Hello,

The next Banach spaces webinar is on Friday November 12 9AM Central time. Please join us at

https://unt.zoom.us/j/83807914306

Title: Umbel convexity and the geometry of trees Speaker: Florent Baudier (Texas A&M)

Abstract. Markov convexity is a powerful invariant, introduced by Lee, Naor and Peres more than 15 years ago, which is related to the geometry of (locally finite) trees and (quantitative) uniformly convex renormings. In a joint work with Chris Gartland we introduced new metric invariants capturing the geometry of countably branching trees. Our main invariant, called umbel convexity, was inspired by Markov convexity and shares many of its desirable features. Most notably, it provides lower bounds on the distortion/compression required when embedding countably branching trees, and it is stable under certain nonlinear quotients. I will explain the close relationship between umbel convexity and Rolewicz's property $\beta$ renormings. If time permits, I will discuss the notion of umbel cotype, a relaxation of umbel convexity, and its relevance to the geometry of Heisenberg groups.

For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach

Thank you, and best regards,

Bunyamin Sari