Working Seminar on Banach and Metric Spaces

Date: March 28, 2017

Time: 10:00AM - 11:00AM

Location: BLOC 220

Speaker: Florent Baudier, Texas A&M University

Title: Bi-Lipschitz embeddability of finitely branching diamonds (after M. I. Ostrovskii and B. Randrianantoanina)

Abstract: Johnson and Schechtman showed that the sequence of binary diamonds admits an equi-bi-Lipschitz embedding into any non super-reflexive Banach space. The analogue question for $k$-branching diamond graphs (k larger than 3 but finite) was solved recently by Ostrovskii and Randrianantoanina. They showed that despite the factorization approach of Johnson and Schechtman has some limitation one can still construct an equi-bi-Lipschitz embedding of the sequence the $k$-branching diamond graphs into any non super-reflexive Banach space, using a different technique. We will talk briefly about the factorization approach and its limitation and spend most of the talk explaining the key points of the rather technical embedding construction.