New Trends in Kinetic and Optimal Transport

Event Overview

Kinetic theory offers an effective approach to reduce the complexity of particle systems by evolving probability density functions instead of tracking individual particles. This reduction in dimensionality significantly simplifies the problem, enabling efficient analysis and computation. Optimal transport, on the other hand, provides a natural geometric framework for understanding gradient flows, diffusive partial differential equations, and diffusion processes.

The connection between these fields dates back to McKean's work in the 1960s, where he establishes an explicit convergence rate for Kac's caricature, a one-dimensional toy model for the Boltzmann equation. Moreover, optimal transport has played a crucial role in establishing the rigorous theory of mean field limits, bridging the gap between particle systems and mean field kinetic equations. Furthermore, it has emerged as a vital numerical analysis tool for studying particle methods. The remarkable contributions of Cédric Villani in both fields has earned him the Fields Medal in 2010. Recent advancements have deepened the connection between the two fields, opening up exciting new research directions. These include the exploration of sampling techniques, solving inverse problems, quantifying uncertainty, and building mathematical foundations for deep learning. 

This workshop aims to foster collaboration and facilitate fruitful discussions among researchers from both backgrounds, with a focus on exploring the interdisciplinary nature of these subjects. 

Speakers

• Luis Chacón, Los Almos National Laboratory 
• Katy Craig, University of California, Santa Barbara
• Lukas Einkemmer, University of Innsbruck
• Ru-Yu Lai, University of Minnesota
• Wonjun Lee, University of Minnesota 
• Yulong Lu, University of Minnesota
• Kunlun Qi, University of Minnesota
• Kui Ren, Columbia University
• John Schotland, Yale University
• Yunan Yang, Cornell University
• Haomin Zhou, Georgia Institute of Technology
• Xiangxiong Zhang, Purdue University

Speaker Abstracts

Schedule

Wednesday, October 25th

Thursday, October 26th

Friday, October 27th

Organizer

Li Wang