I completed my PhD in mathematics at Imperial College London in Spring 2024.
I worked in the intersection of probability theory, Riemannian and discrete geometry and graduated with thesis titled “Coarse Intrinsic and Extrinsic Curvature in Riemannian Geometry”.
Research
My second preprint, on the coarse extrinsic curvature of Riemannian submanifolds and point cloud approximations:
Coarse extrinsic curvature of Riemannian submanifolds
My first preprint, on the coarse Ricci curvature of weighted Riemannian manifolds and convergence of curvature of random geometric graphs:
Coarse Ricci curvature of weighted Riemannian manifolds
My Early Stage PhD report on coarse curvatures by optimal transport:
I wrote my MSci thesis titled Whitney Extension Theorem for Regularity Structures under the supervision of Prof Martin Hairer. The thesis dealt with extending the result of Whitney, 1934, which says that a smooth function defined on a closed subset of a Euclidean space can be smoothly extended and the extension operator is continuous. The thesis extended this result to modelled distributions in Hairer’s theory of regularity structures. See my master’s thesis below:
Projects
The projects below were part of the first year curriculum of my PhD course in the EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Algorithms. I joined the programme in its first cohort in September 2019.
An individual project on curvature of graphs, with applications to clustering and noisy graph alignment problems:
A joint project with my colleague Remy Messadene on stochastic simulation using the method of adaptive biasing force:
A joint project with my colleague Victoria Klein on a McKean-Vlasov stochastic differential equation with a self-exciting effect:
A joint project with my colleague Mateusz Mroczka on the neural tangent kernel (introduced by Jacot et al):
A small coursework on the application of signature of paths in linear regression:
A project on multi-frame image restoration by convex optimization I worked on during my research stay at UBC, British Columbia, Canada in 2017:
Teaching
Past teaching assistantships at Imperial College:
- Advanced Topics in Stochastic Analysis 2020/2021 (PhD course)
- Convex Optimization 2020/2021 and 2021/2022 (Masters course)
- Year 1 Mathematics Project: Martingales 2020/2021
- Differential Equations 2019/2020
- Measure Theory 2019/2020
- Real Analysis 2019/2020
- Statistics 2019/2020
- Year 1 Mathematics Project: Stochastic simulation 2019/2020
700+ hours of private tutoring experience: including probability theory, stochastic calculus, real analysis and topology.
Materials from past teaching:
A project I designed with Dr Andreas Søjmark for the course Convex Optimization. The project was on the topic of entropic regularization for the optimal transport problem: