Sub-Riemannian Geometry of Optimal Transport: Mostly Classical and a Bit of Quantum

Explore a lecture by Tryphon Georgiou from the University of California, Irvine, who delves into the unexplored sub-Riemannian structure of Monge-Kantorovich transport, examining how particle positions during transport can be modeled through holonomy of transportation schedules. Recorded at IPAM's Optimal Transport for Density Operators workshop, this 49-minute presentation focuses on controllability issues and characterizes the structure group before connecting these concepts to quantum theory applications. The talk is based on collaborative research with Dr. Mahmoud Abdelgalil and provides valuable insights for those interested in the intersection of optimal transport theory, sub-Riemannian geometry, and quantum mechanics.