Jerusalem Mathematics Colloquium

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) 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:
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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