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
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.
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
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
Nielsen Equivalence in a Class of Random Groups