Chern Lectures: The (in)compatibility of 3 and 5 dimensional Heisenberg geometry with Lebesgue spaces

Lecture | March 12 | 4:10-5 p.m. | Simons Institute, Auditorium,

 Assaf Naor, Princeton University

 Department of Mathematics

We will discuss the longstanding bi-Lipschitz embedding problem in $\mathbb R^k$, and how over the years it became intertwined with the embeddability properties of the Heisenberg groups into $L_p(\mu )$ spaces. We will explain a recent completion of this project, which exhibits unexpected twists, decisive applications to longstanding open questions in algorithms and metric geometry, and connections to subtle structural issues in analysis.