Dissertation Topics Titles 2022-23
Mathematical Institute
Please note the following topics are only open to Part C Maths, Maths & Phil, Maths & CompSci and OMMS students. For current students please see the full proposals here.
Algebra
Representations of finite Hecke algebras - Prof D Ciubotaru
Conservation Laws of Chemical Reaction Networks - Dr H Rahkooy and Prof H Harrington
Applications of Syzygies in Biochemical Networks - Dr H Rahkooy and Prof H Harrington
Algebraic Methods for Maximum Likelihood Estimation - Dr J Coons
Homotopy Type Theory - Prof Y Kremnitzer
Mathematical Consciousness Science - Prof Y Kremnitzer
Equations in finite groups and probability - Prof N Nikolov
Analysis
Penrose’s impulsive gravitational waves, Lorentzian synthetic spaces and optimal transport - Prof A Mondino
Optimal transport theory applied to PDEs - Dr A Esposito
Convolution equations and mean-periodicity - Prof J Kristensen
On the regularity for elliptic equations and systems - Prof L Nguyen
Cauchy Problems in General Relativity - Prof Q Wang
C*-Algebras - Prof S White
Geometry, Number Theory and Topology
Applications of Topological Data Analysis in Physical Oceanography - Dr A Brown and Prof H Harrington
Number of solutions to equations over finite fields - Prof A Lauder
Modular Forms and Elliptic Curve - Dr A Horawa
The Manin-Mumford conjecture - Prof D Rossler
The Chebotarev density theorem and its effective versions - Prof E Breuillard
Topological data analysis of CODEX multiplexed images in colorectal cancer - Dr I Yoon, Prof H Harrington and Prof H Byrne
The Twin Prime Conjecture - Prof J Maynard
Iwasawa Theory - Prof J Newton
Almost-periodicity in additive number theory - Dr T Bloom
Local Fields and the Hasse Principle - Prof V Flynn
Logic
Ramsey theories - Prof E Hrushovski
Kim Indepdence - Prof E Hrushovski
Mathematical Methods and Applications
Untangling Knots Through Curve Repulsion - Dr R Bailo
Algebraic Topology and Machine Learning for Modelling Flow in Porous Media - Dr A Yim
Droplets on lubricated solid surfaces - Prof D Vella
Pattern formation and travelling waves in heterogeneous populations using aggregation-diffusion equations - Dr D Martinson
Modelling solid-body tides - Dr H Hay and Prof I Hewitt
Evolution of thin liquid films - Prof J Oliver
How directed are directed networks - Prof R Lambiotte
Mathematical Physics
The Classification of 2D Conformal Field Theories - Prof A Henriques
Formation of Planetary Rings - A Granular Gas Approach - Dr R Bailo
Numerical Analysis and Data Science
Machine Learning and Artificial Intelligence in Healthcare - Dr A Kormilitzin
AAA Rational Approximation - Prof N Trefethen
Flood prediction using machine learning - Dr Y Sun
Topics in Randomised Numerical Linear Algebra - Prof Y Nakatsukasa
Stochastics, Discrete Mathematics and Information
String graphs - Prof A Scott
Categorical Approaches to Probability - Dr D Lee
From algorithmic learning in a random world to algorithmic learning - Prof H Oberhauser
Black-Scholes versus stochastic volatility models as hedging tools - Prof M Monoyios
Wasserstein Space of Measures and Distributionally Robust Optimization - Prof J Obloj
History of Mathematics
Students wishing to do a dissertation based on the History of Mathematics should contact Christopher Hollings at @email by Wednesday of week 1 with a short draft proposal. All decisions will be communicated to students by the end of week 2.
All supported proposals , will then be referred to Projects Committee who meet in week 4 for final approval. With the support of Dr Hollings students must submit a COD Dissertation Proposal Form to Projects Committee by the end of week 3.
Department of Statistics
Please note that Part C Mathematics and Statistics students MUST select from the list of the below topics. OMMS students are also able to select the Statistics and Probability projects from the Department of Statistics.
It may be possible for a Maths student to complete a Statistics dissertation, however, the priority when allocating will be the Maths & Stats and OMMS students. If you are interested, please email @email for more information.
An alternative to the log-likelihood for clustering - Dr G Mena
Applications of Machine Learning to Drug Discovery - Prof G M Morris
Bayesian analysis of rank data - Prof G Nicholls
Brownian bees - branching and selection - Prof J Berestycki
Epidemiology models with contract tracing - Prof J Berestycki and Dr F Foutel-Rodier
Kinetic Monte Carlo simulation models of molecular scaffold assembly - Dr D Nissley
Knowledge (Self) distillation in machine learning - Prof F Caron
Limit order book and fundamentals-driven embeddings of financial instruments for portfolio selection - Prof M Cucuringu
Multiple testing and hypothesis aggregation - Prof D Steinsaltz
Parking functions, trees, and parking on trees - Prof C Goldschmidt
Partially Stochastic Networks - Dr T Rainforth
Probability and Statistics for Genetics - Prof R Davies
Proximal Causal Inference - Prof R Evans
Separation results for methods based on implicit regularization - Prof P Rebeschini
Two Sample Mendelian Randomisation - Prof F Windmeijer
Understanding COVID-19 in New York State schools in the 2020-23 and 2021-22 school years - Prof C Donnelly
Upper and Lower Bounds on the Probability of Finite Union of Events - Dr J Yang