Theses

In my master's, I am studying evolutionary discounting. Briefly, human and non-human animals' observed preferences for consumption across different time horizons seem irrational, at least according to standard economic models of welfare optimization. However, there is consistency in our irrationality, which suggests that perhaps there is a good reason for the behaviour we observe. In particular, I propose that observed discounting behaviour is consistent with optimizing evolutionary fitness. In my thesis, I set out to address the question: How does evolution mould our preferences for small, immediate rewards over larger, more delayed rewards?

At the end of my bachelor's degree, I spent a semester researching some algebra under Monica Nevins. We generally think of numbers as having a set size; 1 is less than 2, which is less than 3, and so forth. However, this is not the only choice we could make. It turns out that there are only so many "reasonable" choices for the size of a number, and that it is intimately related to prime numbers. Alternative orderings lead to different notions of closeness, which in turn produce fascinating new systems, called the p-adic numbers. My thesis builds these systems up from scratch to be accessible to those with a basic background in algebra and analysis, and applies the p-adic numbers to the study of quadratic forms.

Course and personal projects

I have completed several projects as a result of my studies and personal interests. I include here a sampling of some completed projects.

  • Cournot-Nash Equilibria in Continuous Games: From a course I took on optimal transport with applications in economics. I start with some classical game theory, which I then extend beyond discrete player games and analyse using some tools from the theory of optimal transport.
  • Squirrelly Bandits: From a course on evolutionary game theory. Reinfrocement learning algorithms tend to discount future rewards exponentially. I put forward a framework which can be analysed both as a reinforcement learning process and an evolutionary process. I find that in the proposed setup, the optimal evolutionary strategy can be recovered by appropriate choice of discounting parameter in the reinforcement learning setup. This project is tangentially related to the evolutionary discounting in my master's thesis.
  • Robust Regression: In 2016, I took a course on regression analysis (how to fit a line of best fit through data). Standard least squares regressions tend to assume large outliers are unlikely, to the extent that a single large outlier could destroy the statistical significance of a hypothesis. I worked in a team of two to analyse alternative, so-called "robust" regression methods.
  • Ontario High School Running: In high school, my cross country/track coach at one point casually remarked that after harder winters, you observe slower races in the spring. I set out to test his hypothesis. I collected both weather data and athletic performance data for different regions in Ontario and ran some simple regressions to conclude that colder winters are associated with worse athletic performance in longer events (1500 meters and up). Unfortunately, the data for this project was lost in a computer upgrade and I have yet to replicate my findings.