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

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