Date: 25 march 2007, at 12 noon

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Speaker: Prof. Yehuda Shalom, Tel Aviv University

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Title: The algebraization of Kazhdan's property (T)

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Abstract: A group is said to have Kazhdan's property (T) if every
isometric (not necessarily linear) action of it on a Hilbert space
fixes a point.  Following a brief discussion of this important
property and some geometric approaches to it, we shall concentrate on
recent developments of algebraic nature, including connections to
K-theory, particularly discussing the following recent result:

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Theorem. Let R be any finitely generated commutative ring with 1, and
let EL(n,R)<GL(n,R) be the subgroup generated by the elementary
matrices over R. Then for all n > 1+ Krull dimension R, this group has
property (T). In particular, SL_n(Z[x_1, ... ,x_m]) has property (T)
for all n > m+2.

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