SMS scnews item created by Emma Carberry at Sun 5 Dec 2010 2249
Type: Seminar
Distribution: World
Expiry: 10 Dec 2010
Calendar1: 10 Dec 2010 1430-1530
CalLoc1: Carslaw 175
Auth: carberry@60-241-127-220.static.tpgi.com.au (carberry) in SMS-WASM

# Joint Colloquium: Ajiev -- Holder classification of spheres and Tsar’kov’s phenomenon

JOINT COLLOQUIUM

Friday 10/12/10

Carslaw 175

2:30pm

We will depart for lunch at 1pm from the 2nd floor of Carslaw.

Title:  "Hölder classification of spheres and Tsar’kov’s phenomenon".

Abstract: This talk is in the areas of infinite-dimensional
and quantum geometry with some elements of algebra
and analysis on infinite-dimensional spaces.

The theory of the uniform classification of
infinite-dimensional spheres has been developed, mainly,
thanks to the solution of the distortion problem by E. Odell and
Th. Schlumprecht and is more balanced than the continuous,
isometric, Lipschitz or uniform classifications of infinite-dimensional
Banach spaces. It allows to transfer a group structure, group
actions and other metric-related constructions from one space
onto another. In particular,  we provide multiple examples of
spaces that do not allow any C*-algebra structure but can be
endowed with a homogeneous Hölder group structure.

We show that the uniformly continuous homeomorphisms
can be "upgraded" to the Hölder ones in the classical setting and
establish the explicit and, occasionally, sharp exponents of the
Hölder regularity for pairs of concrete spaces, including various
Besov, Lizorkin-Triebel, Sobolev, sequence, Schatten-von Neumann
and other Banach spaces (including lattices and more general
non-commutative spaces).

These results appear to have close ties with the presence
of a remarkable phenomenon from the infinite-dimensional
approximation theory discovered by Tsar’kov for the pairs of
Lebesgue spaces.


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