70 KAM Mathematical Colloquium

Abstract

A topological group is called extremely amenable if all its continuous actions on compact spaces have fixed points. Many well-studied non-locally compact groups are extremely amenable, for example, the unitary group of the infinite dimensional separable Hilbert space (Gromov--Milman) or the group of order preserving permutations of the rationals (Pestov). Historically the first groups to be proved extremely amenable (Christensen--Herer) were of the form L_0(phi, H) for carefully chosen submeasures phi and certain locally compact groups H.

Concentrating mostly on automorphism groups of countable structures, as in Pestov's example above, and on L_0(phi, H) groups, for a submeasure phi, I will explain in what way proving extreme amenability of a group involves the mathematical phenomena mentioned in the title. Part of this talk will be based on a joint work with Ilijas Farah.
 

O přednášejícím

Slawomir Solecki je jednim z nejznamejsich matematiku pracujicich v teorii mnozin, topologii a matematicke logice. Studoval na univerzite ve Vratislavi a posleze na Californskem technologickem institutu (Caltech), kde ziskal doktorat pod vedenim A. S. Kechrise. Za svou dizertaci ziskal 2 oceneni, Sacksovu cenu za nejlepsi dizertaci v oboru matematicka logika a W. P. Careyovu cenu za nejlepsi dizertaci na Caltechu v roce 1994/5. Solecki byl hostem prednich svetovych matematickych instituci (napr. IHES ve Francii nebo Fieldsuv Institut v Torontu). V soucasnosti je radnym profesorem na Illinoiske univerzite v Urbane v USA. Solecki je clenem edicnich rad 3 mezinarodnich casopisu a editorem nekolika sborniku konferenci, ktere (spolu)poradal. Je autorem vice nez 50 publikaci vesmes v prednich mezinarodnich casopisech. Jeho prace v deskriptivni teorii mnozin, teorii metrickych prostoru, topologii a v posledni dobe rovnez v kombinatorice jsou velmi citovany. Vzajemnym souvislostem uvedenych oboru bude venovano jeho prazske kolokvium.