Rigidity VI

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: Twelfth chapter of Witte Morris' notes will be covered. To be more specific, my talk will focus on amenability. Amenability is a concept that was introduced by von Neumann to study Banach-Tarski type paradoxes, and in time it became a subject of interest in many areas. Roughly speaking, an amenable group is one whose representations on affine compact convex sets admit a stationary barycenter. I will give a few different definitions of amenability and give sketches on how to switch from one to another, as these definitions come from different areas of mathematics and their equivalence is not immediate. Then I will give some examples of amenable groups and nonamenable groups, and finally I will cover the Furstenberg's Lemma, which will be used later in the proof of Margulis' superrigidity and normal subgroup theorems. Alongside Witte Morris' notes I will also use Zimmer's Ergodic Theory and Semisimple Lie Groups. Also, even though I probably will not have time to talk about the connection between amenability and the Banach-Tarski type paradoxes, Terence Tao has two posts regarding this connection, which is I believe worth a look: https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/ https://terrytao.wordpress.com/2009/01/08/245b-notes-2-amenability-the-ping-pong-lemma-and-the-banach-tarski-paradox-optional/

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Room Reservation Information

Room Number: 114 McAllister

Date: 02/22/2018

Time: 5:30pm - 8:00pm