Recorded 22 May 2025. Sivaraman Balakrishnan of Carnegie Mellon University presents "Stability Bounds for Smooth Optimal Transport Maps and their Statistical Implications" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Abstract: I will present some recent stability bounds for the OT map between two distributions. Under regularity conditions, these bounds allow us to reduce the problem of estimating the OT map to that of estimating densities in the Wasserstein distance. I will then discuss consequences of these stability bounds in statistical optimal transport -- estimating the OT map between smooth distributions, between log-concave distributions, and between moment-bounded distributions from random samples. The talk will be based on joint work with Tudor Manole, Jonathan Niles-Weed and Larry Wasserman. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-and-numerical-methods-for-non-commutative-optimal-transport/