Florian Richter, Northwestern University
"Applications of Ergodic Theory to Combinatorics and Number Theory"
Ergodic Theory offers many ways for analyzing seemingly static number-theoretic and combinatorial problems from a dynamical point of view. We will begin by looking at an intimate connection between the theory of recurrence in dynamical systems and problems in additive combinatorics. This mutually perpetuating relationship started with Furstenberg's work on Szemeredi's Theorem, but also played an important role in a recent proof of a longstanding sumset conjecture of Erdos. In the second half of the talk we will explore a new dynamical framework for treating questions in multiplicative number theory. This includes a new type of ergodic theorem which contains various classical number-theoretic results, such as the Prime Number Theorem, as special cases.
A post-colloquium meet and greet will be held at 2:00 pm using the same Zoom meeting link.
Zoom meeting: https://zoom.us/j/99574298257?pwd=UWUwSUNQQjlvajJvRFk1OS8yekR5dz09