Jayadev Athreya (University of Washington)

Variance estimates and geometric counting


We discuss how in a variety of situations (in particular, unimodular lattices in Euclidean spaces, translation surfaces, and hyperbolic surfaces), one can derive variance estimates for counting problems in random geometry. We will discuss motivations for this circle of problems, and applications to Diophantine approximation and understanding various correlations of curves and arcs on random surfaces. This talk includes joint work with G. Margulis; work with Y. Cheung and H. Masur; work with S. Fairchild and H. Masur; and work with F. Arana-Herrera.