# Interview with Alejandro Sarria

by David Ariyibi ’19

Sarria explains to Ariyibi his goal of finding a mathematical link to the physical properties of pressure in fluids.

What’s your favorite part of math?

I work in nonlinear partial differential equations, and the main reason I like partial differential equations is that they’re wild. There isn’t much theory for how to deal with many of them. You have to figure it out yourself. It’s not always about applying methods already in the literature. In most cases you have to come up with the tools to study a problem.

What are you working on right now?

Right now, I’m working with a student assistant on the incompressible Euler equations, which model ideal fluid flow. We incorporated damping into the system. We’re studying the impact of this damping term on the behavior of solutions to these equations.

Do you have some overarching goal for your mathematics research?

When you model fluids, there is something called the pressure. For example, in the sea, when you go very deep, the pressure can actually kill you. Unfortunately, this pressure term is not very well understood from a mathematical perspective, so I would like very much to understand it better. That would be really nice.

Do you have any advice for aspiring math students?

Keep an open mind.  Don’t restrict yourself to studying just one area of math and one methodology or theory, because later on you may find yourself at a disadvantage if new theories are developed using tools from different fields. Just keep an open mind. Keep on researching. Keep on studying other areas of math, and stay up with new developments through attending conferences and workshops.

Throughout graduate school, what was the most difficult point for you?

Coming up with the topic for my dissertation. There was this Millennial problem on fluid flow. It kinda sounded interesting to study a problem whose solution is worth a million bucks. Of course I didn’t solve the problem, but I was able to find some related problem that I could work on. So coming up with the topic was probably the most difficult part in graduate school. The next most difficult part was managing my time. I found myself reading tons of papers and attending all these conferences. I would do a little bit over here and a little bit over there. At the end, you have  to be very well-organized and have some sort of structure. Know what it is that you want to do and what it is that you actually can do.

What else do you like outside of Mathematics?

Physics. I like physics a lot. Outside of the office, I like to go hiking and running. I play soccer whenever I find people to play with. I like exercising in general. I like the outdoors a lot.

What exactly brought you to Williams?

I wanted to work on my teaching skills as well as interact and work with students. At Williams the interaction between faculty and students is fantastic. There are lots of workshops for teaching. The professors are top tier, some of the best teachers in the country when it comes to math. You can get very good advice from them. It is a good opportunity to keep on doing research while working on my teaching skills.

You’ve mentioned the million-dollar “Millennial” problem on fluid flow. Are there any others you are interested in?

The Poincaré conjecture. It already got solved using, in part, differential equations. That would have interested me if I would have known that was the method to solve it, but it has already been solved, so actually, I think I’ll stick with the fluid problem.

Sarria is Visiting Assistant Professor at Williams College. Ariyibi is in the Class of 2019 studying mathematics and economics; he likes multivariable calculus and playing the saxophone.