Lucien W
- Research Program Mentor
PhD at California Institute of Technology (CalTech)
Expertise
Mathematics, computer science, music theory, engineering, sustainability
Bio
I am a mathematician interested in the theory of cyber-physical systems, which include large-scale networks like the power grid and the Internet of Things. My goals are to advance the mathematics that underlie these systems and accelerate the adoption of renewable sources that contribute to sustainable energy production. My past research has been on the dynamics of vegetation pattern formation in arid ecosystems threatened by desertification, drought, and human encroachment. I am currently pursuing a PhD in Computing & Mathematical Sciences at Caltech as a Resnick Graduate Fellow. Outside of mathematics, I have a career as a cellist and continue to perform around the world–often with my three sisters who are all also musicians and mathematicians. Prior to joining Caltech, I received degrees in mathematics, music, and politics from Northwestern University, Harvard University, and Montana State University.Project ideas
Algebra through the millenia
This typically dry high school math topic in fact has a rich and entertaining history. Starting with Babylonian accountants, proceeding to dueling Italian monks, and finally arriving at the abstract theory of groups, you will build up a mathematical understanding of algebra alongside the thinkers who dreamed it up. Some key topics we will touch upon include - roots of general polynomial equations - defining numbers through algebraic equations - determinants and linear equations - basic group theory We will work together on picking an appropriate topic or equation to explore in depth and then you will make a short "Numberphile"-style Youtube video that presents your concept to an interested but non-expert audience.
Introduction to Machine Learning
There's hardly anything hotter in tech than machine learning and AI. Beyond the unreasonable hype, what makes machine learning so successful for some tasks and not for others? We will explore this question in the context of several key modern methods in machine learning: regression, SVMs, probabilistic models, and neural networks. Emphasis will be placed on exploring mathematical foundations of the discipline. You will get your hands dirty by implementing some of these methods yourself and testing them on real datasets. We will works towards presenting your experiments in a short conference-style paper.
Why does Bach sound like Bach?
We revere master composers like Bach, Vivaldi, and Mozart but their monumental works were not just a product of genius inspiration. Rather a lost tradition of counterpoint pedagogy deserves a good deal of credit for giving classical music its characteristic sound and polish. We will put aside traditional (and unhelpful!) notions of harmony and approach counterpoint the way the great composers did. By the end of this project, you will be able to harmonize bass lines just by looking at them, write simple 3-voice fugues, and apply these skills directly to improvising on your instrument. The excitement of rediscovering the ingenuity of this old tradition comes from realizing just how useful it is for a practicing musician.
Coding skills
Python, Matlab, Mathematica, CLanguages I know
German, French, LatinTeaching experience
I have been a teaching assistant for undergraduate courses in physics, biology, math, and electrical engineering. I also have extensive experiencing mentoring and tutoring young students in math, computer science, machine learning, and music.Credentials
Work experience
Education
Reviews
"Luc was really exciting to learn with and I really enjoyed my time"