EVENT DETAILS AND ABSTRACT

Title: A dynamical approach to the asymptotic behavior of the sequence \Omega(n)
Speaker: Kaitlyn Loyd
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Abstract:

For $n$ a positive integer, let $\Omega(n)$ denote the number of prime factors of $n$, counted with multiplicity. The study of the asymptotic behavior of $\Omega(n)$ has a rich history, particularly in its applications to number theory. In this talk, I will discuss a recent dynamical approach to the study of $\Omega(n)$, as introduced by Bergelson and Richter. Furthering this approach, I will show that a Pointwise Ergodic Theorem does not hold along $\Omega(n)$. Time permitting, I will also discuss a dynamical sense in which we can consider the Prime Number Theorem and Erdos-Kac Theorem to be disjoint from one another, yielding a number theoretic corollary on the behavior of $\Omega(n)$.