Degrees & Accolades:
Ph.D. (University of California Los Angeles)
I am interested in questions in analysis, probability, and number theory. I have especially focused on problems at the interface of analytic number theory and random matrix theory.
Analytic number theory is the branch of mathematics concerned with quantitative and approximate questions about the integers and prime numbers (e.g. roughly how many primes are less than a given number). Random matrix theory is the study of matrices with randomly chosen entries, with much of its original interest coming from statistical physics. That there is a connection at all between the two areas is surprising but first emerged in the 1970s in work on the distribution of zeros of the Riemann zeta-function. Many open questions remain about this connection, and cross-fertilization between the two areas continues to occur.
More broadly still I am interested in the frequent appearance of randomness in discrete mathematical structures.