Degree Program: Ph.D., Applied Mathematics
Graduate Institution: UC Santa Cruz
Undergraduate Institution: UC Riverside
Department: Applied Mathematics
What brought you to UC Santa Cruz?
The physical environment and the academic environment. I think it’s a wonderful environment to be in as a grad student. It’s the optimal place to be when you can just go outside and feel the radiant sunshine and still feel the calmness of the rain when it’s misty.
What research are you currently working on?
I work in optimal transport. There’s a lot of applications in science and engineering. There’s this principle called the least action principle and the idea is that when you want to move objects from one point to a set target, it’s favorable to do it with the least amount of effort possible. In mathematics they call this the path of least energy, the geodesic path. Say you’re on a flat surface. The shortest path from one point to another would be a straight line. Optimal transport generalizes this idea to when you’re moving several objects simultaneously from one configuration to another. So my research is kind of a way to generalize these ideas and develop practical computations for engineering and science applications.
One application of this research that I’m doing is controlling this equation called the fulcrum plath equation and it’s a very important equation in math and physics. Basically it governs the evolution of the probability distribution of a particle as it’s moving in space and instead of just making a particle move freely between one point to another, we want to try to control it by adding a forcing term and we get to decide what the optimal forcing term is to move this particle from one point to another another.
The great thing about optimal transport is that it arose from being an interdisciplinary field, so the reason it was created is because people wanted a different perspective to all these math subjects such as partial differential equations, calculus variations, machine learning, AI, all these things kind of group into one tool that tries to unite all these fields and so what I’m doing is applying these tools to a subject called control theory and I’m hoping to make progress there because it’s a fertile ground for research and I think we’re making some strides in making really impressive applications.
What drew you to Applied Mathematics?
As an undergrad I took a class on probability theory and although it’s a very pure subject nowadays, it arose from theories of how to win games, or gambling. So that was a really fun class and it allowed me to explore how probabilists think. They don’t necessarily think in the most straightforward way but they do have some axioms or some first principles to carry on their theorems. Probability theory is very involved in my research even though it’s about optimizing paths. In some ways we are optimizing paths that are moving randomly in some way.
What’s the most surprising thing you’ve learned as a grad student?
I’m mentoring an undergrad right now in pure math and what I realized over the course of working with him is the importance of giving students support. That’s something I’ve always appreciated from my professors. I didn’t think I was going to go to grad school until my third year of college. My professors and older grad students always gave me that support so it feels good for me to pay that forward because it’s nice to have a supportive environment where one can thrive.
What do you do for fun?
I really like to cook. It’s pretty much the only thing I spend my money on. If I wasn’t going to grad school right now I’d probably be going to culinary school to become a top chef. For dinner tonight I’ll probably make mashed potatoes and a ribeye, with a little bit of vegetables because I need those too.
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