Past Event: Oden Institute Seminar

Convex Programming Relaxations for Many-Body Physics

Yuehaw Khoo, University of Chicago

Abstract

 In this talk, we explore adaptations of semidefinite programming relaxations for solving many-body physics problems. Our approach transforms a high-dimensional PDE problem into a convex optimization problem, setting it apart from traditional non-convex methods that rely on nonlinear re-parameterizations of the solution. In the context of statistical mechanics, we demonstrate how a mean-field type solution for an interacting particle Fokker-Planck equation can be provably recovered without resorting to non-convex optimization. For quantum mechanical systems, we present a similar technique to obtain the ground state of a quantum system and introduce a near-linear time algorithm for solving the convex program using hierarchical matrices.

Biography

Yuehaw Khoo is an assistant Professor at the University of Chicago. He works in computational math, focusing on high-dimensional problems in physics and biology. He did his postdoctoral study at Stanford University and graduate study at Princeton University.