Congratulations to Pure Mathematics PhD candidate Jacob Campbell and recent Computer Science master’s graduate Mahbod Majid, the 2023 recipients of the Faculty of Mathematics Graduate Research Excellence Awards. The prestigious recognition comes with a $5,000 cash prize and is conferred annually to two graduate students in the Faculty of Mathematics who have authored or co-authored an outstanding research paper.
Jacob Campbell
Jacob Campbell is a PhD candidate in Pure Mathematics who is finishing his final semester of graduate education before beginning a postdoctoral position in the Department of Mathematics at the University of Virginia. In 2021 and 2022, he published two papers and posted the preprint of a third: "Finite free convolutions via Weingarten calculus," (with Zhi Yin, research fellow at Harbin Institute of Technology) “A Central Limit Theorem for Star-Generators of S¥, Which Relates to Traceless CCR-GUE Matrices,” (with Claus Köstler, lecturer in Mathematical Sciences at University College Cork, Ireland, and Alexandru Nica, professor of Pure Mathematics at Waterloo and Campbell’s advisor) and “Commutators in finite free probability, I” (preprint, as sole author).
In the paper published with Köstler and Nica, the authors found a novel random matrix model for a certain family of probability distributions related to characters of symmetric groups. In the two other papers, the authors used techniques from combinatorial representation theory to study sums, products, and commutators of random matrices, in the context of the new theory of "finite free probability."
Campbell emphasizes the importance of collaboration to pure math research: “solving problems that other people are interested in” is a driver for his work. The area of inquiry that Campbell investigated, explains his Alexandru Nica, his advisor and a professor of Pure Mathematics, ”has been studied since the 1970s, but he recently found new interpretations within the framework.”
Mahbod Majid
Majid, who is currently a first-year PhD student in the Machine Learning Department at Carnegie Mellon University’s School of Computer Science, received the award in recognition of the paper “Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism.” This paper, which he co-authored with his graduate advisor Professor Gautam Kamath and Professor Samuel Hopkins at MIT, was presented at STOC 2022, the 54th ACM Symposium of Theory of Computing, one of two top conferences in theoretical computer science.
Mahbod’s paper solved a core problem in private statistical estimation, one that has plagued researchers for years: how do you estimate the mean in a distribution or population efficiently and accurately while also preserving the privacy of sensitive data? “Previously developed algorithms had achieved two out of three of these goals at any given time,” explains Kamath, “but Mahbod’s elegant solution satisfies all three simultaneously. It is not only a nearly-optimal solution for the most fundamental statistical task under strong privacy constraints, but it also closes a long-standing gap in our understanding of private multivariate statistics.”