Brandon Levin, an assistant professor of mathematics at Rice University, has won a prestigious National Science Foundation CAREER Award to pursue his research on major unsolved problems in number theory.
The highly-competitive grants, awarded to only about 500 faculty each year across all disciplines, support early career faculty who have the potential to serve as academic role models and leaders in research and education.
“I build theoretical bridges between the arithmetic world of the Galois theory and complex analysis, representation theory and even topology,” Levin said. “The existence of such connections is part of the Langlands program, a web of problems that has been a driving force in modern number theory for the past fifty years or so. Using an arithmetic analogue of Hodge theory, I introduced new geometric structures that promise to shed light on some of the deepest mysteries in the field.”
“Brandon’s research to date has several strands, but a unifying theme is the quest to put on solid ground a set of deep conjectures of Jean-Pierre Serre, a 20th century luminary,” said Rice mathematics professor Anthony Várilly-Alvarado. “At a basic level, these conjectures attempt to explain what appear to be numerical coincidences between two very different kinds of mathematical objects, modular forms and Galois representations.
“When you see these coincidences, you just feel in your bones that there must be a reason for them; one cannot imagine a world in which there is no explanation for them,” Várilly-Alvarado said. “The hope is that these numerical coincidences are shadows of underlying geometric phenomena, that they result from quantifying properties of geometric spaces in different ways.”
In addition to research, CAREER Awards include funding for educational and public outreach initiatives.
Levin is the current director of the Southwest Center for Arithmetic Geometry and the principal investigator for the most recent NSF grant funding the Arizona Winter School, a yearly five-day conference that brings together roughly 300 researchers, including 200 Ph.D. students, and is currently in its 25th year.
“The Arizona Winter School is the premier graduate student training program in number theory,” Levin said. “It brings together world-class mathematicians and graduate students from around the world for an intensive educational and research experience. It has been a great honor for me to run this program. I’m especially excited about our new virtual program for undergraduates and graduate students from underrepresented groups.”
“Brandon is not only a world-class researcher but also a community builder,” Várilly-Alvarado said. “He puts in an inordinate amount of time to make this event an extraordinary success. Having Brandon as a colleague at Rice has been transformational for me. His insights during our lab meetings, as well as his lectures in our learning seminars, have provided fresh perspectives on topics that are sure to influence all of our research moving forward.”