Three UC San Diego Math Professors Win Simons Fellowships

Adrian Ioana, a professor of mathematics since 2015, earned his Ph.D. from UCLA and B.S. from the University of Bucharest in Romania. His areas of focus include operator algebras (von Neumann algebras and C*-algebras), ergodic theory, group theory and logic.

“Under the support from the Simons Fellowship, I plan to work on two main research projects at the intersection of operator algebras and group theory,” Ioana said. “The first project concerns a well-known rigidity conjecture of Connes from 1980. The second project concerns three related themes: almost commuting matrices, group stability and the lifting properties for C*-algebras. In particular, I would like to approach an old question asking if two matrices, which almost commute with respect to the Hilbert-Schmidt norm, are necessarily close to commuting matrices.”

Melvin Leok is a UC San Diego professor of mathematics and co-director of the computational science, mathematics and engineering (CSME) graduate program. He is interested in computational genomic mechanics, computational geometric control theory, discrete geometry, and structure-preserving mechanical schemes, particularly how these subjects relate to systems with a symmetry. He received his Simons Fellowship on the strength of his research in geometric numerical integration. This draws on his recent work constructing geometrical methods preserving geometric invariants of dynamical systems, particularly variational integrators for both Lagrangian and Hamiltonian mechanical systems.

“The Simons Fellowship will provide me with uninterrupted research time to focus on the challenge of constructing numerical methods that respect the geometric properties of Einstein’s theory of gravity,” said Leok. “This will help us to better infer properties of astrophysical objects from the gravitational waves that they emit.”

Rayan Saab came to mathematics from an academic background in electrical engineering, becoming an associate professor of mathematics at UC San Diego in 2017. His research draws on and develops tools and ideas in information theory, random matrix theory, frame theory, and geometric functional analysis to address issues relevant to the acquisition, digitization, and processing of signals and data. 

“Machine learning algorithms are nearly ubiquitous,” said Saab. “Their applications in data science are on the rise. With this rise in applications is an opportunity and a challenge to develop rigorous mathematical methods to solve fundamental theoretical problems as well as problems on the frontiers of current technology. During my sabbatical, I intend to focus on three loosely related problems, developing new computationally efficient algorithms with rigorous mathematical guarantees, for solving problems in the context of neural networks, and machine learning more generally.”