Thesis Defense

Title: Pointwise Ergodic Averages along Sequences of Slow Growth
Speaker: Kaitlyn Loyd
Speaker Info: Northwestern University
Brief Description: PhD Thesis Defense
Special Note:

Following Birkhoff's 1931 proof of the Pointwise Ergodic Theorem, it is natural to consider whether convergence holds along various subsequences of integers. In 2020, Bergelson and Richter showed that in uniquely ergodic systems, pointwise convergence holds along the number theoretic sequence $\Omega(n)$, where $\Omega(n)$ denotes the number of prime factors of $n$ with multiplicities. In my thesis, I continue this study of the asymptotic behavior of $\Omega(n)$ from the dynamical point of view. I show that by weakening Bergelson and Richter's assumptions, a pointwise ergodic theorem does not hold along $\Omega(n)$. In fact, $\Omega(n)$ satisfies the strong sweeping out property. In joint work with S. Mondal, we further classify the strength of this non-convergence behavior by considering weaker notions of averaging.
Date: Thursday, June 06, 2024
Time: 02:00pm
Where: Lunt 107
Contact Person: Kaitlyn Loyd
Contact email: loydka@math.northwestern.edu
Contact Phone:
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