Paul Minter

Dr. Paul Minter is a Clay Research Fellow currently visiting Stanford University and the University of Cambridge, where he also holds a position as Junior Research Fellow at Homerton College. His primary academic affiliation is with the Department of Pure Mathematics and Mathematical Statistics within the Faculty of Mathematics at the University of Cambridge. Previously, he was a Veblen Research Instructor at Princeton University and the Institute for Advanced Study (IAS), working with Professor Camillo De Lellis.

Dr. Minter completed both his undergraduate studies and PhD at the University of Cambridge, receiving his doctorate in 2022 under the supervision of Professor Neshan Wickramasekera. During his graduate studies, he was affiliated with St. Catharine's College.

Dr. Minter's research lies at the intersection of differential geometry, geometric analysis, and geometric measure theory, with a specific focus on the regularity theory of minimal surfaces. His work addresses fundamental questions regarding the structure and behavior of minimal submanifolds, particularly concerning singularities and regularity properties. He investigates how analytical techniques can be used to understand geometric phenomena, with special attention to area-minimizing objects and their singular sets.

His research portfolio demonstrates a consistent focus on regularity and compactness questions for minimal hypersurfaces in Riemannian manifolds. Dr. Minter has developed powerful new techniques for analyzing singularities of measure-theoretically defined minimal hypersurfaces with stable regular parts. His publications show remarkable progression in establishing the uniqueness of tangent structures and understanding the fine structure of singular sets, with increasingly general results that remove previous restrictions on multiplicity or dimension.

Among his notable achievements is being appointed as a Clay Research Fellow for four years beginning July 1, 2023, a prestigious recognition of his contributions to geometric measure theory.

Dr. Minter has taught graduate-level courses including 'Regularity Techniques in Geometric Measure Theory' at Princeton University in Spring 2024. He has presented his research at numerous institutions including SLMath, the IAS, and NCTS. His work has been featured in top mathematical journals such as the Journal of the American Mathematical Society, Archive for Rational Mechanics and Analysis, and Calculus of Variations and Partial Differential Equations. He is also mentoring a course at the 6th British Isles Graduate Workshop on 'Minimal Surfaces' scheduled for September 2025.