Seminar in Algebraic Geometry and Number Theory

Abstract: Consider an orbit Gv, where G is a discrete group of invertible 2-by-2 matrices and v is a vector in the Euclidean plane. Under certain conditions on G and v, this is a discrete set in the plane. Such sets are instrumental to the study of the linear flow on Veech surfaces and in particular we want to understand how such discrete sets are distributed in the plane. I will give examples and explain which features make this problem amenable to tools from number theory and harmonic analysis. This talk is based on joint works with Chaika, Fairchild, and Nevo, Ruehr, Weiss.