Speaker: Lifan Guan (Gottingen)
14 April, 2021 13:30 UTC
Abstract: Thanks to Dani correspondence, it is now well-known that the set of singular vectors is closely related to the set of points with divergent trajectories in certain homogeneous dynamical systems. Since Yitwah Cheung’s breakthrough work on the Hausdorff dimension of the set of 2-dim singular vectors, there have been lots of progress in singular vectors and divergent trajectories in the so-called “unweighted” cases. Otherwise, our understanding is quite limited. In this talk, I will mainly discuss the dimension formula for the set of divergent trajectories in products of “unweighted” homogeneous dynamical systems. This is a joint work with Jinpeng An, Antoine Marnat and Ronggang Shi.