Elijah French
Hi! My name is Elijah and I am a first year PhD student in Statistics at the University of Toronto. My interests lie in Mean-Field Games, Optimal Transport, and Mathematical Finance. I am being jointly supervised by Professors Sebastian Jaimungal and Leonard Wong. I completed a bachelor’s degree in Economics and Mathematics at the University of Toronto in 2024.
Interests
- Mean-Field Game Theory
- Optimal Transport
- Statistical Theory
Education
BsC in Economics and Mathematics, 2024
University of Toronto
PhD in Statistics
University of Toronto
PhD
Courses:
- Probability Theory
- Applied Probability for Math Finance
- Advanced Theory of Statistics
Awards:
- Ontario Graduate Scholarship (OGS)
- FAST Fellowship
- Recruitment Award
Bachelor of Science
Program:
- Economics and Mathematics Specialist
- Statistics Minor
Courses:
- Graduate Real Analysis I/II
- Stochastic Processes
- Game Theory
- Advanced Econometrics I/II
Awards:
- George Roderick Fraser Scholarship (UC, University of Toronto)
- First Norman McLarty Scholarship (UC, University of Toronto)
Experience
Teaching Assistant
- Teaching STA237: Probability, Statistics and Data Analysis I
Research Assistant
- I worked under the supervision of Sebastian Jaimungal using deep reinforcement learning techniques inside a geological carbon storage environment
- Created environments in geo-physical modelling programs which were imported to Python for applications
Presenter
- Attends weekly seminars by PhD students in the mathematics department. Topics include Optimal Transport Theory, Monte Carlo methods for Sampling, and Adjoint Methods for Parameter Estimation
- Presented the Actor-Critic Reinforcment Learning algorithm DDPG to the group. Introduced reinforcement learning, deep neural networks, and their applications to geological carbon storage over three separate presentations
Vice President
- As the Vice President, I contributed towards the planning and execution of the investment banking training program alongside my board. Executed a stock pitch competition involving 10 pitches from 3 different universities.
- Assisted in the creation of interactive modules and activities for 40+ club members and 16 analysts
- Performed extensive recruitment for the 2022-2023 session. Filled roles for our 25+ analysts and executives
Projects
Optimizing Geological Carbon Storage With Reinforcement Learning
In this project, my partner and I present findings related to the implementation of the deep reinforcement learning algorithm DDPG to geological carbon storage. Pressure buildup is a major concern in large scale carbon storage operations. The DDPG agent is able to find a schedule of injection and extraction rates that optimizes storage with this constraint.
Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC), a method to sample from high dimensional distributions, is introduced. Standard sampling methods run into problems in high dimensional space and with distributions that have sticking points. Applications of HMC are described, in particular that of sampling from various empirical distributions.
Are All Convergences Topological?
This project attempts to answer whether all convergences in math can be described topologically. This turns out not to be the case. Convergence almost everywhere, which is fundamental in probability theory, is not topological. I present these findings, the equivalency of the various formulations of compactness in metric spaces, and more.