Abstract: In Banach space theory, Rademacher type is an important invariant that controls many geometric and probabilistic properties of normed spaces. It is of considerable interest in various settings to understand to what extent such powerful tools extend to general metric spaces. A natural metric analogue of Rademacher type was proposed by Enflo in the 1960s-70s, and has found a number of interesting applications. Despite much work in the intervening years, however, the relationship between Rademacher type and Enflo type has remained unclear. This basic question is settled in joint work with Paata Ivanisvili and Sasha Volberg: in the setting of Banach spaces, Rademacher type and Enflo type coincide. The proof is based on a very simple but apparently novel insight on how to prove dimension-free inequalities on the Boolean cube. I will not assume any prior background in Banach space theory in the talk.
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