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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: