The Alfred P. Sloan Foundation awarded three Brown professors with early career research fellowships last week.
The foundation named Assistant Professor of Mathematics Eric Larson, Assistant Professor of Applied Mathematics Brendan Keith and Assistant Professor of Economics Jonathan Roth as three recipients of the fellowship. Across the United States and Canada, 126 researchers were selected for the fellowship.
The Sloan Research Fellowship awards $75,000 in research funding over the course of two years to researchers who have shown creativity and innovation early in their careers.
Eric Larson: Algebraic geometry, polynomial equations and the interpolation problem
Larson studies algebraic geometry — investigating the geometric properties of solutions to polynomial equation systems, he explained in an interview with The Herald.
In 2022, Larson was widely recognized for solving the centuries-old interpolation problem, alongside his wife, Associate Professor of Mathematics Isabel Vogt, The Herald previously reported.
“Truth be told, when I started thinking about the interpolation problem, I had not decided on a field of mathematics,” Larson said. “I loved math, and I was interested in many different things, and these problems — the maximal rank conjecture and the interpolation problem — led me to journey into algebraic geometry.”
For Larson, solving these problems was “so much fun” that he made algebraic geometry his primary research focus.
Larson, who published his proof in 2022, said that it took over a decade to arrive where he is today. From his time as a PhD student at the Massachusetts Institute of Technology, Larson collaborated with many people in an attempt to solve the interpolation problem.
Drawn by the interpolation problem into algebraic geometry, Larson found himself specializing in geometric curves.
“The motivation for studying it is the intrinsic appeal of the problem itself,” he said.
Larson said he looks forward to the “flexibility” provided by the Sloan Fellowship to organize conferences and fund collaboration on his studies.
Brendan Keith: Using math to model the world
Keith specializes in scientific computing, using computer simulations to model physical processes. Since arriving at Brown in 2022, his research has focused on developing computer algorithms to simulate variational inequalities, or “physical laws for phenomena that have inequality constraints,” he explained.
“A basketball can’t go through the floor when you bounce it, right?” Keith said. “There’s an inequality constraint that it can’t penetrate the floor. When you simulate that, you want to make sure every particle in the discretized basketball stays on the right side of the floor.”
While completing his PhD at the Oden Institute for Computational Engineering and Science at the University of Texas at Austin, Keith created the DPG-star method for performing computer simulations
He described his career as “definitely not linear.”
“I wasn’t somebody who got into every PhD program I applied for,” he added. But Keith went on to complete three postdoctoral stints in California, Rhode Island and Germany.
Keith emphasized the value of interdisciplinary knowledge in mathematics. Growing up, he wanted to be a physicist, but eventually turned to math and computer simulations to seek out a more “rigorous explanation” behind physics.
“Math, from every angle, has beauty in it,” Keith said. “I found that no matter what I study, mathematics always presents itself. With that in mind, I’ve found it more inspiring to develop mathematics that can be used in the world around me.”
Keith’s interdisciplinary curiosity also applies to his research projects, which range across a variety of topics including black holes, car crashes and turbulent wind interactions. Currently, he is working on modeling hurricanes in a project with a national renewable energy laboratory.
“At the end of the day, I think I have the coolest job in the world,” he said.
Keith said the Sloan Fellowship will help him further develop a method called the Proximal Galerkin Finite Element Method in collaboration with Visiting Scholar in Applied Mathematics Thomas Surowiec.
Jonathan Roth: Combining social policy with quantitative analysis in econometrics
Roth shares Keith’s interdisciplinary curiosity. As an economics professor at Brown, Roth specializes in econometrics, which he describes as “a statistical tool kit” for measuring the effects of policies and changes in law.
As an undergraduate student at the University of Pennsylvania, Roth enjoyed learning about social policy and politics but was also drawn to math and quantitative analysis. Seeking a way to combine his interdisciplinary passions, he landed on economics.
In designing application-based research methodology, Roth enjoys the fact that he can influence various studies at once. His work has been used on a wide range of policies, from tax reform in France to policies increasing the labor force participation of women in Saudi Arabia, he said.
“I’m interested in answering social policy questions and helping make social science as credible as possible,” Roth said. Day-to-day, though, he likes “challenging math problems.”
“I’m lucky to be in a field that combines those two things,” Roth said.
Roth’s knowledge on issues such as labor economics allows him to tailor statistical theory to be useful for economic researchers.
Roth hopes to use the Sloan Fellowship to translate his methodology into something “easier to use” by writing programs in computer languages such as Python. With the funds, he intends to hire graduate and undergraduate research assistants at Brown to help code his projects.
Correction: This article has been updated to more accurately reflect Brendan Keith's research.
