There are many parallels between Lie group actions on homogeneous spaces and the action of $\SL_2(\R)$ and its subgroups on strata of translation or half-translation surfaces. I propose to investigate these two spaces in parallel, focusing on the dynamical
behavior, and more specifically, the description of orbit-closures.
I intend to utilize existing and emerging measure rigidity results, and to develop new topological
approaches. These should also shed light on the geometry and topology of the spaces. I propose to apply results concerning these spaces to the study of diophantine approximations (approximation on fractals), geometry of numbers (Minkowski's conjecture), interval exchanges, and rational billiards.
Fields of science
Call for proposal
See other projects for this call