My most current project is with Dr. Victoria Booth building up a Gradient-based optimization of noisy ODE models for polyphasic rodent sleep-wake behavior.
Past projects:
Senior Honors Thesis: Biases Among Prime and Prime-like Numbers
Culminated in 30 page paper and hour long defense, received honors distinction. I essentially compiled a list of the most well-studied biases among the prime numbers, and then pitched some other kinds of numbers to extend the results to. My options included square-free and Mersenne numbers.
This was a very introductory number theory reading project. I chose this project when I was deciding whether to apply to pure or applied PhD programs, so I could "rule out" my interest in number theory as a serious career path. It was a fun project, but I indeed ruled it out.
IUREU (Indiana University) Project: Probability of Tree Changes in the Ancestral Recombination Graph (ARG)
Culminated in 16 page paper and 30 minute presentation. I studied the coalescent process that's typically used to create a phylogenetic tree, and compared the algorithms (ARG and SMC/SMC'). Eventually, I produced (original) formulas for the probability of a few different events that can happen in the creation of that tree.
I used a lot of techniques from advanced probability, in particular studied Poisson processes. This was also my first introduction to mathematical biology and our work with experimental geneticists is what made me want to pursue an interdisciplinary PhD.
VERSEIM-REU (Tufts University): Orthogonal Polynomials on Bubble-Diamond Fractals
Culminated in 22 page paper and hour long presentation. We spent a long time studying fractal "calculus" on the Sierpinski Gasket (SG), which was an uphill battle for us because it required a lot of advanced math like measure theory. Eventually we designed a new fractal class (the bubble fractal) and recreated the "calculus" we saw on SG.
Our paper was published on August 1, 2025 in the journal Complex Analysis and Operator Theory.
This was my first major research project, and was key in my decision to pursue a career in research. I loved working with my group, learning in a non-classroom environment, and reporting to an advisor. I did not, however, fall in love with analysis, which is reflected in the subjects I chose to research afterwards.
Lean Proof Assistant Project: Bernoulli Numbers in Lean's Mathlib
Culminated in several additions to Lean's Mathlib proof library, particularly on the subject of Bernoulli Numbers. I started by learning Lean's syntax and eventually went to the Xena Project Undergraduate Workshop in London to work on a more cutting-edge project with other people working in Lean.
At the time, my favorite math course was logic and I wanted to get better at coding, so this was a great project for me. At the workshop in London, I worked with Dr. Kevin Buzzard, who is generally credited with the mainstream popularization of Lean, which was very cool. He makes fantastic dinner conversation.
Research Assistant: Office of Institutional Research
I organized hundreds of thousands of data points for internal Tufts research over the course of 3 years. Not strictly a math research position, but I got a lot of great experience working with large sets of data and getting familiar with odd software.
Here is my full CV.