Recorded 02 April 2025. Tryphon Georgiou of the University of California, Irvine, presents "Sub-Riemannian geometry of Optimal Transport: mostly classical and a bit of quantum" at IPAM's Optimal Transport for Density Operators: Theory and Numerics Workshop. Abstract: We explore a hitherto unstudied sub-Riemannian structure of the Monge-Kantorovich transport, where the relative position of particles along their journey is modeled by the holonomy of the transportation schedule. We focus on controllability issues and characterize the structure group. The talk will conclude with a flashback on related concepts introduced in quantum theory that pertain to holonomy. This is based on joint work with Dr. Mahmoud Abdelgalil. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-optimal-transport-for-density-operators-theory-and-numerics/?tab=schedule