Department of mathematics

Faculty of Electrical Engineering



Prof. Thomas Schlumprecht


Texas A&M University, USA
katedra matematiky FEL ČVUT

On the coarse embedability of Hilbert space
and the metric characterization
of asymptotic properties


Thursday 31 May 2018, 14:00

Jugoslávských partyzánů 1580/3,  Prague 6
 5th floor,  room no. 507  (JP:B1-507)



A new concentration inequality is proven for Lipschitz maps on the infinite Hamming graphs taking values
into Tsirelson's original space. This concentration inequality is then used to disprove the conjecture, originating
in the context of the Coarse Novikov Conjecture, that the separable infinite dimensional Hilbert space coarsely
embeds into every infinite dimensional Banach space. Some positive embeddability results are proven for the
infinite Hamming graphs and the countably branching trees using the theory of spreading models. A purely metric
characterization of finite dimensionality is also obtained, as well as a rigidity result pertaining to the spreading
model set for Banach spaces coarsely embeddable into Tsirelson's original space. Using part of the proof we also
obtain a metric characterization of the property that a Banach space is reflexive and asymptotically c0.
This is joint work with Florent Baudier, Gilles Lancien, and Pavlos Motakis.




Responsible person: doc. RNDr. Martin Bohata, Ph.D.