Please join us on Friday March 4 at 9AM (Central US time) for the following talk. (Please note the zoom link different than before)

Zoom link: https://unt.zoom.us/j/85738310731

Best regards, Bunyamin Sari

Title: Dvoretzky-type theorem for locally finite subsets of a Hilbert space Speaker: Mikhail Ostrovskii (St. John's)

Abstract. The main result of the talk: Given any $\varepsilon>0$, every locally finite subset of $\ell_2$ admits a $(1+\varepsilon)$-bilipschitz embedding into an arbitrary infinite-dimensional Banach space.

The result is based on two results which are of independent interest:

(1) A direct sum of two finite-dimensional Euclidean spaces contains a sub-sum of a controlled dimension which is $\varepsilon$-close to a direct sum with respect to a $1$- unconditional basis in a two-dimensional space.

(2) For any finite-dimensional Banach space $Y$ and its direct sum $X$ with itself with respect to a $1$-unconditional basis in a two-dimensional space, there exists a $(1+\varepsilon)$-bilipschitz embedding of $Y$ into $X$ which on a small ball coincides with the identity map onto the first summand and on a complement of a large ball coincides with the identity map onto the second summand.

(joint with F. Catrina and S. Ostrovska)