Expository Work and Research Experience
Expository Work and Research Experience
Research Experience
Master's Thesis, Imperial College London (November 2025 - September 2026)
Topic: XXX
Supervised by: Prof. G. Pavliotis and Dr. A. Menegaki.
Bachelor's Thesis, University of Bristol. (September 2024 - February 2025)
Topic: Perturbation Theory for Linear Operators
Thesis and associated Presentation Slides.
Supporting Text: Perturbation Theory for Linear Operators, by Tosio Kato.
Supervised by: Dr. Thomas Bothner.
LMS Undergraduate Summer School 2024, University of Essex. (July 2024)
Studied 6 mini courses and attended 8 colloquia in an intense 2-week period.
Mini Courses: (i) Continued Fractions and Integrable Systems. (ii) Knot Theory and Graph Theory. (iii) Interactive Theorem Proving and Filters. (iv) Algebraic Curves. (v) PDEs and Pattern Formation. (vi) Matrices and Machine Learning.
Notes from Colloquia. Topics include: Cryptography, Zeta Functions of Groups, Isoperimetric Inequalities, etc.
More information can be found here.
Polymath Junior, Online. (June - August 2024)
Title of Project: Toeplitz and Hankel Operators on Bergman Spaces
Areas of Exploration: (i) Lp Boundedness of Toeplitz Operators. (ii) Compact Toeplitz Operators, the Berezin Transform and the Axler-Zheng Theorem. (iii) Weak-type Regularity and the Bergman Projection. (iv) Endpoint Estimates for Hankel Operators.
Courses Studied (Fields Institute): (i) Operators on Function Spaces. (ii) Theory of Bergman Spaces. (iii) The Berezin Transform.
Supervised by: Dr. Zhenghui Huo (Duke-Kunshan), Dr. Nathan Wagner (Brown), Dr. Yunus Zeytuncu (Dearborn) and Dr. Adam Christopherson (OSU).
See mini-course/office hour/sketch notes here.
Mathematical Investigations Projects, University of Bristol. (September 2022 - May 2023)
Areas of Exploration: (ii) Ramanujan's Approximations of π. (Awarded 91.8%) (ii) Orthogonal Polynomials. (Awarded 81.6%)
Supervised by: Dr. Henna Koivusalo.
Additional Projects
On Knot Theory and Recursion, supervised by Dr. Andrew Donald (March 2024 - May 2024). (Awarded 81%)
Abstract: We aim to introduce knot theory using a variety of programming techniques, particularly employing recursion to develop algorithms on characteristics of arbitrary knots. We explore knot invariants, and write code to compute the d-invariant of a set of knots and links. Throughout, we run tests to deduce/test our hypotheses, such as periodic behaviour of 2-bridge links. Part of MATH20014: Mathematical Programming Coursework.