Hello all,
We have a Banach spaces webinar on Friday 12/10 9AM by Chris Gartland of Texas A&M. Please use the following zoom link (different than the usual webinar link).
-------------------------------------- Join Zoom Meeting https://tamu.zoom.us/j/92668666936?pwd=R2duYmxsQ0REakpIbzRDKzB0K3hwdz09
Meeting ID: 926 6866 6936 Passcode: 519913 --------------------------- Speaker: Chris Gartland (TAMU) Title: Non-embeddability of Carnot groups into $L^1$.
Abstract: Motivated by the Goemans-Linial conjecture on the Sparsest Cut problem, Lee-Naor conjectured in 2006 that the Heisenberg group does not biLipschitz embed into $L^1$, and this was proven true by Cheeger-Kleiner in the same year. The Heisenberg group is the simplest example of a nonabelian Carnot group, and Cheeger-Kleiner noted that their non-embeddability proof should hold for any Carnot group $G$ satisfying the following regularity property: For every subset $E \subset G$ with finite perimeter, ``generic" metric-tangent spaces of $E$ at points in $\partial E$ are vertical half-spaces.
It was expected that this property should hold for every nonabelian Carnot group, but at present, the problem remains open. The most significant achievement towards a solution is due to Ambrosio-Kleiner-Le Donne who proved that ``generic" \emph{iterated} metric-tangent spaces are vertical-half spaces.
In this talk, we'll describe how intermediate results of Ambrosio-Kleiner-Le Donne together with an adaptation of the methods of Cheeger-Kleiner may be used to deduce the non-biLipschitz embeddability of nonabelian Carnot groups in $L^1$. Based on joint work with Sylvester Eriksson-Bique, Enrico Le Donne, Lisa Naples, and Sebastiano Nicolussi-Golo.