Speaker: Nattalie Tamam (UC San Diego)
19 May, 2021 15:30 UTC
Abstract: It is well known that the only singular numbers are rational numbers. Dani’s correspondence ties this property to a simple algebraic description of divergent trajectories in $\mathrm{SL}_2(\mathbb{R})$ under the action of the diagonal group. Similar principles can be utilised to define obvious divergent trajectories in a more general setting. We will discuss the existence of non-obvious divergent trajectories under the action of different diagonal subgroups, and the diophantine meaning of their existence (or lack thereof). This is a joint work with Omri Nisan Solan.