| Date: | February 15, 2019 |
| Time: | 11:00am |
| Location: | BLOC 628 |
| Speaker: | Petros Valettas, University of Missouri |
| Title: | Gaussian concentration and convexity |
| Abstract: | We will discuss new forms of concentration and anti-concentration phenomena explained by convexity rather than isoperimetry. On the side of applications, this perspective allows for superconcentration and convexity to be melted together in order to obtain strong small ball and small deviation estimates in normed spaces. In this framework, the l∞-structure arises naturally as the (approximate) extremal. The underlying principle dictating these phenomena is rooted in the sensitivity of the variance. Based on a joint work with G. Paouris and K. Tikhomirov. |
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| Date: | February 22, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Alexandros Ezkenasis, Princeton University |
| Title: | Progress on Enflo's conjecture |
| Abstract: | In modern terminology, Enflo's conjecture (1978) asserts that a Banach space X has Rademacher type p if and only if it satisfies a metric property called Enflo type p. Loosely speaking, the conjecture suggests that all X-valued functions on the Hamming cube satisfy a dimension independent Lp Poincare inequality if and only if the same inequality is satisfied merely for linear functions. In his 1986 work, Pisier showed that Banach spaces of Rademacher type p have Enflo type q for every q |
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| Date: | April 2, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Gilles Lancien, Universite de Bourgogne Franche-Comte |
| Title: | Concentration phenomenon vs non coarse embeddability |
| Abstract: | We will discuss the coarse embeddability of the Hamming graphs and of Kalton's interlaced graphs into Banach spaces. Concentration inequalities for Lipschitz maps defined on these graphs have proven to be very important coarse invariants for Banach spaces. We will explain in each case, why they are different from the "non equi-coarse embeddability" of the corresponding family of graphs.
These remarks are taken from joint works with C. Petitjean and A. Prochazka and with F. Baudier, P. Motakis and Th. Schlumprecht. |
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