460 McBryde Hall, Virginia Tech
225 Stanger Street
Blacksburg, VA 24061-1026
Below are some specific types of questions I worked on: Structure theorems for measurable systems, L^2 convergence problems for multiple ergodic averages, and their applications to Ramsey-type questions. Structure theorems for topological systems, and their applications to pointwise convergence problems for multiple ergodic averages. Structure theorems for multiplicative functions (on integers and on number fields), and their applications in number theory. Equidistribution properties for nil manifolds.