Abstract:

In this talk, we will explore the fascinating world of motion and shape, as we delve into the mathematical study of least-action flows. We investigate the various ways a convex body in Euclidean space can break into countably many pieces that move apart rigidly at constant velocity, following geodesic motions derived from optimal transport theory. Through a surprising connection to Minkowski’s classification of convex polytopes through their face areas and normals, we will classify the many ways in which a given body can fragment optimally. We will provide intriguing and paradoxical examples of fractal fragmentation, involving fat Cantor sets and Apolloian packings. The presentation will interweave geometry, optimization, and motion in an attractive and accessible manner.“

Bio:

Jian-Guo Liu is a Mathematics and Physics professor at Duke University and also co-directs the Zu Chongzhi Center for Mathematics and Computational Sciences at Duke Kunshan University. He studied at Fudan University for his Bachelor’s and Master’s degrees before earning his Ph.D. from the University of California, Los Angeles. As a recognized Fellow of the American Mathematical Society, Liu spends his time researching and teaching about complex equations and how they can be used in different areas like fluid dynamics, material science, biology, and machine learning. Lately, he’s been concentrating on optimal control and Hamilton-Jacobi equations and their applications in various scientific areas.