Dissertation Topics Titles 2023-24
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
Algebraic Methods for Maximum Likelihood Estimation – Dr J Coons
Homotopy Type Theory – Prof Y Kremnitzer
Mathematical Consciousness Science – Prof Y Kremnitzer
D-modules – Prof K Ardakov
Reducibility hyperplanes for filtered quantizations of nilpotent co-adjoint orbits – Dr L Mason-Brown
Equations in finite groups and probability – Prof N Nikolov
Analysis
von Neumann algebras and Tomita-Takesaki theory – Prof A Henriques
Regularity Theory for the Kinetic Landau Equation – Dr I B Porat
Convolution equations and mean-periodicity – Prof J Kristensen
On the regularity and partial regularity for elliptic systems – Prof L Nguyen
Stability of geometric inequalities – Dr M Tiba
Harmonic maps into the sphere – Prof M Rupflin
CStar-Algebras – Prof S White
Nonlinear Fokker Planck Equations with Nonlocal Diffusions – Prof J Carrillo (please note that there is only 1 space available)
Geometry, Number Theory and Topology
Torsion of elliptic curves and abelian varieties – Dr A Horawa
Symplectic geometry and quantisation – Prof A Dancer
The Hardy-Littlewood Method – Prof B Green
Hodge Theory in positive characteristic - Prof D Rossler
Varieties which cannot be lifted to a field of characteristic - Prof D Rossler
Topics in Riemannian holonomy groups – Prof D Joyce
Interactions between Ergodic Theory and Number Theory – Prof E Breulliard
Injective metric spaces and Helly groups – Dr H Petyt
Goldbach's Conjecture – Prof J Maynard
Galois representations – Prof J Newton
The Positive Mass Theorem – Prof J Lotay
HKR Character Theory – Dr L Brantner
Serre-Tate Theory – Dr L Brantner
Automatic groups – Dr S Hughes
Analysis of Boolean Functions – Prof T Sanders
Logic
Model theory of valued fields – Dr J Ye
Model theory of ordered abelian groups – Prof J Koenigsmann
Taming Topological Properties – Dr R Suabedissen
Set-theoretic forcing – Prof E Hrushovski
Mathematical Methods and Applications
Mathematical modelling of the mechanics of sport – Prof D Moulton
Elastocapillarity - Dynamics and Statics – Prof D Vella
Modelling aspects of cells and Stokes flows in mathematical biology – Prof E Gaffney
Modelling aspects of cellular signalling beyond the simplest Turing mechanism – Prof E Gaffney
Modelling floating ice shelves – Prof I Hewitt
All-atom molecular dynamics and coarse-grained simulations of biomolecules – Prof R Erban
Hilbert's 16th problem, limit cycles and polynomial vector fields – Prof R Erban
Similarity and percolation on networks – Prof R Lambiotte
Branching process models for estimating the probability of a major infectious disease epidemic – Dr R Thompson and Dr W Hart
Numerical Analysis and Data Science
Machine Learning and Artificial Intelligence in Healthcare – Dr A Kormilitzin & Prof N Buckley
Optimization problems and algorithms – Prof C Cartis
Compressed sensing, matrix completion, and related low complexity sampling models – Prof J Tanner
Multilevel Radial Basis Function Approximation of PDEs – Dr K Gillow
Numerical Solution of Problems in Electrochemistry – Dr K Gillow
Topics in Randomised Numerical Linear Algebra – Prof Y Nakatsukasa
Stochastics, Discrete Mathematics and Information
String graphs – Prof A Scott
Probabilistic approaches to Stefan type problems – Prof B Hambly
New examples of rough paths in stochastic analysis and data science – Dr E Rossi Ferrucci
The Erdos-Kac Theorem and its Extensions – Prof L Arguin
Combinatorical applications of hypercontractivity – Prof P Keevash
Combinatorical applications of hypercontractivity – Prof P Keevash
Rough paths and anomalous streams in electrictiy data – Prof T Lyons
Conditional diffusion laws and random vortex method – Prof Z Qian
Simulations of turbulent flows via PDF method - Prof Z Qian
History of Mathematics
Supervised by Prof C Hollings.
Department of Statistics
Brownian bees: branching and selection – Prof J Berestycki
Knowledge (Self) distillation in machine learning – Prof F Caron
Bayesian modelling of change points – Dr O Crook
Statistical properties of Denoising Diffusion Models – Prof G Deligiannidis
How many have died due to the COVID-19 pandemic and who was at greatest risk? An analysis of excess deaths – Prof C Donnelly
Proximal Causal Inference – Prof R Evans
Epidemiology models with contract tracing – Dr F Foutel-Rodier
Corner Cutting in Statistical Alignment – Prof J Hein
Contagious sets in random networks – Dr B Kolesnik
Random Matching Models – Prof J Martin
Applications of Machine Learning to Drug Discovery – Prof G Morris
Bayes Methods for rank data arising in sporting competitions and social hierarchies – Prof G Nicholls
Statistical learning theory and algorithms – Prof P Rebeschini
Two Sample Mendelian Randomisation – Prof F Windmeijer