Monthly Archives: June 2014

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 →

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 →

-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 →

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 →

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 →

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 →

Width of simple and wreath product groups with respect to palindromes With Andreas Thom. 1. Width Let be a group, a set, possibly infinite. Say has width with respect to if every element is the product of at most elements … Continue reading →

Cubulating Gromov-Thurston manifolds 1. Gromov-Thurston manifolds These are compact negatively curved manifolds which are not hyperbolic. They arise as branched coverings of simple type arithmetic real hyperbolic manifolds. Theorem 1 Gromov-Thurston groups are virtually special cubical, i.e. act properly and … Continue reading →

-Betti numbers, continued Recall Kyed-Petersen-Vaes’ definition as von Neumann dimension of . 1. How to compute them Type I groups have the property that we have a Plancherel measure on the unitary dual . A Fourier type formula gives the … Continue reading →