Monthly Archives: April 2017

Notes of Pierre-Emmanuel Caprace’s fourth Cambridge lecture 27-04-2017

Exotic lattices and simple locally compact groups, IV 1. Subgroup separability and residual finiteness Theorem 1 (Kropholler-Reid-Wesolek-Caprace) Let be a finitely generated group, let be a commensurated subgroup (every conjugate commensurates ). Let be the profinite closure of , i.e. … Continue reading

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Notes of Emmanuel Breuillard’s sixth Cambridge lecture 26-04-2017

Introduction to approximate groups, VI Recall the weak version of the structure theorem for approximate groups. Theorem 1 (Breuillard-Green-Tao) Let . Let be a finite group such that . Then there exists a virtually nilpotent subgroup of and such that … Continue reading

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Notes of Marc Burger’s fourth Leverhulme lecture 25-04-2017

Towards higher Teichmuller theory, IV 1. To infinity and beyond Today, . We consider maximal representations . They are quasi-isometric embeddings. The class is deformation invariant. If , they coincide with holonomies of hyperbolic structures on . The goal is … Continue reading

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Notes of John Parker’s Cambridge lecture 25-04-2017

Non arithmetic lattices With Martin Deraux and Julien Paupert. 1. Arithmetic lattices We are interested in lattices in . One source of examples is the following arithmetic construction due to Borel-Harish Chandra. Let be an algebraic linear group defined over … Continue reading

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Notes of Frederic Paulin’s Cambridge lecture 25-04-2017

On continued fractions, diagonal group actions and trees in positive characteristic With Uri Shapira. 1. Continued fractions Consider the ring of 1-variable polynomials over a finite field. Its fraction field can be completed with respect to the absolute value into … Continue reading

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Notes of Marc Burger’s third Leverhulme lecture 24-04-2017

Towards higher Teichmuller theory, III 1. On integer points in the Hitchin moduli space Let be a simple Lie group of real split type (…). Then has a Hitchin component. In the sequel, we focus on . The Hitchin component … Continue reading

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Notes of Brian Bowditch’s Cambridge lecture 20-04-2017

Bounding genera of singular surfaces Ultimate motivation: understand the curve complex for non-compact surfaces. But today, only closed surfaces around. 1. Genus distance The curve complex of is hyperbolic, pseudo-Anosov diffeos act loxodromically, moving vertices at a linear speed. Say … Continue reading

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