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. Download my thesis below:

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: