Huy Tuan Pham will receive his PhD in 2023 from Stanford University, where he is advised by Jacob Fox.
Pham is a highly inventive and prolific researcher who has already made fundamental contributions to combinatorics, probability, number theory, and theoretical computer science. While still an undergraduate, he showed with Fox and Zhao that Green’s popular difference theorem, an extension of Roth’s theorem on arithmetic progressions in dense sets of integers, requires tower-type bounds – the first known application of Szemerédi’s regularity method that truly requires tower-type bounds. Subsequently, with Park, he proved the Kahn-Kalai conjecture on the location of phase transitions and Talagrand’s conjecture on selector processes; with Conlon and Fox, he solved various long-standing conjectures of Erdős in additive combinatorics concerning subset sums and Ramsey complete sequences; and with Cook and Dembo, he developed a quantitative nonlinear large deviations theory for random hypergraphs.
Huy Tuan Pham has been appointed as a Clay Research Fellow for five years beginning 1 July 2023.
Paul Minter obtained his PhD in 2022 from the University of Cambridge, advised by Neshan Wickramasekera. Since then he has been a Veblen Research Instructor at Princeton University/IAS and a Junior Research Fellow at Homerton College, Cambridge.
Minter works in Geometric Measure Theory, tackling regularity and compactness questions for minimal hypersurfaces in Riemannian manifolds. He has advanced the subject by introducing powerful new techniques for analysing singularities of measure-theoretically defined minimal hypersurfaces with stable regular part, establishing, in particular, the uniqueness of classical tangent cones when they arise, and (with Wickramasekera) the uniqueness of tangent hyperplanes at branch points, in the absence of lower density classical singularities nearby. His remarkably general results – the first with no restrictions on multiplicity or the dimension of the hypersurface – provide a much sought-after extension to what is known about uniqueness of tangent cones and the asymptotic behaviour of minimal submanifolds near singularities. Applications include an understanding of the structure of area minimising hypersurfaces mod p, for any even integer p, near a singular point with a planar tangent cone.
Paul Minter has been appointed as a Clay Research Fellow for four years beginning 1 July 2023.