Title: The Prime Number Theorem, Topological Dynamics, and Sarnak's Conjecture
Speaker: Vitaly Bergelson
Abstract: We will discuss the intriguing connections between PNT (The Prime Number Theorem) which describes the asymptotic distribution of the prime numbers among the positive integers, Topological Dynamics which studies the iterations of homeomorphisms of compact spaces, and Sarnak's conjecture which deals with the randomness properties of the classical Liouville function λ(n) that takes value +1 if n is the product of an even number of prime numbers, and −1 if it is the product of an odd number of primes. After reviewing some background material, we will describe some recent results and formulate interesting open problems.
Vitaly Bergelson, Florian K. Richter
Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions
https://arxiv.org/abs/2002.03498
https://terrytao.wordpress.com/2012/10/14/the-chowla-conjecture-and-the-sarnak-conjecture/
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for one or two credit hours of Math 6193 with Professor Nimish Shah.