Impact of Geometric Group Theory
July 13 – 17, 2015
The methods which have originated from dynamical systems on one hand and from geometry on the other have become central in present day group theory.
The theorem of Rips-Bestvina-Paulin constitutes an emblematic occurrence where geometric and dynamical methods are blended together to prove a deep result in group theory: the group of outer automorphisms of a hyperbolic group G without torsion is infinite if and only if G splits over an infinite cyclic group. Indeed, the idea of the proof is to use first the hyperbolicity of G in order to derive, via a renormalization process, an action of G on an R-tree T. In a second step this action has to be analyzed sufficiently precisely: the « Rips machine » allows to approximate the action of G on T with actions of G an simplicial trees, both at a metric and a dynamical level.

More generally,  R-trees have played a key role in geometric group
theory during the last 25 years: in particular, they appear as natural limit objects in the degeneration of hyperbolic structures (used for instance to compactify spaces such as the Teichmüller spaces).

By now, the areas of dynamics and of geometric group theory extend to numerous active branches of mathematics such as low-dimensional topology, algebraic topology, complex dynamics, Teichmüller theory, logics, Riemannian geometry, representation theory, operator algebras etc.
The present conference will be the opportunity not only to present the most recent progress in dynamics of group and/or geometric group theory, but also to report on their recent impact on related domains.
Besides, during this conference we will celebrate the sixtieth birthday of two mathematicians:
– Gilbert Levitt, Université de Caen,
– Martin Lustig, Université Aix-Marseille,
whose work on the dynamics and geometry of groups have contributed importantly to the development of this area in the past 30 years (in particular through their joined work on R-trees and automorphisms of free groups).

Scientific Committee

Mladen Bestvina (University of Utah)
Thomas Delzant (Université de Strasbourg)
Frédéric Paulin (Université Paris-Sud)
Karen Vogtmann (Cornell University)

Organizing Committee

Goulnara N. Arzhantseva (University of Vienna)
Nicolas Bédaride (Aix-Marseille Université)
Damien Gaboriau (ENS Lyon)
Arnaud Hilion (Aix-Marseille Université)


Rank and Homology Log Torsion Growth in Higher Rank Lattices

Virtual Thurston Norms and Simplicial Volume

Automorphisms of the Free Factor Complex

Index Realization for Automorphisms of Free Groups

Automorphisms of Lacunary Hyperbolic Groups

Recognition of Relatively Hyperbolic Groups by Dehn Fillings ; Rigidity and Exibility

Kazhdan Projections

The Boundary of the Free Splitting Complex

Variations on Gilbert’s First Paper

Subgroups of Automorphisms of Hyperbolic Groups

Dual Digraphs and Entropy

Growth Under Random Products of Automorphisms of a Free Group

Endomorphisms, Train Track Maps, and Fully Irreducible Monodromies

Full Groups, Cost, Symmetric Groups and IRSS

Wise’s w-Cycle Conjecture and Homological Coherence for One-Relator Groups

The Cubical Geometry of Higman’s Group

Nielsen Equivalence Revisited

Invariant Trees and Surfaces for Some Surface Groups Acting on A2-Buildings

Word Equations

Nielsen Equivalence in a Class of Random Groups