BC mathematician Spencer Leslie
wins NSF CAREER Award
Assistant Professor of Mathematics Spencer Leslie—who did his graduate studies in the department where he now teaches—has won a National Science Foundation CAREER Award that will enable him to continue his research on automorphic forms.
The five-year awards support early-career faculty who, according to NSF, “have the potential to serve as academic role models in research and education and to lead advances in the mission of their department or organization.”
Spencer Leslie
“This was a huge, and welcome, surprise,” said Leslie, who earned master’s and doctoral degrees in mathematics at BC and did his postdoctoral work at Duke University before joining the Mathematics faculty in the fall of 2022. “I feel very fortunate to be part of a special research program that I really love, and to be part of a larger community of colleagues that supports this work. It’s just a wonderful environment.”
Automorphic forms, the focus of Leslie’s work, are highly symmetrical functions or objects that play a significant role in various areas of mathematics, including number theory, representation theory, and algebraic geometry. A set of conjectures called the Langlands program suggest deep connections between automorphic forms and other areas of mathematics via the properties of L-functions—special mathematical functions that connect different areas of math.
A more recent development, the relative Langlands program, seeks to make the connection between L-functions and automorphic forms even more precise, by linking L-functions to certain features of automorphic forms called “periods.” To understand these periods, mathematicians use the relative trace formula (RTF) to break down a complex period into simpler, building-block pieces, which are often directly related to important values of L-functions.
Supported by the NSF CAREER grant, Leslie will work on a concept called endoscopy to stabilize a large family of RTFs by developing new theories related to endoscopy and adapting some existing mathematical techniques to a new context. These new tools can be used to solve problems in arithmetic geometry—which combines number theory and geometry—and to test the ideas of the relative Langlands conjectures.
A key feature of the project is that it goes beyond research, noted Leslie: “It will create opportunities for both undergraduate and graduate students to get involved in this fast-moving field, enable me to organize workshops for graduate students to learn from each other, and help them practice giving presentations about their work.”
As a former grad student and now a faculty member, Leslie cites the department’s smaller-is-better approach to research as one of its most important features.
“Instead of looking at all aspects of mathematics, the department built groups which each have a specific focus—number theory, geometry and topology, algebraic geometry, and more recently, machine learning,” he said. “We’ve been able to develop world-class research and offer our students an intellectually stimulating experience.”
“We are delighted to see Spencer’s outstanding work recognized by this prestigious early-career award,” said Professor Renato Mirollo, the department chair. “Spencer has been extremely productive since joining the department, and most recently had a paper accepted in the Annals of Mathematics, arguably the most competitive journal in our field. As the youngest member of our number theory group, Spencer brings boundless energy to our department, and we look forward to watching his research deepen in the years ahead. He is eminently deserving of this CAREER award.”