Department of Mathematics and Statistics

My research explores the intersection of dynamics, probability theory, ergodic theory, number theory, and mathematical physics. My goal is to investigate the extent to which classical objects from number theory can be regarded as random; while the results are often of probabilistic nature, the methods I use are dynamical – combining spectral theory of ergodic group actions, the study of flows on homogenous spaces, and classical analytic tools from ergodic theory. 

Number theory supplies us with a multitude of deterministic sequences that depend on a a small number of parameters. It is of great interest to understand the degree to which these sequences exhibit random features. In other words, I aim to study whether familiar results from probability theory (or variations thereof) hold for sequences of number-theoretical origin, and explore the applications to other fields (e.g. quantum mechanics).