Monthly Archives: February 2017

Notes of Arindam Biswas’ informal Cambridge lecture 28-02-2017

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 Bourgain-Gamburd’s work, … Continue reading

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Notes of Anastasia Khukhro’s Cambridge lecture, 23-02-2017

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

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Notes of Emmanuel Breuillard’s informal talk in Cambridge 21-02-2017

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

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Notes of Roland Bauerschmidt’s Cambridge lecture 7-02-2017

Local Kesten-McKay law for random regular graphs Joint with Jiaohuang Huang ans Hong-Tzer 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

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Notes of Pierre Pansu’s informal Cambridge lecture 07-02-2017

Coarse spaces associated to dynamics and spectral gaps As an incentive for a working seminar, I informally survey papers by Roe, Drutu-Nowak, Vigolo, Benoist-De SaxcĂ© (+ Sawicki). Goal: understand ways of encoding dynamical properties of group actions in a coarse … Continue reading

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Notes of Eric Swenson’s Cambridge lecture 2-2-2017

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

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