Ergodic methods in combinatorics and number theory

Seminar in Mathematics

Abstract: What can the study of orbits in dynamical systems tell us about seemingly static, discrete objects such as the prime numbers, integer solutions to equations, or set partitions? Far more than one might expect. Ergodic theory, which studies the long-term statistical behavior of such orbits, has found remarkable applications in combinatorics and number theory. In this talk, I will introduce the main ideas behind this connection, explaining how arithmetic problems can be recast in dynamical terms and how this perspective has led to breakthroughs beyond the reach of other methods.