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SUMMARY:Robert Young (New York University)
DTSTART:20201030T150000Z
DTEND:20201030T160000Z
DTSTAMP:20260423T035738Z
UID:SRS/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SRS/1/">Metr
 ic differentiation and embeddings of the Heisenberg group</a>\nby Robert Y
 oung (New York University) as part of Sub-Riemannian Seminars\n\n\nAbstrac
 t\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 the Heise
 nberg group makes it impossible to embed into any $L_p$ space for $p\\in (
 1\,\\infty)$.  Recently\, with Assaf Naor\, we proved sharp quantitative b
 ounds on embeddings of the Heisenberg groups into $L_1$ and constructed 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 surface 
 in $\\mathbb{H}$ which is as bumpy as possible. In this talk\, we will des
 cribe what are the best ways to embed the Heisenberg group into Banach spa
 ces\, why good embeddings of the Heisenberg group must be "bumpy" at many 
 scales\, and how to study embeddings into $L_1$ by studying surfaces in $\
 \mathbb{H}$\n\nVIRTUAL SESSION\n
LOCATION:https://researchseminars.org/talk/SRS/1/
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