Trevor Wooley

Analytic and additive number theory, arithmetic geometry, arithmetic combinatorics, discrete harmonic analysis – especially “Analytic methods for Diophantine problems”: the Hardy-Littlewood method; applications and theory of exponential sums; Diophantine equations and inequalities in many variables; local (p-adic) solubility of Diophantine systems; distribution of fractional parts of polynomials; density of rational points on varieties.