skip to content

How to quickly generate a nice hyperbolic element

Presented by: 
Emmanuel Breuillard
Friday 12th May 2017 - 13:30 to 14:30
INI Seminar Room 1
In the 60's Rota and Strang defined the notion of joint spectral radius of a finite set of matrices. This adequately generalizes the spectral radius of a single matrix to several matrices, and the relation between the limit norm of powers and the maximal eigenvalue (spectral radius formula) can be extended to this setting. In this talk I will present a general geometric formulation in which one considers a finite set of isometries S and the joint minimal displacement L(S), which is closely related to the joint spectral radius of Rota and Strang. The main result is a spectral radius formula for isometric actions on spaces with non-positive curvature (in particular symmetric spaces of non-compact type and \delta-hyperbolic spaces) which extends the previously known results about matrices. Applications to uniform exponential growth will be given. Joint work with Koji Fujiwara.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons