Université Paris-Sud, Centre d'Orsay

13:30 C. Cashen (U. Utah et Caen)

14:45 T. Coulbois (Marseille)

15:45 A. Hilion (Marseille)

17:15 A. Martino (Southampton)

11:00 S. Schleimer (Warwick)

14:00 M. Bridson (Oxford)

15:15 A. Minasyan (Southampton)

16:45 E. Ventura (U. P. Catalunya)

Notes of all lectures available on blog http://metric2011.wordpress.com/

Chris Cashen (University of Utah et Université de Caen) Quasi-isometries of Mapping Tori of Free Group Automorphisms

I will discuss progress, joint with Natasa Macura, towards a quasi-isometry classification of mapping tori of free group automorphisms, focusing on the linearly growing case.Thierry Coulbois (Université P. Cézanne, Marseille) Botanic of Trees in Outer Space

We use train track techniques to produce an invariant decomposition of a mapping torus. We then analyze the "line patterns" that record incidence relations between pieces of this decomposition.

[joint work with Arnaud Hilion] We describe advanced properties of trees in the boundary of Outer Space.

The best understand ones are surface trees: those are dual to foliation on a surface (with boundary). Alternatively they can be described by an Interval Exchange Transformation. Then come the geometric trees: they are transverse to a foliation on a band complex (which may not be a surface). They can be of Levitt type like the examples studied for instance by Boshernitzan and Kornfeld. But trees can also be non-geometric and, as in the geometric case, they can be of Surface type or of Levitt type.

We will present indices computed on the tree or on its dual lamination that characterize those properties.

We will give examples of attractive trees of iwip outer automorphisms.

Arnaud Hilion (Université P. Cézanne, Marseille) Automorphisms of free groups and free Burnside groups

[joint work with R. Coulon] An automorphism of the free group of rank r induces an automorphism of the free Burnside group of rank r and of exponent n. We will discuss the connections between the exponential growth rate of the automorphism of the free group and the order of the induced automorphism of the free Burnside group.

Armando Martino (University of Southampton) The Lipschitz metric on Outer space and spectral rigidity

Ashot Minasyan (University of Southampton) Residual finiteness of outer automorphism groups of relatively hyperbolic groups

[joint work with G. Levitt and D. Osin] Let G be a finitely generated group. We will discuss various approaches for proving that Out(G) is residually finite, starting with a classical theorem of Grossman that Out(G) is residually finite when G is free, and proceeding to more recent results about Out(G) when G is a hyperbolic or a relatively hyperbolic group.

Saul Schleimer (University of Warwick) The structure theorem for train track splitting sequences

[joint work with Howie Masur and Lee Mosher] The structure theorem details how train track splitting sequences interact

with subsurface projections to curve complexes. I will briefly describe the corresponding structure theorems for hierarchies (Masur-Minsky), Teichmuller geodesics (Rafi) and three-manifolds (Minsky, Bowditch). If time permits we will also discuss the recent work of Bestvina and Feighn on folding paths in outer space and their projections to free factor complexes.

Enric Ventura (Universitat Politècnica de Catalunya) On the difficulty of inverting automorphisms of free groups

[joint work with P. Silva and M. Ladra] Let G be a group and X a finite set of generators. In this talk, we will introduce a

function f(n) whose asymptotic behavior measures how difficult it is to invert automorphisms of G. More precisely, f(n) is the

maximum norm of the inverses of all those automorphisms of G$ whose norm is less than or equal to n.

After analyzing some general properties of this function, we will restrict our attention to the free case. For all such groups we will show that f(n) is polynomial. More specifically, it will be proven that, in rank r, f(n) is bounded below by a polynomial of degree r ; and above by a quadratic polynomial in the special case of rank 2. We obtain these results essentially by abelianizing and playing with matrices and eigenvalues, and by arguing directly in the free group in the very special case of rank 2.

General upper bounds for f(n) are more complicated to obtain: the main result in the talk is an upper bound in arbitrary rank, by a polynomial of big enough degree M(r), depending only on the ambient rank r. The main ingredient in the proof of this last inequality is a recent result by Algom-Kfir--Bestvina, about the asymmetry of the metric in outer space.

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Last update/Mise à jour le 19 août 2011