Recorded 02 May 2025. Marius Junge of the University of Illinois at Urbana-Champaign presents "Why Ricci curvature (almost) failed us in noncommutative dynamics" at IPAM's Dynamics of Density Operators Workshop.
Abstract: We certainly tried to formulate Ricci curvature for von Neumann or matrix algebras, but it turns out not to work. In this talk I will review the connection between Wasserstein distance-entropy inequalities and concentration, and how to circumvent Ricci curvature for log-Sobolev inequalities. Order inequalities and Lipschitz norm replace (some of) the Ricci-curvature tools in a noncommutative Bakry-Emry program.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-dynamics-of-density-operators/