Hanna Kim, a PhD candidate in mathematics at the University of Illinois Urbana-Champaign, has been awarded the 2024 Kuo-Tsai Chen Prize in Mathematics.

The Kuo-Tsai Chen Prize, established in 1989, is given in recognition of outstanding scholastic achievement by a graduate student whose research examines relationships between analysis and either geometry or algebra.

Kim’s research focuses on spectral geometry—which establishes relationships between partial differential equations and differential geometry.

According to her nominators, Kim’s work has advanced spectral theory in significant ways. Early in her graduate career, she produced a paper, “Maximization of the second Laplacian eigenvalue on the sphere,” that focused on an open problem related to the Laplace-Beltrami operator. In the paper, she demonstrated significantly simpler 2-dimensional methods for the problem, bulding on the previous work of her advisor, Prof. Richard Laugesen. Her paper also revealed that the prevailing theory about whether these same results would occur in higher dimensions had been incorrect.

More recent work from Kim tests the applicability of her methods in other manifolds and higher eigenvalues. Kim’s future research plans look to conjectures involving higher eigenvalues on spheres and sharp results on real projective spaces.