Colloquium: Tuesday Dec. 17, 2024. Speaker: Amos Nevo (Technion). Title: “Lattice points, effective dynamics, and Diophantine approximation on homogeneous spaces”.
Place: Room 614, Education and Sciences Building, University of Haifa
Date and Time: December 17, 2024, 14:00-15:00
Abstract: Let G be a Lie group, L a lattice subgroup in G, and H a closed subgroup of G. Suppose that L acts on the homogeneous space G/H with dense orbits. Naturally, we would like to measure how dense these orbits actually are, or equivalently, gauge the efficiency of approximation of a general point on G/H by a lattice orbit. Our focus will be on groups such as the group of isometries of hyperbolic space, or the general linear or affine group. We will present a solution to this problem for lattice actions on a large class of homogeneous spaces, emphasizing sufficient conditions for when an optimal result holds, and give some examples. We will then explain some more refined problems related to equidistribution and discrepancy of lattice orbits, as time permits.
Zoom link: https://us02web.zoom.us/j/87282501214?pwd=gnoO4TOG9LKBQJrfQ89Od7nUkoy0S3.1
Meeting ID: 872 8250 1214
