热点爆料入口 mathematician Spencer Leslie
wins NSF CAREER Award
Assistant Professor of Mathematics Spencer Leslie鈥攚ho did his graduate studies in the department where he now teaches鈥攈as 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, 鈥渉ave the potential to serve as academic role models in research and education and to lead advances in the mission of their department or organization.鈥�
Spencer Leslie
鈥淭his was a huge, and welcome, surprise,鈥� said Leslie, who earned master鈥檚 and doctoral degrees in mathematics at 热点爆料入口 and did his postdoctoral work at Duke University before joining the Mathematics faculty in the fall of 2022. 鈥淚 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鈥檚 just a wonderful environment.鈥�
Automorphic forms, the focus of Leslie鈥檚 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鈥攕pecial 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 鈥減eriods.鈥� 听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. 听
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鈥攚hich combines number theory and geometry鈥攁nd to test the ideas of the relative Langlands conjectures.
A key feature of the project is that it goes beyond research, noted Leslie: 鈥淚t 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.鈥�
As a former grad student and now a faculty member, Leslie cites the department鈥檚 smaller-is-better approach to research as one of its most important features.
鈥淚nstead of looking at all aspects of mathematics, the department built groups which each have a specific focus鈥攏umber theory, geometry and topology, algebraic geometry, and more recently, machine learning,鈥� he said. 鈥淲e鈥檝e been able to develop world-class research and offer our students an intellectually stimulating experience.鈥�
鈥淲e are delighted to see Spencer鈥檚 outstanding work recognized by this prestigious early-career award,鈥� said Professor Renato Mirollo, the department chair. 鈥淪pencer 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.鈥�
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