Research Interests

My research interests include analytic and probalistic number theory, additive combinatorics, spectral (hyper)graph theory, and discrete geometry. Broadly speaking, I am most attracted to problems in number theory, combinatorics and theoretical computer science that require tools from other areas such as analysis and probability to solve. I am particularly interested in Fourier analytic tools.

My papers and expository writing give a fairly good idea of what kind of mathematics interests me.

The problems I am currently working on relate to:

  • Moments of \(L\)-functions (particularly the Hurwitz zeta function).

  • Extremal problems in spectral (hyper)graph theory.

  • Large gaps between zeroes of the Riemann zeta function.

  • Random multiplicative functions.