Density functional theory and multi-marginal optimal transport: Introduction


Density functional theory (DFT) is one of the workhorses of quantum chemistry and material science. In principle, the joint probability of finding a specific electron configuration in a material is governed by a Schrödinger wave equation. But numerically computing this joint probability is computationally infeasible, due to the complexity scaling exponentially in the number of electrons. DFT aims to circumvent this difficulty by focusing on the marginal probability of one electron. In the last decade, a connection was found between DFT and a multi-marginal optimal transport problem with a repulsive cost. I will give a brief introduction to this topic, including some open problems, and recent progress.

2024, Apr 4 10:00 AM PDT
KI Seminar
Online (zoom)
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Speaker Biography

Yair Shenfeld is an Assistant Professor of Applied Mathematics at Brown University. Previously, he was a C.L.E. Moore instructor and an NSF postdoctoral fellow in the Mathematics department at MIT. He completed his PhD at Princeton University under the supervision of Ramon van Handel, and received his B.Sc. from MIT.

Dr. Shenfeld’s work in high-dimensional probability and its interactions with analysis, geometry, and mathematical physics. His current research interests include stochastic analysis and functional inequalities, optimal transport, and renormalization group methods. He is also interested in extremal problems in convex geometry.