Katy Loyd
Department of Mathematics
Northwestern University
Office: Locy Hall 212
Email: loydka at math.northwestern.edu
I am a sixth year Ph.D. candidate in Mathematics, working under the supervision of Bryna Kra. My research interests lie in dynamical systems, specifically ergodic theory and symbolic dynamics. I like to think about pointwise ergodic theorems with connections to analytic number theory.
Here is a copy of my CV (Last updated: Oct 2023).
Pointwise ergodic theorems

A dynamical approach to the asymptotic behavior of the sequence \(\Omega(n)\),
Ergodic Theory and Dynamical Systems 2023, 43(11), 3685–3706
We study the asymptotic behavior of the sequence \( \{\Omega(n) \}_{ n \in \mathbb{N} } \) from a dynamical point of view, where \( \Omega(n) \) denotes the number of prime factors of \( n \) counted with multiplicity. First, we show that for any nonatomic ergodic system \( (X, \mathcal{B}, \mu, T) \), the operators \( T^{\Omega(n)}: \mathcal{B} \to L^1(\mu) \) have the strong sweepingout property. In particular, this implies that a pointwise ergodic theorem does not hold along \( \Omega(n) \). Second, we show that the behaviors of \( \Omega(n) \) captured by the Prime Number Theorem and ErdosKac Theorem are disjoint, in the sense that their dynamical correlations tend to zero.

Ergodic averaging along the sequence \( \Omega(n) \), joint with S. Mondal, In preparation
Abstract TBA
Symbolic dynamics

New points in the Heinis spectrum, arXiv preprint coming soon in 2023!
Abstract TBA
Research Talks

Analysis Seminar, Virginia Tech, Oct 2023
Title: Convergence of ergodic averages along the sequence \( \Omega(n) \)

Low Complexity Dynamical Systems Conference, University of Maryland, Oct 2023
Title: New points in the Heinis spectrum

Ergodic Theory and Analysis Seminar, Rutgers University, Sep 2023
Title: Convergence of ergodic averages along the sequence \( \Omega(n) \)

Chicago Action Now Conference, UIC, Apr 2023
Title: Convergence of ergodic averages along the sequence \( \Omega(n) \)

IAS Special Year Seminar, Institute for Advanced Study, Feb 2023
Title: Convergence of ergodic averages along the sequence \( \Omega(n) \)

Midwest Dynamical Systems Conference, IUPUI, Nov 2022
Title: A dynamical approach to the asymptotic behavior of the sequence \( \Omega(n) \)

AMS Spring Western Sectional Meeting, University of Denver, May 2022
Title: A dynamical approach to the asymptotic behavior of the sequence \( \Omega(n) \)

Midwest Dynamical Systems Early Career Conference, Notre Dame, May 2022
Title: Convergence of ergodic averages along the sequence \( \Omega(n) \)

Dynamical Systems Seminar, Northwestern University, Nov 2022
Title: A dynamical approach to the asymptotic behavior of the sequence \( \Omega(n) \)
Expository Talks
Continuing Studies Instructor, Northwestern University School of Professional Studies

Summer 2022:
 MATH 2400: Linear Algebra, First Course
Graduate Teaching Assistant, Northwestern University

Fall 2021:
 MATH 2302: Multivariable Integral Calculus

Winter 2021:
 MATH 2301: Multivariable Differential Calculus (2 Sections)

Fall 2020:
 MATH 3540: Chaotic Dynamical Systems
 MATH 2202: Single Variable Integral Calculus

Winter 2020:
 MATH 2301: Multivariable Differential Calculus (2 Sections)

Fall 2019:
 MATH 2202: Single Variable Integral Calculus (2 Sections)

Summer 2023: Coordinated with faculty leaders to run three undergraduate research projects.

Project topics:

Dynamics and Representation Theory: Two projects on dynamics of \( Aut(F_n) \)

Dynamics and Graph Theory: Spectra of Periodic Schrodinger Operators
Teaching Assistant, Bridge Program, Northwestern University

Summer 2021: "Introduction to Quantitative and Scientific Reasoning"

Winter 2020:

MATH 110: Introduction to Mathematics
For further information on my teaching philosophy and practices, please see my
teaching ePortfolio
PW: 'LoydTeach'
Other
More About Me

I have an orange cat named Dumpling.
Cat tax: Dumpling and his littermate Toast

I train at a competitive boxing gym. My favorite boxers are GGG and Lomachenko.
Last updated: October 21, 2023