Robert Brown was the first to describe the interesting unpredictable behavior of a certain type of pollen in water while looking through a microscope. These trajectories were named after him; Brownian motion. About eighty years later, Einstein explained the motion by molecular bombardment from the water particles. Brownian motion has also been used to describe the fluctuations of the stock market. Indeed, Brownian motion occurs frequently in physics, economics as well as in biology and in mathematics itself.
My name is Jordan Paillé. I’m entering my 4th year in mathematics at McGill. I decided on this program because I always enjoyed how in mathematics everything is black and white. Argumentation with my colleges is always short as a simple counter-example can prove someone wrong. I also love helping students out on problem sets. This is why I work at the math help desk of McGill. Outside of my program, I’m involved with the chess club. I represented my university at the Canadian University Chess Championship more than once.
Within mathematics, I have always liked probability; hence my interest in the Brownian motion. I am very grateful to the McGill Alumni and Friends Science Undergraduate Research Award who made it possible for me to study this topic from a mathematical point of view with a professor who is an expert in the topic. This area of mathematics is still blooming and so my supervisor and I are helping it grow. Our work is mainly theoretical. We hope to prove some properties of these motions for the goal of pure mathematics. Specifically, we are looking closely at stochastic differential equations on a manifold.
This research was truly beneficial for me as I was exposed to various interesting concepts and I had to apply tools developed in my previous courses in this study. Moreover, I believe this project is a great asset to my curriculum as I am applying to graduate school at McGill to pursue research in math. Finally, it was the best job I ever had.
Thank you again to the McGill Alumni and Friends Science Undergraduate Research Award for this amazing opportunity.