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Monthly Archives: February 2017
Notes of Arindam Biswas’ informal Cambridge lecture 28022017
Spectral gaps for 1. Context Goal: produce expanders. These will be Cayley graphs of finite quotients of a group, , which does not have property (T). Therefore, the method is new. Lubotsky had pointed out that, prior to BourgainGamburd’s work, … Continue reading
Notes of Anastasia Khukhro’s Cambridge lecture, 23022017
Geometry of finite quotients of groups With Thiebout Delabie. 1. Box spaces Call a filtration of group a nested sequence of finite index normal subgroups whose intersection is trivial. Definition 1 The box space of a filtration is the disjoint … Continue reading
Notes of Emmanuel Breuillard’s informal talk in Cambridge 21022017
Informal discussion on spectral gaps for isometric group actions 1. Finite Kazhdan data 1.1. Banach Kazhdan data ? Cornelia Drutu wants a finite subset of a Lie group which is a Kazhdan set for every affine isometric action of on … Continue reading
Notes of Roland Bauerschmidt’s Cambridge lecture 7022017
Local KestenMcKay law for random regular graphs Joint with Jiaohuang Huang ans HongTzer Yau. 1. Motivation: quantum chaos Consider billiard motion in a rectangle. It is a classically integrable system. The corresponding quantum problem consists in studying the Laplacian with … Continue reading
Notes of Pierre Pansu’s informal Cambridge lecture 07022017
Coarse spaces associated to dynamics and spectral gaps As an incentive for a working seminar, I informally survey papers by Roe, DrutuNowak, Vigolo, BenoistDe SaxcĂ© (+ Sawicki). Goal: understand ways of encoding dynamical properties of group actions in a coarse … Continue reading
Notes of Eric Swenson’s Cambridge lecture 222017
Infinite torsion subgroups of groups Question. Let act geometrically on a proper space. Can have an infinite torsion subgroup ? Expected answer is no. Known. For cube complexes, Wise and Sageev show that a torsion group fixes a point (eventually … Continue reading