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.