Thursday, 21st December 2006, 4:00 pm

Mathematics Building, Lecture Hall 2

Yehuda Shalom

(Tel Aviv University)

"The algebraization of Kazhdan's property (T)"

** Abstract: **
A group is said to have *Kazhdan's property (T) i*f 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:

**Theorem.** *Let R be any finitely generated commutative ring with unit, 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*.

Light refreshments will be served in the faculty lounge at 3:30.

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