Numerical calculation of resonances on convexcocompact surfaces via zeta-functions

Convex-cocompact surfaces are a certain class of noncompact constantcurvature surfaces, that can be obtained by taking the quotient of theupper half-plane with respect to a certain discrete subgroup ofPSL(2,R). Thanks to their strong geometric and algebraic structures,these surfaces are an ideal class of geometries to study of resonancesof the geodesicflow transfer operator as well as resonances of theLaplacian. Concerning the distribution of those resonances there havebeen established a large number of interesting results and conjecturesduring the past years. In this talk we will explain how theresonances on convex-cocompact surfaces can be efficiently calculatednumerically. This allows to test existing conjectures as well as todiscover new interesting structures in the resonances spectrum. Themethod of these numerical calculations is entirely based onapproximating dynamical zeta functions and uses techniques developedby Jenkinson-Pollicott and in joint work with David Borthwick.