Georgia Institute of Technology College of Sciences

This talk will focus on the multifaceted and mutually perpetuating relationship between ergodic theory, combinatorics and number theory. We will begin by discussing Furstenberg’s ergodic approach to Szemerédi’s Theorem and how it has inspired a recent solution to a long-standing sumset conjecture of Erdős. Thereafter, we will explore a new dynamical framework for treating questions in multiplicative number theory. This leads to a variant of the ergodic theorem that contains the Prime Number Theorem as a special case, and reveals an intriguing new connection between the notion of entropy in dynamical systems and the distribution of the number of prime factors of integers.