Mathematician Michael Hill honored for helping solve 50-year old geometry problem

By Max Gordy

Michael Hill, professor of mathematics in the UCLA College, has received the 2022 American Mathematical Society Oswald Veblen Prize in Geometry for his paper, “On the nonexistence of elements of Kervaire invariant one,” along with his co-authors Michael Hopkins and Douglas Ravenel.

This paper solved a 50-year-old problem in geometric topology by showing that framed manifolds with Kervaire invariant one can only exist in finitely many dimensions, introducing deeply influential new ideas and techniques in algebraic topology.

“I feel profoundly honored and grateful to the AMS for this award,” Hill said. “This is the award that as a graduate student, I dreamed of someday receiving, and I am all the more delighted that it is for the theorem that I had dreamed of someday proving, working with mathematicians I so admired.

Hill is a member of the topology group, and his research focuses on algebraic topology. He co-founded the Talbot workshop series for early career researchers as well as Spectra: the Association for LGBTQ Mathematicians. Spectra works to make math more inclusive for LGBTQ people, allowing them to bring their whole selves to their mathematical lives. He received a Sloan Research Fellowship in 2010, was an invited speaker at the 2014 ICM in Seoul, South Korea, and was elected a Fellow of the American Mathematical Society in 2021.

The Oswald Veblen Prize in Geometry is awarded every three years for a notable research work in geometry or topology that has appeared in the last six years. The work must be published in a recognized, peer-reviewed venue. The 2022 prize will be presented Jan. 5 at the 2022 Joint Mathematics Meetings in Seattle.

This article originally appeared in the UCLA Newsroom. For more news and updates from the UCLA College, visit college.ucla.edu.