Research
How Network Structure Shapes Epidemics
Comparing random, small-world and scale-free contact networks with SIR simulations
With Dr. Deena Schmidt, Department of Mathematics and Statistics, University of Nevada, Reno · Fall 2026
I simulate outbreaks on 500-person contact networks (random, small-world, and scale-free) to ask which structural properties, beyond the average number of contacts, predict how large and how fast an epidemic gets. Building on Ames et al. (2011) and Pérez-Ortiz et al. (2022), early results suggest that clustering, not the distance between people, keeps outbreaks small, and that global efficiency is the best single predictor. Next: separating clustering from the spread in contacts.
In progress
p-adic Pseudorandom Number Generators
Euler Circle · Spring 2026
A pseudorandom number generator turns a seed into a sequence that looks random. I build one by repeatedly applying a function on the p-adic integers, a number system that matches how computers do arithmetic at a fixed precision. Using a theorem of Anashin, I show how to check, one modulus at a time, that the generator gives uniform output and the longest possible period at every precision. I also show what this approach cannot give: unpredictability, which cryptography needs.
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Fourier Analysis Through the Lens of Linear Algebra
Euler Circle · March 2026
Fourier analysis rests on the claim that a broad class of functions can be written as an infinite sum of sines and cosines. I argue that both the claim and the coefficient formulas become natural once viewed through linear algebra: the integral of a product of two functions behaves like a dot product, the trigonometric functions form an orthogonal set, and the coefficient formulas follow from the same orthogonal projection used for vectors in Rn.
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AI and the Future of Work: Analyzing Job Exposure to Generative AI
Inspirit AI Scholars Program · Summer 2026 · Inspirit AI Scholar certificate
In a six-person team, we studied how AI is changing jobs, using occupation data from O*NET and job-posting trends from Indeed. Each of us built an app; mine, the AI Insight Dashboard, is an interactive dashboard showing which jobs AI affects and by how much, and whether it automates tasks or helps people do them better. Our takeaway: AI is changing jobs more than replacing them.
