Research

I am currently interested in the following topics:

• Connections between sieve theory and automorphic forms, for example level of distribution results and the divisor function

• GL(3) automorphic forms

I have previously worked on:

• Binary problems in (subsets of) the primes

• The Fourier-Analytic transference principle

Research Paper:

• On a conjecture of Elliott concerning a probabilistic variant of Titchmarsh's divisor problem (with O. Gorodetsky) Preprint Available. 

• The exceptional set in Goldbach's Problem with Almost Twin Primes (with J. Teräväinen). Preprint available

• Additive Problems in Almost Prime Squares (with V. Blomer, J. Li, S. Myerson). To appear in GAFA.  Preprint available

• Goldbach Numbers in Short Intervals. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. Preprint available

• Vinogradov's Theorem with Fouvry-Iwaniec Primes. To appear in  Algebra and Number Theory. Preprint available

• Representation of Squares by nonsingular Cubic Forms (with W. Sawin). Israel Journal of Mathematics . Preprint available

Thesis:

• Modern Applications of the Circle Method, PhD Thesis. Available online