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SUMMARY:Robert Young (New York University)
DTSTART:20201030T150000Z
DTEND:20201030T160000Z
DTSTAMP:20260404T143359Z
UID:SRS/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/SRS/1
 /">Metric differentiation and embeddings of the Heisenberg group</a>\nby R
 obert Young (New York University) as part of Sub-Riemannian Seminars\n\n\n
 Abstract\nPansu and Semmes used a version of Rademacher's differentiation 
 theorem to show that there is no bilipschitz embedding from the Heisenberg
  groups into Euclidean space. More generally\, the non-commutativity of th
 e Heisenberg group makes it impossible to embed into any $L_p$ space for $
 p\\in (1\,\\infty)$.  Recently\, with Assaf Naor\, we proved sharp quantit
 ative bounds on embeddings of the Heisenberg groups into $L_1$ and constru
 cted a metric space based on the Heisenberg group which embeds into $L_1$ 
 and $L_4$ but not in $L_2$\; our construction is based on constructing a s
 urface in $\\mathbb{H}$ which is as bumpy as possible. In this talk\, we w
 ill describe what are the best ways to embed the Heisenberg group into Ban
 ach spaces\, why good embeddings of the Heisenberg group must be "bumpy" a
 t many scales\, and how to study embeddings into $L_1$ by studying surface
 s in $\\mathbb{H}$\n\nVIRTUAL SESSION\n
LOCATION:https://stable.researchseminars.org/talk/SRS/1/
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