The 2022 New Horizons in Mathematics Prize was awarded to Sebastian Hurtado-Salazar of the University of Chicago and Aaron Brown of Northwestern University for their contributions to the proof of Zimmer’s conjecture.
Hurtado-Salazar and Brown will share $100,000 as winners of a New Horizons Prize, given to early-career scientists and mathematicians who have made a substantial impact on their fields. This year, six New Horizons Prizes were awarded to 13 scholars.
The prizes are part of a larger set awarded by the Breakthrough Prize Foundation and its founding sponsors: Sergey Brin, Priscilla Chan and Mark Zuckerberg, Yuri and Julia Milner, and Anne Wojcicki.
“I feel very fortunate that all the pieces fell into place, and we were able to put this proof together,” said Hurtado-Salazar, an assistant professor of mathematics. “I’m very thankful for the many people—including my colleagues, collaborators, students and advisors—who have helped me over the years.”
Hurtado-Salazar focuses on understanding the structure of Lie groups, its subgroups and group actions on manifolds. These topics are of importance in different branches of mathematics, including geometry, dynamical systems and number theory.
In 2018, Hurtado-Salazar, Brown and Indiana University Prof. David Fisher announced a breakthrough proof of Zimmer’s conjecture. First outlined in the early 1980s by University of Chicago Chancellor Robert J. Zimmer, the Edwin A. and Betty L. Bergman Distinguished Service Professor in the Department of Mathematics, the conjecture concerns a fundamental concept in mathematics called symmetries. Hurtado-Salazar, Brown and Fisher’s proof shows there are some restrictions in how many symmetries a space can have and some special properties about higher-rank lattices.
“I really liked the question; it’s very simple from a mathematical perspective, and yet it appeared so intractable,” Hurtado-Salazar said.
Zimmer commented on the research in a 2017 interview with UChicago Magazine: “Their arguments are original, powerful and beautiful, and I was surprised by some of the particular techniques that were involved.”
Hurtado-Salazar plans to donate his share of the prize money to organizations that provide math and science education in developing countries.