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Monthly Archives: April 2017
Notes of PierreEmmanuel Caprace’s fourth Cambridge lecture 27042017
Exotic lattices and simple locally compact groups, IV 1. Subgroup separability and residual finiteness Theorem 1 (KrophollerReidWesolekCaprace) Let be a finitely generated group, let be a commensurated subgroup (every conjugate commensurates ). Let be the profinite closure of , i.e. … Continue reading
Notes of Emmanuel Breuillard’s sixth Cambridge lecture 26042017
Introduction to approximate groups, VI Recall the weak version of the structure theorem for approximate groups. Theorem 1 (BreuillardGreenTao) Let . Let be a finite group such that . Then there exists a virtually nilpotent subgroup of and such that … Continue reading
Notes of Marc Burger’s fourth Leverhulme lecture 25042017
Towards higher Teichmuller theory, IV 1. To infinity and beyond Today, . We consider maximal representations . They are quasiisometric embeddings. The class is deformation invariant. If , they coincide with holonomies of hyperbolic structures on . The goal is … Continue reading
Notes of John Parker’s Cambridge lecture 25042017
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 BorelHarish Chandra. Let be an algebraic linear group defined over … Continue reading
Notes of Frederic Paulin’s Cambridge lecture 25042017
On continued fractions, diagonal group actions and trees in positive characteristic With Uri Shapira. 1. Continued fractions Consider the ring of 1variable polynomials over a finite field. Its fraction field can be completed with respect to the absolute value into … Continue reading
Notes of Marc Burger’s third Leverhulme lecture 24042017
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
Notes of Brian Bowditch’s Cambridge lecture 20042017
Bounding genera of singular surfaces Ultimate motivation: understand the curve complex for noncompact surfaces. But today, only closed surfaces around. 1. Genus distance The curve complex of is hyperbolic, pseudoAnosov diffeos act loxodromically, moving vertices at a linear speed. Say … Continue reading