College of Liberal Arts and Sciences

# Department of Mathematics

## Analysis and Probability Seminar

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Title: Embeddings of the Heisenberg group and the Sparsest Cut problem
Speaker: Robert Young (Courant Institute)
Time: Friday, January 19, 2018 at 1:30 pm
Place: MONT 414Abstract: The Heisenberg group $\mathbb{H}$ is a sub-Riemannian manifold that is hard to embed in $\mathbb{R}^n$. Cheeger and Kleiner introduced a new notion of differentiation that they used to show that it does not embed nicely into $L_1$. This notion is based on surfaces in $\mathbb{H}$, and in this talk, we will describe new techniques that let us quantify the "roughness" of such surfaces, find sharp bounds on the distortion of embeddings of $\mathbb{H}$, and estimate the accuracy of an approximate algorithm for the Sparsest Cut Problem. (Joint work with Assaf Naor)

Organizer: Vasileios Chousionis and Oleksii Mostovyi