Preface t o th e origina l IMP A editio n
This set o f lecture notes is an attemp t t o present a n accoun t o f basic ideas of a
small ne w theor y locate d o n th e crossroad s o f geometric functiona l analysis , topo -
logical groups of transformations, an d combinatorics . Th e presentatio n i s certainl y
The lectur e note s ar e organized o n a "need-to-know " basis , an d i n particular I
try to resist the temptation t o achieve extra generality for its own sake or introduc e
concepts o r result s tha t wil l not b e use d mor e o r les s immediately .
The notes have grown out o f mini-courses given by me at th e Nipissing Univer -
sity, Nort h Bay , Canad a (26-2 7 Ma y 2004) , a t th e 8iem e atelie r su r l a theori e de s
ensembles, CIRM , Luminy , Pranc e (20-2 4 September 2004) , and i n preparation fo r
a mini-cours e t o b e give n a t IMPA , Ri o de Janeiro , Brazi l (25-2 9 Jul y 2005) .
In thi s are a o f study, I was most influence d b y conversations wit h El i Glasner ,
Misha Gromov , an d Vital i Milman , t o who m I a m profoundl y grateful .
Special thank s g o to m y co-author s Thierr y Giordano , Aleko s Kechris , Mish a
Megrelishvili, Stev o Todorcevic, an d Volodj a Uspenskij , from who m I have learne d
much, an d I a m equall y gratefu l t o Pierr e d e la Harpe an d Anatol y M . Vershik .
I want to acknowledge important remark s made by, and stimulating discussion s
with, Jo e Auslander, V . Bergelson, Pete r Cameron , Michae l Cowling , Ed Granirer ,
John Clemens , Ilijas Farah , Davi d Fremlin, S u Gao, C. Ward Henson, Gre g Hjorth ,
Menachem Kojman , Julie n Melleray , Be n Miller , Carlo s Gustav o "Gugu " T . d e A .
Moreira, Christia n Rosendal , Matatyah u Rubin , Slawe k Solecki , an d Benj y Weiss .
This manuscrip t ha s muc h benefitte d fro m stimulatin g comment s an d sugges -
tions mad e b y V . Uspenskij , to o numerou s fo r mos t o f the m t o b e acknowledged .
Many usefu l remark s o n th e first versio n o f th e note s wer e als o mad e b y T . Gior -
dano, E . Glasner , X . Dommguez , I . Farah , A . Kechris , J . Melleray , V . Milman , C .
Rosendal, an d A . Vershik .
As always , th e autho r bear s ful l responsibilit y fo r th e remainin g error s an d
omissions, which ar e certainly there; the hop e is that non e of them ar e too serious.
The reade r i s warmly welcome d t o sen d m e comments a t .
During the past nine years that I have been working, on and off, i n this area, th e
research support wa s provided by two Marsden Fun d grant s of the Royal Societ y of
New Zealand (1998-2001, 2001-03), a Victoria University of Wellington research de-
velopment grant (1999), University of Ottawa internal grants (2002-04 , 2004-), an d
an NSER C discover y gran t (2003 - ). Th e Field s Institute ha s supporte d th e work -
shop "Interaction s between concentration phenomenon, transformation groups , an d
Ramsey theory " (Universit y o f Ottawa , 20-2 2 Octobe r 2003) .
Vladimir Pesto v
Gloucester, Ontario , 12 May 200 5
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