## Norm Convergence of Nonconventional Ergodic Averages

Miguel Walsh
Buenos Aires
March 27, 2013

Consider a group of measure preserving transformations acting on a probability space. The limiting behavior of the nonconventional ergodic averages associated with this action has been the subject of much attention since the work of Furstenberg on Szemerédi’s theorem. We will discuss this problem, and how to establish the convergence of these averages whenever the group is nilpotent.

## A Zero-Density Approach to Smooth Numbers

University of Montreal
March 27, 2013

A number is said to be $y$-smooth if all of its prime factors are less than $y$. Such numbers appear in many places throughout analytic and combinatorial number theory, and much work has been done to investigate their distribution.

Brown University
March 27, 2013