Monthly Archives: June 2014

Notes of Camille Horbez’ lecture

Horoboundary of Outer space, and growth under random automorphisms 1. Random growth Question. Pick an element of free group . Apply a sequence of random elements of . How fast does the length grow after cyclic reduction ? Theorem 1 … Continue reading

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Notes of Dominik Gruber’s lecture

Acylindrical hyperbolicity of graphical small cancellation groups With Sisto. We prove the theorem in the title and use it to exhibit new behaviours for the divergence function of a group. Graphical small cancellation It is an extension of small cancellation … Continue reading

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Notes of Indira Chatterji’s Rennes lecture

-cube complexes and the median class Joint with Talia Fernos and Alessandra Iozzi. 1. Motivation The following corollary. Theorem 1 A cocompact, irreducible lattice in is not cubical. Completed by Fernos, Caprace, Lecureux in order to prove that anay such … Continue reading

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Notes of Romain Tessera’s Rennes lecture nr 2

Our main concern: let be a bounded degree graph which does not coarsely embed into Hilbert space. Does this imply that weakly contains an expander ? I will show that the answer is no. 1. A step towards a positive … Continue reading

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Notes of Yves Cornulier’s Rennes lecture nr 2

During the first lecture, we saw that, up to compact and cocompact groups, locally compact groups of polynomial growth can be reduced to simply connected Lie groups. Therefore we continue with a thorough study of these groups. 1. The lower … Continue reading

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Notes of David Hume’s lecture

Acylindrically hyperbolic groups from Kac-Moody groups Joint with Caprace. Recall that a group is hyperbolically embedded in , denoted by , if there exists an isometric action of on some hyperbolic metric space such that is quasiconvex in . Tubular … Continue reading

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Notes of Miklos Abert’s lecture

1. Spectral radius of a random walk Let be a countable group. Start walking randomly on (for instance, using uniform measure on a symmetric generating set). The Markov operator is The norm of is called the spectral radius of the … Continue reading

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