I am a Clay Research Fellow visiting Stanford University and the University of Cambridge, where I am also a Junior Research Fellow at Homerton College.
Previously, I was a Veblen Research Instructor at Princeton University and the IAS, working with Professor Camillo De Lellis. I completed my PhD in 2022 at the University of Cambridge under the supervision of Professor Neshan Wickramasekera. A copy of my thesis is here. I was at St. Catharine’s College during my undergraduate and PhD.
I can be contacted at [email protected].
Research
My main interests lie within differential geometry, geometric analysis, and geometric measure theory. One of my main research focuses has been on regularity and compactness questions for minimal submanifolds, in particular under degenerations where multiplicity occurs. An instance of this is when taking a tangent cone to a stationary integral varifold at a singular point, with natural questions being whether this object is unique and to what extent it determines the local structure or asymptotic behaviour of the varifold about the singularity. See here for more information.
See also:
1) This NSF article from the IAS for an overview of my research, intended for a broad audience.
2) The IAS Newsletter Spring 2024 which, among other things, includes an article (p10-p13) written about my joint work with Camillo De Lellis and Anna Skorobogatova (and their own work) on area minimisers.
Papers
Summaries of some of my papers can be found under the “Research” tab above.
13) Quantitative Estimates on the Topology and Singular Set for Prescribed Mean Curvature Hypersurfaces
Joint with Nicolau Sarquis Aiex and Sean McCurdy
arXiv (Feb 2026)
12) Entire Area-Minimizing Surfaces in R^4 are Algebraic
Joint with Nick Edelen and Luis Atzin Franco Reyna
arXiv (Feb 2026)
11) On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes
Joint with Spencer Becker-Kahn and Neshan Wickramasekera
arXiv (Jul 2025)
10) Rectifiability of the Singular Set and Uniqueness of Tangent Cones for Semicalibrated Currents
Joint with Davide Parise, Anna Skorobogatova, and Luca Spolaor
arXiv (Sep 2024)
9) Fine Structure of Singularities in Area Minimizing Currents Mod(q)
Joint with Camillo De Lellis and Anna Skorobogatova
arXiv (Mar 2024)
8) Uniqueness of Regular Tangent Cones for Immersed Stable Hypersurfaces
Joint with Nick Edelen
arXiv (Jan 2024) | Archive for Rational Mechanics and Analysis (Nov 2024)
7) Stable Minimal Hypersurfaces in R^5
Joint with Otis Chodosh, Chao Li, and Douglas Stryker
arXiv (Jan 2024) | Annals of Mathematics (to appear)
6) The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and \H^{m-2}-a.e. Uniqueness of Tangent Cones
Joint with Camillo De Lellis and Anna Skorobogatova
arXiv (Apr 2023)
5) The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density Q + 1/2
arXiv (Oct 2022) | Calculus of Variations and Partial Differential Equations (Jan 2024)
4) Quantitative Estimates on the Singular Set of Minimal Hypersurfaces with Bounded Index
Joint with Nicolau Sarquis Aiex and Sean McCurdy
arXiv (Sep 2022) | Journal of Geometric Analysis (Oct 2024)
3) A Structure Theory for Stable Codimension 1 Integral Varifolds with Applications to Area Minimising Hypersurfaces mod p
Joint with Neshan Wickramasekera
arXiv (Nov 2021) | Journal of the AMS (Oct 2023) | Erratum (last updated: Jun 2025)
2) The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density 5/2
arXiv (Aug 2021) | Journal of Differential Geometry (Mar 2025)
1) A Campanato Regularity Theory for Multi-Valued Functions with Applications to Minimal Surface Regularity Theory
arXiv (Aug 2021) | Journal of Functional Analysis (Mar 2025)
Taught Courses
Regularity Techniques in Geometric Measure Theory
Princeton University, Spring 2024
A graduate learning course I created and taught in Princeton. See the “Teaching” page for more details.
Excess Decay and the Blow-Up Method
Geometric Measure Theory and Applications, UCL, 25–27 July, 2022.
My notes from the mini-course I taught at the workshop. (The above course “Regularity Techniques in GMT” is a much expanded version of this mini-course.)
Some Talks
Stationary Integral Varifolds near Multiplicity 2 Planes
SLMath, Nov 2024
Video Link
An Overview of Geometric Measure Theory, Area Minimising Currents, and Recent Work
IAS Members Colloquium, Apr 2024
YouTube
Singularities in Minimal Submanifolds — this is a short introduction to some aspects of my work
IAS Short Talks by Postdoctoral Members, Oct 2023
YouTube
Quantitative Estimates on Minimal Hypersurface Singular Sets
NCTS Differential Geometry Seminar, Nov 2022
Slides
Branched Regularity Theorems for Stable Minimal Hypersurfaces Near Classical Cones of Density Q+1/2
IAS Analysis & Mathematical Physics Seminar, Nov 2022
YouTube
A Structure Theory for Branched Stable Hypersurfaces
NCTS International Geometric Measure Theory Seminar, Jan 2022
Slides
Compactness 