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(Dec. 6) Embeddability and non-embeddability results for Carpets, and a resolution of a question of Heinonen and Semmes

Last updated :2019-12-02

Topic: Embeddability and non-embeddability results for Carpets, and a resolution of a question of Heinonen and Semmes
Speaker: Dr. Sylvester Eriksson-Bique
(University of California, Los Angeles)
Time: 15:00-16:30, Friday, December 6, 2019
Venue: Room 219, No. 8 Red Building, Zhuhai Campus, SYSU

Abstract:
Abstract: Carpets are a natural class of metric spaces that has been the focus of much research recently. Here, I present recent results on quasisymmetrically embeddability of large classes of carpets; and other results showing that one can often not get bi-Lipschitz embeddings. In particular, this latter component, when specialized to the case of slit carpets, that were studied by Merenkov and others, leads to a resolution of an open question from the influential list of problems by Heinonen and Semmes. Some of this is joint work with Jeff Cheeger and Guy C. David, and some based on prior results by Bruce Kleiner.