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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Rothschild Lecture: Classification of von Neumann
algebras - Stefaan Vaes (KU Leuven)
DTSTART;TZID=Europe/London:20170612T160000
DTEND;TZID=Europe/London:20170612T170000
UID:TALK72890AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72890
DESCRIPTION:The theme of this talk is the dichotomy between am
enability and non-amenability. Because the group o
f motions of the three-dimensional Euclidean space
is non-amenable (as a group with the discrete top
ology)\, we have the Banach-Tarski paradox. In dim
ension two\, the group of motions is amenable and
there is therefore no paradoxical decomposition of
the disk. This dichotomy is most apparent in the
theory of von Neumann algebras: the amenable ones
are completely classified by the work of Connes an
d Haagerup\, while the non-amenable ones give rise
to amazing rigidity theorems\, especially within
Sorin Popa'\;s deformation/rigidity theory. I w
ill illustrate the gap between amenability and non
-amenability for von Neumann algebras associated w
ith countable groups\, with locally compact groups
\, and with group actions on probability spaces.

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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