Dear all, The next Banach spaces webinar is on Friday August 14 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Robert Young (NYU) Title: Metric differentiation and Lipschitz embeddings in $L_p$ spaces Abstract Kadec and Pełczyński showed that if $1\le p\lt 2\lt q\lt \infty$ and $X$ is a Banach space that embeds into both $L_p$ and $L_q$, then $X$ is isomorphic to a Hilbert space. The search for metric analogues of such a result is intertwined with the Ribe program and metric theories of type and cotype. Recently, with Assaf Naor, we have constructed a metric space based on the Heisenberg group which embeds into $L_1$ and $L_4$ but not in $L_2$. In this talk, we will describe this example, explain why embeddings of the Heisenberg group into Banach spaces must be "bumpy" at many scales, and discuss how to bound the bumpiness of Lipschitz maps to Banach spaces. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule August 21: Gilles Pisier (TAMU) Thank you, and best regards, Bunyamin Sari