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Luke Robitaille

Luke Robitaille

2022 Davidson Fellow
$10,000 Scholarship

Age: 18
Hometown: Euless, TX

Mathematics: “Topological Entropy of Simple Braids”

About Luke

I am Luke Robitaille, a first-year college student from Euless, Texas. I was homeschooled throughout my pre-college years, and I will be attending MIT in the fall, majoring in math, and possibly also linguistics or physics.

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"I greatly appreciate that the Davidson Institute provides such generous scholarships to me and to students like me doing outstanding work. I am grateful that, in our modern society, there are still institutions left dedicated to encouraging students at the highest academic level."

Project Description

My project is about mathematical objects called braids, which are formed from strands (like pieces of string or yarn) that intertwine. Certain braids called "simple braids" are, in some sense, building blocks for all braids, somewhat similarly to how prime numbers are building blocks for all positive integers. A braid can be thought of as corresponding, in some sense, to a way of mixing fluids, where each strand tracks the motion of a stirring rod through time. By using methods like this, we can think of some braids as giving an “orderly” mixing, while others give a “chaotic” mixing, in some sense.

My main theorem is that as the number of strands get larger and larger, almost all of the simple braids with a given number of strands give a “chaotic” mixing.

Deeper Dive

Because my work is in pure mathematics, it likely is not as directly applicable to the real world as some other projects may be. Nevertheless, it is possible that my project, or the ideas contained in it, could have applications to science; specifically, in fluid mixing. It also could help serve as an inspiration to other students to show them that they too could do novel, interesting research in math, even while still in high school.

I have been homeschooled throughout my pre-college years. This gave me the freedom to be less encumbered by busywork than I likely would have been had I gone to normal school. Not only did my mother homeschool me, she also helped facilitate educational opportunities for me in various subjects. In particular, my parents found a Math Circle at a nearby university for me to attend. The professor who ran the Math Circle ended up helping me unofficially audit several advanced math classes over the years, giving me unusual mathematical avenues and opportunities.

Q&A

What is your absolute dream job?

A math professor but somehow my work is super useful in the real world.

If you could have dinner with the five most interesting people in the world, living or dead, who would they be?

Jesus, Leonhard Euler, Noam Chomsky, Katherine Johnson, and Ludwig van Beethoven.

What is your favorite hobby?

I like playing chess and solving and making puzzles.

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In The News

Euless, Texas – The Davidson Fellows Scholarship Program has announced the 2022 scholarship winners. Among the honorees is 18-year-old Luke Robitaille of Euless. Robitaille won a $10,000 scholarship for his project, Topological Entropy of Simple Braids. He is one of only 21 students across the country to be recognized as a 2022 scholarship winner.

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