May 15, 2023

Carlos Martinez is a doctoral candidate in applied mathematics from Guayaquil, Ecuador. He earned his B.S. in civil engineering at the University of Illinois at Urbana-Campaign and now studies discrete mathematics under the guidance of Samitha Samaranayake at Cornell.

What is your area of research and why is it important?

I am broadly interested in discrete mathematics, from its real-world applications to foundations in optimization and combinatorics. For instance, I develop mathematical models and algorithms for problems arising in transportation (e.g., designing a “good” set of bus routes for a public transit system). In a separate line of work, I study parking functions, which are combinatorial objects related to permutations.

What are the larger implications of this research?

To me, applied mathematics offers a nice balance between basic and translational research. I like working on applied problems because of the opportunity to make progress toward important societal goals. In my case, this means improving urban mobility. I also like working on less applied problems, particularly in combinatorics, because it is a challenging yet accessible area: problems are often easy to state but hard to solve. I treat it as an opportunity to build a more inclusive mathematics research community.

What does it mean to you to have been selected as a Schmidt Science Fellow? What will this fellowship allow you to do that you might not have otherwise?

It is a tremendous opportunity to advance my career goals. It gives me the freedom to take a risk and pivot into an area of mathematics different from that of my Ph.D., without any set expectations other than my commitment to an ambitious line of research. As a Schmidt Science Fellow, I will pivot into algorithmic fairness and algorithmic game theory. My goal is to develop mathematical foundations for the design of equitable public infrastructure.

What are your hobbies or interests outside of your research or scholarship?

I have various hobbies, but my favorite one is making espresso. Besides the coffee itself, I really enjoy the process: It is a nice balance between technique, creativity, and precision. I also keep a list of all the airports I have ever been to: 68 and counting!