88. Mathematical Colloquium
Damien Gaboriau
Ecole Normale Superieure de Lyon
MEASURED GROUP THEORY, PERCOLATION AND NON-AMENABILITY
Thursday December 12, 2013, 10:30refektář, 1st floor
Malostranské nám. 25
118 00 Praha 1
Abstract
Amenability of groups is a concept introduced by J. von Neumann in his seminal article (1929) to explain the so-called Banach--Tarski paradox. It is easily shown that the free groups F on two generators are non-amenable. It follows that the countable discrete groups containing F are non-amenable. von Neumann's problem asked whether the converse holds true. In the 80's Ol'shanskii showed that his Tarski monsters are counter-examples. However, in order to extend certain results from groups containing F to any non-amenable countable group Gamma, it may be enough to know that Gamma contains F in a more dynamical sense. Namely, to know that Gamma admits an ergodic probability measure preserving action on some standard space for which the orbits can be partitioned into orbits of some ergodic free action of F.
The solution to this measurable von Neumann's problem involves percolation theory on Cayley graphs and measured laminations by subgraphs. I will present an introduction to this subject.
About the speaker
Damien Gaboriau studoval na Ecole Normale Superieure v letech 1986--1990. Habilitoval se v roce 2002 praci Stromy, grupy a faktory pred komisi excelentniho slozeni (M. Burger, A. Connes, T. Fack, E. Ghys, F. Ledrappier, G. Levitt, A. Louveau, S. Popa, A. Valette). D. Gaboriau byl pak clenem C.N.R.S. na Ecole Normale Superieure v Lyonu, reditelem ustavu ciste a aplikovane matematiky (UMPA) a take profesorem na Ecole Polytechnique (Palaiseau). Byl hostem a prednesl zvane prednasky na prednich evropskych a svetovych universitach (napr. Hebrejska Universita v Jeruzaleme, Universita v Gottingen) a v roce 2010 mel zvanou prednasku na Mezinarodnim kongresu matematiku v Hajdarabadu. D. Gaboriau je clenem edicnich rad 5 mezinarodnich casopisu. V roce 2003 mu byla udelena cena Francouzske Akademie ved.
Ve vedecke praci se venuje rozsahle oblasti zahrnujici deskriptivni teorii mnozin, dynamicke systemy, geometrickou teorii grup, ergodickou teorii a teorii pravdepodobnosti. Sem se dnes radi rovnez spocetna kombinatorika, strukturalni Ramseyova teorie a v posledni dobe rovnez dynamicky se rozvijejici teorie grafovych limit, kde Gaboriau nalezi k zakladatelskym osobnostem.
Gaboriau je znam jako skvely prednasejici a v prazskem kolokviu se bude venovat hlavni oblasti sveho vedeckeho zajmu.
