph.D. in Mathematics from UCLA in 1990. Before joining Duke University, he held academic positions at the University of Maryland and Temple University.
Title: Rigidly Breaking Potential Flows and a Countable Alexandrov Theorem for Polytopes
Abstract: The variational relaxation of the least-action principle for free-boundary incompressible flow leads to pressureless Euler flows that follow Wasserstein geodesics. These action-minimizing incompressible flows exhibit local rigidity, characterized by convex and locally affine velocity potentials for initially convex bodies. An alternative characterization involves the absence of mass concentration in Monge-Ampère measures associated with certain Hamilton-Jacobi equations. This work closely connects with geometric theorems by Minkowski and Alexandrov on convex polytopes, as well as with the adhesion model in cosmology, a multi-dimensional framework that reduces to sticky particle flow in 1D. I will also describe several intriguing and paradoxical examples with fractal structures.
