Mathematisches Institut, Sidlerstrasse 5, CH-3012 Bern Philosophischnaturwissenschaftliche Fakultät Departement Mathematik und Statistik Mathematisches Institut Mathematical Colloquia ____________________________________________________________________________ Monday, 14 March 2016 17:15 h, Lecture Room B 78 Prof. Dr. Jeremy Tyson, University of Illinois Bi-Lipschitz embeddings and differentiation Abstract: An embedding of metric spaces is bi-Lipschitz if it distorts distances by a fixed multiplicative factor. Which metric spaces admit a bi-Lipschitz embedding into a finite-dimensional Euclidean space? Into a (fixed) Banach space? Quantitative versions of this problem arise in connection with algorithmic computer science. Bi-Lipschitz embeddability is closely tied to the differentiability of real-valued Lipschitz functions. I will discuss theorems of Pansu and Cheeger on the differentiability of Lipschitz functions between Carnot groups and of real-valued Lipschitz functions on metric measure spaces supporting a Poincare inequality, and the implications of such results for bi-Lipschitz nonembeddability. I will also describe recent examples of non-equiregular subRiemannian spaces and other metric spaces which do bi-Lipschitz embed into Euclidean space. Sekretariat, Mathematisches Institut, Sidlerstrasse 5, CH-3012 Bern, Tel. +41 (0)31 631 88 21, Fax +41 (0)31 631 85 10 [email protected], www.math.unibe.ch
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