CCMS Colloquium: Sharp Comparisons Between Sliced and Standard 1-Wasserstein Distances — Yi Wang (John Hopkins University)

Abstract: Optimal transport describes the process of finding the most efficient way to move mass between two distributions. Wasserstein distance measures the minimal transportation cost achieved by that optimal plan. However, in higher dimensions, computing the Wasserstein distance becomes computationally expensive. The sliced Wasserstein distance offers an effective and efficient way to alleviate this burden. In this talk, I will talk about the quantitative estimates between the sliced \(1\)-Wasserstein distance and the \(1\)-Wasserstein distance. I will then discuss our construction of a concrete example that demonstrates the exponents in the estimate are sharp. This is joint work with Guillaume Carlier, Alessio Figalli, Quentin Merigot.

Bio: Yi Wang is a Professor of Mathematics at Johns Hopkins University and a faculty member of the Johns Hopkins Data Science and AI Institute. Her research spans geometric analysis, nonlinear partial differential equations, and the mathematical foundations of machine learning and artificial intelligence. She received her Ph.D. from Princeton University and previously held positions at Stanford University and the Institute for Advanced Study. Her work has been supported by an NSF CAREER Award, and her recent research explores the geometry, optimization, and reasoning capabilities of modern AI systems.

For questions about the event, please contact your CCMS Colloquium chairs:

Prof. Robert Cass (Robert.Cass@ClaremontMcKenna.edu) or Prof. Qidi Peng (Qidi.Peng@cgu.edu)

For logistical questions, contact Maxwell Kooiker (Maxwell.Kooiker@cgu.edu), the CCMS Colloquium Assistant.