PhD Student, DPMMS, Cambridge
Welcome! I am a PhD student in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge. My research is focused on problems within geometric analysis and geometric measure theory, with a particular focus on regularity questions concerning minimal submanifolds. My PhD supervisor is Professor Neshan Wickramasekera.
Workshop: Geometric Measure Theory and Applications, at UCL organised by Costante Bellettini and Neshan Wickramasekera, 25 – 27 July, 2022
Summaries of my research works can be found under the “Research” tab above. Here is a copy of my PhD thesis.
- A Structure Theory for Stable Codimension 1 Integral Varifolds with Applications to Area Minimising Hypersurfaces mod p, Nov 2021 (joint with N. Wickramasekera) (https://arxiv.org/abs/2111.11202)
- The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density 5/2, Aug 2021 (https://arxiv.org/abs/2108.02614)
- A Campanato Regularity Theory for Multi-Valued Functions with Applications to Minimal Surface Regularity Theory, Aug 2021 (https://arxiv.org/abs/2108.03085)
See also Geometric Analysis References for a list of references in Geometric Analysis.
I have taught (supervised/examples classes/office hours) undergraduates and master’s students in:
- (First Year) Vectors & Matrices; Probability; Analysis I;
- (Second Year) Analysis II; Analysis & Topology;
- (Third Year) Analysis of Functions; Differential Geometry;
- (Fourth Year/Part III) Distribution Theory; Elliptic PDEs; Geometric Measure Theory; Differential Geometry.
This website serves numerous purposes, such as being a place to discuss my research and to give advice and resources I wish I had at the relevant time in my life. I hope some will find these useful. Any feedback is appreciated; I am happy to be contacted about any of the content on this website.
If you are interested in lecture notes, see the `Lecture Notes’ menu tab (or simply click here).