Free Probability and Free Transport - Part 1

In this lecture, Dima Shlyakhtenko from the Institute for Pure and Applied Mathematics presents the first part of "Free Probability and Free Transport" at IPAM's Non-commutative Optimal Transport Tutorials at UCLA. Explore Voiculescu's free probability theory through a comprehensive introduction that covers transport notions in this setting and the Biane-Voiculescu extension of the Wasserstein distance concept. Discover various applications to operator algebra problems as Shlyakhtenko builds a foundation for understanding non-commutative probability structures. Recorded on March 13, 2025, this 82-minute presentation serves as an essential resource for mathematicians interested in the intersection of probability theory and operator algebras.