Analysis Seminar: Embedding snowflakes of the Heisenberg group into Euclidean space
Abstract: One consequence of Assouad's embedding theorem is that the snowflaked Heisenberg group has a bi-Lipschitz embedding into Euclidean space. (Those terms will be defined in the talk.) Terence Tao improved this result by constructing an embedding which is in some sense optimal. His proof uses the Nash-Moser iteration scheme, Littlewood-Paley theory on the Heisenberg group, and quantitative homotopy lifting arguments. (Those terms will not be defined in the talk.) We present an alternative proof of Tao's result which relies primarily on the lattice structure of the Heisenberg group as well as one of the oldest tricks in harmonic analysis. This is joint work with Seung-Yeon Ryoo.
*Please note this Analysis Seminar has a location change to Crow Hall, Room 205