Rigidity VII

Meeting Details

For more information about this meeting, contact Kendra Stauffer, Alp Uzman.

Speaker: Alp Uzman, Penn State

Abstract Link: https://arxiv.org/abs/math/0106063

Abstract: Thirteenth chapter of Witte Morris' notes will be covered, viz. our topic will be Kazhdan's property (T). Last week we observed that considering the so-called left regular representation of the additive group of real numbers on the space of square-integrable numerical functions defined on it, we can find nonzero almost-invariant vectors, yet this representation admits no nonzero invariant vectors. Kazhdan's insight from 1967 is that for many semisimple Lie groups and their lattices this phenomenon does not occur, instead the existence of nonzero almost-invariant vectors for any unitary representation guarantees the existence of an actual nonzero invariant vector. Thus Kazhdan's property is something to utilize in tandem with amenability. Just as last week I will present the proofs of some basic results and exhibit quintessential examples. My sources are, alongside Witte Morris' notes, Zimmer's book Ergodic Theory and Semisimple Lie Groups, and Kazhdan's original 1967 paper, together with an addentum to it by Prof. Vaserstein that came a year after: Kazhdan, D.. "Connection of the dual space of a group with the structure of its closed subgroups". Funct. Anal. Appl. 1. 1967. pp. 63-65. Vasershtein, L.N.. "Groups having the property (T)". Funct. Anal. Appl. 2. 1968. p. 174.

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Room Reservation Information

Room Number: 114 McAllister

Date: 03/01/2018

Time: 5:30pm - 8:00pm