Effective equidistribution of expanding translates in ASL_d(R)/ASL_d(Z)

Abstract:

In this talk, we discuss effective versions of Ratner’s theorems in the space of affine lattices. For d>= 2, Let Y=ASL_d(\mathbb{R})/ASL_d(\mathbb{Z}), H be a minimal horospherical group of SL_d(\mathbb{R}) embedded in ASL_d(\mathbb{R}), and a_t be the corresponding diagonal flow. Then (a_t)-push-forwards of a piece of H-orbit become equidistributed with a polynomial error rate under certain Diophantine condition of the initial point of the orbit. This generalizes the previous results of Strömbergsson for d=2 and of Prinyasart for d=3.

WEB SITE:  http://www.crm.sns.it/event/497/

Those who are unable to be physically present may attend the talk via Zoom by following the link: https://us02web.zoom.us/j/83965821067?pwd=YU9MRHVVMlRQMXZycjVzVGR3VmlXZz09