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Local testability in group theory I

Presented by: 
Alex Lubotzky Hebrew University of Jerusalem
Tuesday 9th May 2017 - 09:00 to 10:00
INI Seminar Room 1
A finitely generated group  G is be called TESTABLE ( or stable w.r.t. to the symmetric groups) if every almost homomorphism from G into a symmetric group Sym(n) is "close" to a real homomorphism. In the talk (which is a first in a series of two; the second will be given by Oren Becker), we will present this notion, its relation to local testability in computer science and its connections with other group theoretic concepts such as sofic groups, amenability, residual finiteness, the profinite topology, LERF and Kazhdan's property (T). 
The goal is to develop methods to distinguish between testable and non testable groups. Some results and some conjectures will be presented.
Joint work with Oren Becker.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons