Adam Kanigowski: Ergodic Theorems along sparse subsets of the integers.

Abstract: Let A be a subset of the positive integers. For a dynamical system (T,X) we are interested in ergodic averages along A, i.e. for x\in X and f\in C(X) we look at the limiting behavior of \frac{1}{|A_N|}\sum_{k\in A_N}f(T^kx), where A_N=\{k\in A: k\leq N\}. We will focus on the case where A is the set of primes or values of polynomials with integer coefficients. We will recall some classical results, mention some recent developments and highlight some interesting open problems.