We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral
invariants of sequences of locally symmetric spaces. Our main results are uniform versions …

We give a distance estimate for the disk complex. We use the distance estimate to prove that
the disk complex is Gromov hyperbolic. As another application of our techniques, we find an …

We give an inductive description of a Teichmüller geodesic, that is, we show that there is a
sense in which a Teichmüller geodesic is assembled from Teichmüller geodesics in smaller …

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out
(F n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we …

On the complexity of braids Page 1 J. Eur. Math. Soc. 9, 801–840 c European Mathematical
Society 2007 Ivan Dynnikov · Bert Wiest On the complexity of braids Received June 20, 2005 …

We say that a finitely generated group G has property (QT) if it acts isometrically on a finite
product of quasi-trees so that orbit maps are quasi-isometric embeddings. A quasi-tree is a …

We review some elements of Teichmueller's metric and of Thurston's asymmetric metric on
Teichmueller space. One of our objectives is to draw a parallel between these two metrics …

While there may be many Thurston metric geodesics between a pair of points in Teichm\"
uller space, we find that by imposing an additional energy minimization constraint on the …

This chapter is a survey about the Thurston metric on the Teichmüller space. The central
issue is the construction of extremal Lipschitz maps between hyperbolic surfaces. We review …

We study the geometry of the Thurston metric on the Teichmüller space of hyperbolic
structures on a surface of finite type; however, we focus particular attention on the case …