Recorded 21 May 2025. Alessio Figalli of ETH Zurich presents "On the regularity of optimal transport maps" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Abstract: In optimal transport, understanding the regularity of optimal maps is an important topic. This talk aims to discuss the regularity theory for optimal maps and provide an overview of some important applications. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-and-numerical-methods-for-non-commutative-optimal-transport/