Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Description

The dynamics of horocycle flow in infinite-area hyperbolic surfaces turns out to be related to the properties of optimal Lipschitz functions and their stretch laminations. For surfaces that are Z-covers of a compact surface we can obtain a complete description of all nontrivial horocycle orbit closures, including the somewhat surprising fact that their Hausdorff dimensions are always integer in spite of their fractal-like nature. For Z^d covers with d>1, our work in progress links the picture to the stable norm on homology of the surface, with a full understanding coming from some delicate proximality properties of the geodesic flow. For non-periodic surfaces we construct some new examples of minimal orbit closures with arbitrary Hausdorff dimension between 1 and 3. I will try to give an accessible account of this story, which is joint work with J. Farre, O. Landesberg and F. Dal'bo.