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Seminar

Working Seminar: Median Spaces: Quantitative rectifiability and differentiation in the Heisenberg group November 08, 2016 (01:30 PM PST - 03:00 PM PST)
Parent Program: Geometric Group Theory MSRI: Baker Board Room
Speaker(s) Robert Young (New York University, Courant Institute)
Description No Description
Video
I will discuss the relationship between the geometry of cut metrics and embeddings into L_1.  Cheeger and Kleiner used this notion to show that there are no bilipschitz embeddings from the Heisenberg group to $L_1$, and I will describe their work, along with recent work (joint with Assaf Naor) that gives sharp bounds on such embeddings by quantifying the "roughness" of surfaces in the Heisenberg group.  One application of this work finds sharp lower bounds on an algorithm for approximating the Sparsest Cut Problem.