UArizona Mathematician and Cosmologist Awarded Sloan Research Fellowships

Man teaching math at a chalk board

Brandon Levin teaching.

Courtesy: Brandon Levin

The University of Arizona's Brandon Levin, an assistant professor in the Department of Mathematics, and Elisabeth Krause, an assistant professor in the Department of Astronomy and Department of Physics, are two of 128 researchers from the United States and Canada to be awarded 2021 Sloan Research Fellowships.

The Alfred P. Sloan Foundation annually awards two-year $75,000 fellowships to early-career faculty with doctoral or equivalent degree in mathematics, physics, chemistry, computer science, Earth system science, economics, molecular biology, neuroscience or a related field. The fellowships seek to stimulate fundamental research by pre-tenure scientists with outstanding potential, according to the foundation.

"It is critical for our early-career researchers to receive recognition of their talent as well as support for their work," said Elizabeth "Betsy" Cantwell, UArizona senior vice president for research and innovation. "I extend my gratitude to the Sloan Foundation for playing this important role in the research ecosystem, and my sincere congratulations to Drs. Krause and Levin on the receipt of these richly deserved Sloan Fellowships."

Brandon Levin

Brandon Levin

Brandon Levin

"The Sloan Foundation has a lot of programs, but this is their most prestigious for young scientists," said math department head Doug Ulmer, who nominated Levin. "Brandon is on a great trajectory. He has had an avalanche of work and breakthrough papers published in the most competitive journals. He's emerging as a leader in his field."

Levin earned his doctoral degree in mathematics from Stanford in 2013 before becoming a postdoctoral fellow for one year at the Institute for Advanced Study in Princeton and for three years at the University of Chicago. He has been at the University of Arizona since 2017, teaching students at all levels and doing research in number theory – the study of whole numbers.

"It's a real honor, and I'm excited to be recognized for all the things my collaborators and I have been doing together," Levin said. "We have discovered new geometric structures underlying a 20-year-old conjecture by Christophe Breuil and Ariane Mézard, which arose out of Andrew Wiles' proof of Fermat's Last Theorem. This breakthrough raises as many new questions as it answers. The Sloan gives me the flexibility to really pursue these ideas and their ramifications for number theory more broadly."

Levin came to work at the University of Arizona in part because the math department has a long and distinguished history in number theory, he said. His specific area of study is the Langlands program – a vast network of conjectures connecting number theory and geometry.

"Our department has a very strong group in number theory," Ulmer said. "It's one of the traditional strengths of the department, along with applied math, math education, and statistics and data science. This award is an affirmation of the fact that our faculty are doing important work in a fundamental area of science."

Levin said he pursued number theory because he has always enjoyed probing for hidden patterns in numbers. He knew math was a passion from the time he was in high school, but he didn't know what area of math he would one day study.

"My introduction to number theory was at a historic summer program for high schoolers, the Program in Mathematics for Young Scientists at Boston University, where I also served as a counselor for four years," he said.

He explored numerous areas of math in college and graduate school, and he even considered chemistry, but was consistently drawn back to number theory.

"I was drawn to number theory because of its connection to so many other areas of mathematics," he said.

Levin's work also was recently recognized with a National Science Foundation Focused Research Group grant for a collaborative project called "Geometric structures in the p-adic Langlands program." The grant will support the training of more students in number theory.

Elisabeth Krause

Elisabeth Krause

Elisabeth Krause

The Sloan Fellowship is the latest in a list of prestigious awards Krause has received in her two- and-a-half years at the University of Arizona. She also recently received a five-year, $875,000 Packard Fellowship for Science and Engineering, as well as a five-year, $750,000 Early Career Research Award from the U.S. Department of Energy.

Krause earned a degree in physics from the University of Bonn in Germany in 2007, and she received a doctorate in astrophysics from the California Institute of Technology in 2012. She joined UArizona in 2018 after holding postdoctoral positions at the University of Pennsylvania, Stanford and the Jet Propulsion Laboratory.

As a cosmologist and through her work with the Dark Energy Survey and the Vera C. Rubin Observatory (formerly the Large Synoptic Survey Telescope), Krause seeks to determine what the universe is made of.

"This award gives me, my students and colleagues from around the world the flexibility to really follow our most interesting leads and newest ideas," Krause said. "The question we're after is: What is dark energy? What is this mysterious stuff that drives the expansion of the universe? We're not going to solve this with a two-year grant, but it will help us put a few pieces of the puzzle together."

As observatories become more powerful and collect more data, Krause develops algorithms that help astronomers and cosmologists make sense of it all by bridging the gap between observational data and theory.

"The future of cosmology in the 2020s is extremely exciting, as unprecedentedly large, high-quality new datasets will become available from new facilities and missions. This flood of information will require the development of very sophisticated and bias-free analysis tools – one of many areas in which Dr. Krause has demonstrated unique talent and leadership," said Buell Jannuzi, head of the UArizona Department of Astronomy. "The departments of astronomy and physics are extremely proud to have her as a member of our departments and an international leader in improving our understanding of the universe."

Krause and her research group are gearing up for two major highlights in the future. The first is a huge influx of year-one data from Chile's Vera C. Rubin Observatory, run by the National Science Foundation and the U.S. Department of Energy. Krause expects it will be "a treasure trove for cosmology," since it will provide over a billion galaxies to analyze, which is an order-of-magnitude increase from current datasets.

The second highlight is the launch of NASA's SPHEREx mission in 2024. Krause is a co-investigator on the two-year mission, which will provide a unique window into inflation – a phase of rapid expansion of the universe shortly after the Big Bang. SPHEREx stands for Spectro-Photometer for the History of the Universe, Epoch or Reionization and Ices Explorer.

"Both Brandon and Elisabeth are real assets to the University of Arizona and the College of Science," said College of Science interim dean Elliott Cheu. "His work in number theory and her work in cosmology are impressive and well-deserving of this recognition. I expect they will continue to impress us throughout their careers."