Lipschitz Continuity of Diffusion Transport Maps and Exponential Convergence of Sinkhorn's Algorithm via Creation of Log-Semiconcavity Along Heat Flows

Explore the mathematical foundations of optimal transport theory in this 30-minute conference talk examining the Lipschitz continuity properties of diffusion transport maps and the exponential convergence characteristics of Sinkhorn's algorithm. Delve into advanced mathematical concepts as the speaker demonstrates how log-semiconcavity creation along heat flows provides crucial insights into the convergence behavior of computational optimal transport methods. Learn about the theoretical underpinnings that govern the stability and efficiency of diffusion-based transport mappings, with particular emphasis on how heat flow dynamics influence the geometric properties of these mathematical objects. Discover the connections between differential geometry, probability theory, and computational optimization through rigorous analysis of transport map regularity and algorithmic convergence rates. Gain insights into cutting-edge research at the intersection of optimal transport theory, stochastic processes, and numerical analysis, presented as part of the "Optimal transport: stochastics, projections, and applications" program at the Fields Institute.