Previous Dissertations

The Virasoro Algebra - Prof A Henriques 

Symmetric Tensor Rank - Dr A Seigal and Prof J Tanner

D-modules and the Beilinson-Bernstein localisation - Dr C Koppensteiner 

Construction of Non-Liftable Varieties in Positive Characteristic - Prof D Roessler

Representation theory of quivers - Dr F Haiden

Representation type of finite-dimensional algebras - Prof K  Erdmann

Homotopy Type Theory - Prof K Kremnizer

Relative Algebraic Geometry - Prof K Kremnizer

Crystal graphs and the representation theory of the symmetric group - Prof K McGerty

Generalised Character Theory - Dr L Brantner

Derived deformation rings - Dr L: Brantner

Representations of finite Hecke algebras - Prof D Ciubotaru

Homotopy Type Theory - Prof K Kremnitzer

Integrated Information Theory - Prof K Kremnitzer

Enumerating finite groups - Prof N Nikolov

Hyperquiver Representations - Prof V Nanda

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

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

The Virasoro algebra - Prof A Henriques

 Nilpotent orbits in semisimple Lie algebras - Prof D Ciubotaru

 Homotopy Type Theory - Prof K Kremnitzer

 Mathematical Consciousness Science - Prof K Kremnitzer

 Profinite groups - Prof N Nikolov

 Quiver representation theory - Dr S Lewis

Homogenization of partial differential equations - Dr B Fehrman

Mean value inequalities for second order elliptic equations - Prof L Nguyen

Operator spaces and completely bounded- Prof S White

von Neumann Algebras - Prof S White

Application of the conformal method in the hyperbolic PDE - Prof Q Wang

Hausdorff dimension, fractals and multifractals - Prof D Belyaev

Minimal surfaces - Prof M Rupflin

Non-local PDEs and fractional Sobolev - Dr D Gomez-Castro

Fundamental solutions of linear partial differential equations - Prof J Kristensen

Extensions of Lipschitz maps, type and cotype - Dr K Ciosmak

Multi-dimensional Monge-Kantorovick system of PDE's - Dr K Ciosmak

von Neumann Algebras - Prof S White

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

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

Stochastic mean-field derivations of partial differential equations -Dr A Holzinger

 CStar-Algebras - Dr A Seth

 Gradient flowss approach to PDEs and statistics - Dr J Skrzeczkowski

 On the regularity and partial regularity for elliptic systems - Prof L Nguyen

 Geometric inequalites in the Heisenberg group - Dr M Magnabosco

 Harmonic maps into the sphere - Prof M Rupflin

Ribbon knotoids - Agnese Barbensi and Prof U Tillmann

Persistent homology of knotted proteins - Dr A Barbensi, Prof H Harrington and Prof U Tillmann

Explicit Coleman Integration and its Application - Prof A Lauder

Prime Numbers in Residue Classes - Prof B Green

Symplectic Topology - Dr F Haiden

Poisson Geometry and Symplectic Groupoids - Dr F Bischoff

The Riemann Hypothesis- Prof J Maynard

Geometry and Topology of Black Holes - Prof J Lotay

Twisted topological K-theory - Dr M Upmeier

Local Fields and the Hasse Principle - Prof V Flynn

Graded rings and projective varieties - Dr B Szendroi

Milnor—Wood inequality - Prof A Dancer

Algebraic fundamental group - Dr M Gallauer

Asymptotic dimension and boundaries of hyperbolic groups - Prof P Papazoglou

Modular Forms - Prof A Lauder

Graded rings and projective varieties - Prof B Szendroi

The Hardy-Littlewood Method - Prof B Green

Divergence of finitely generated groups - Dr B Sun

Geometric Class Field Theory - Prof D Rossler

The Semistable Reduction Theorem for Curves over Function Fields - Prof D Rossler

Poisson geometry and symplectic groupoids - Dr F Bischoff

Sieve Methods - Prof J Maynard

Galois Representation - Dr J Newton

Hodge Theory, Morse Theory and Supersymmetry - Prof J Lotay

Number Theory and Random Matrices - Prof J Keating

HKR Character Theory - Dr L Brantner

A bound for the systole of an aspherical manifold - Prof P Papazoglou

Analysis of Boolean Functions - Prof T Sanders

Chabauty techniques in Number Theory - Prof V Flynn

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

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

Explicit Coleman integration and its applications - Prof A Lauder

 Symplectic Geometry and Quantisation - Prof A Dancer

 Euler systems - Dr A Graham

 Higher-order Fourier analysis - Prof B Green

 Computable Topology - Prof C Douglas

 Construction of non-liftable varieties in positive characteristic - Prof D Rossler

 CAT(0) cube complexes - Dr D Spriano

 Kahler manifolds and Kahler geometry - Prof D Joyce

 Infinity categories - Prof D Joyce

 Galois representations and L-functions - Prof J Newton

 Einstein Manifolds - Prof J D Lotay

 Applications of automorphic forms in ANT - Dr Grimmelt and  Dr J Merikoski

 Distribution of values of the Riemann zeta function - Prof LP Arguin

 Serre-Tate Theory - Dr L Brantner

 Automorphisms of free groups - Dr N Andrew

 The Hardy-Littlewood method - Prof T Sanders

 Chabauty techniques in Number Theory - Prof V Flynn

Ramsey theories - Prof E Hrushovski

Kim Indepdence - Prof E Hrushovski

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

Geometric stability - Prof E Hrushovski

 Continuous Model Theory - Dr J Pi

 Pseudofinite Fields - Prof J Koenigsmann

 Definability of types for stable and NIP formulas - Prof M Bays

 Descriptive set theory and measurable paradoxes - Dr M Bowen

Traveling wave solutions for the thin film - Prof A Muench

Advanced machine learning methods for drug discovery for Alzheimer’s disease - Dr A Kormilitzin and Dr N Buckley

Geometry and mechanics of seashells - Prof D Moulton

Modelling the formation of laccoliths - Prof I Hewitt

Modelling of ice shelves - Prof I Hewitt and Dr M McPhail

Mathematical modelling of hydrogels - Dr M Hennessy

Dynamics on hypergraphs - Prof R Lambiotte

Mathematics at the nanoscale: moving beyond Fourier law of conduction - Dr M Hennessy

Tensor and matrix eigenvalue perturbation theory - Prof Y Nakatsukasa

Mathematical Modelling of Plant - Prof D Moulton

Magneto-active elastic objects - Combining magnetism with elasticity - 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 geothermal boreholes using pertubation methods - Prof I Hewitt

Viscoplastic models for geophysical flows - Prof I Hewitt

The time-elapsed model for neural networks - D P Roux

Dynamics on signed networks - Prof R Lambiotte

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 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

Modelling aspects of cellular signalling beyond the simplest Turing mechanism -Prof E Gaffney

 Snap-through of elastic structures - Prof D Vella

 Modelling of ground-source heating - Prof I Hewitt

 Hilbert's 16th problem and its algebraic and chemical variants - Prof R Erban

 All-atom molecular dynamics and coarse-grained simulations of biomolecules - Prof R Erban

 Modelling networks with complex weights - Prof R Lambiotte

 Random graphs and multibody interactions - Prof R Lambiotte

Quantum circuit optimisation with the ZX-calculus - Prof A Kissinger

Deformation Quantisation - Prof C Beem

Kontsevich Deformation Quantization - Dr E Panzer

The classification of 2d conformal field theories - Prof A Henriques

Scattering Theory - Prof L Mason

The Classification of 2D Conformal Field Theories - Prof A Henriques

Formation of Planetary Rings - A Granular Gas Approach - Dr R Bailo

 The Virasoro algebra - Prof A Henriques

 Equivariant localization and AdS4 solutions in supergravity - Dr C Couzens

 Landau singularities - Dr F Tellander

 Variations of Dyson-Schwinger equations - Dr P Balduf

 Symmetries and tensor networks - Dr N Jones

 Carrollian Structure of Scattering Amplitudes - Dr R Ruzziconi

 3d N=4 Quiver gauge theories - Dr Z Zhong

Complexity of Optimization Problems - Prof C Cartis 

Compressed sensing, matrix completion, and related low complexity sampling models - Prof J Tanner

Approximation of functions in a square, cube, and hypercube - Prof N Trefethen

C ∞ but nowhere analytic functions - Prof N Trefethen

Eigenvalue avoided crossings - Prof N Trefethen

Lightning PDE solvers - Prof N Trefethen

Numerical conformal mapping - Prof N Trefethen

Pseudospectra of random matrices - Prof N Trefethen

Solving ODEs in Chebfun - Prof N Trefethen

The field of values and Crouzeix’s conjecture - Prof N Trefethen

Machine Learning and Artificial Intelligence In Healthcare - Dr A Kormilitzin

Approximation of functions in a square, cube, and hypercube - Prof N Trefethen

Lightning Helmholtz solver - Prof N Trefethen

Numerical conformal mapping - Prof N Trefethen

Development and Calibration of Models for Pedestrian Dynamics - Dr R Bailo

Numerical Schemes for Crystal Growth - Dr R Bailo

(Randomised) Numerical Linear Algebra - Prof Y Nakatsukasa

Characterizing the structure of networks with discrete Ricci curvature - Dr M Weber

Optimization algorithms for data science - Prof C Cartis

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

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

 Anderson Acceleration Algorithms for Nonlinear Systems and Optimization Problems - Prof C Cartis

 Structure preserving operator learning - Dr G Maierhofer

 Numerical Solution of Problems in Electrochemistry - Dr K Gillow

 Analysis and Algorithms in Randomised Numerical Linear Algebra - Prof Y Nakatsukasa

Random fractals and branching processes - Prof B Hambly

Proposal - Spin glass theory and its applications - Dr M D Wong

Convergence of finite Markov chains on abelian groups- Prof Z Qian

Heat kernel estimates for second order parabolic equations- Prof Z Qian

Probability concentration inequalities - Prof Z Qian

Integrated Information Theory - Prof K Kremnitzer

Random walk in random environment - Prof B Hambly

Blockchains and (Decentralized) Exchanges - Prof H Oberhauser

Bismut formula, Feynman-Kac formula and estimates for second order parabolic equations - Prof Z Qian

Convergence of finite Markov chains on abelian groups - Prof Z Qian

PDF method in turbulence - Prof Z Qian

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

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

 String graphs - Prof A Scott

 Brownian motion and fractals - Prof B Hambly

 AI Alignment and Mechanistic Interpretability - Prof H Oberhauser

 Entropic Optimal Transport structural properties, convergence and beyond - Prof J Obloj

 The Ramsey property in random graphs - Dr R Hancock

 The duality of conditional diffusion processes - Prof Z Qian

 Random vortex method – 2D viscous incompressible flows - Prof Z Qian

 Signatures in technical analysis of financial data - Prof Z Qian

Applications of Machine Learning to Drug Discovery - Prof G Morris

Contrastive Learning and new computational tools for Bayesian inference - Prof G Nicholls

Edge-exchangeable random graph models - Prof F Caron

Estimating exponential random graph models - Prof G Reinert

Generating random trees - Dr A Caraceni

Identification and estimation of causal effects using instrumental variables - Prof F Windmeijer

Levy processes - Prof M Winkel

Miracles and Applications of Mirror Descent - Prof P Rebeschini

Random recursive trees - Prof C Goldschmidt

Recombination in Covid-19 - Jotun Hein

Some Martingales associated to Branching random walks - Prof K Berestycki

Stable Matchings - Prof J Martin

The critical window for random graphs - Dr D Yeo

Random graphs and the multiplicative coalescent - Dr D Yeo

Time series prediction and classification via generative adversarial networks - Prof M Cucuringu

Understanding the link between mobility and SARS-CoV-2 transmission - Prof C Donnelly

X in Algebraic Statistics (where X is the actual topic selected) - Prof R Evans

Stochastic models and statistical analysis of the human sex ratio at birth - Prof D Steinsaltz

A novel deconvolution method based on entropic optimal transport - Dr G Mena

Applications of Machine Learning to Drug Discovery - Prof G Morris

Bayesian Optimal Experimental Design - Dr T Rainforth

Co-jumping behaviour in time series and financial networks - Prof M Cucuringu

Concentration inequalities and applications - Prof G Deligiannidis

Convergence Complexity for Markov Chain Monte Carlo in High Dimensions - Dr J Yang

Extreme Classification - Prof F Carron

Genealogies of Sequences experiencing Recombination - Prof J Hein

 How many have died due to the COVID-19 pandemic and who was at greatest risk - Prof C Donnelly

Instrumental Variable Estimation with Weak Instruments - Prof F Windmeijer

Kernel-based tests and dependence measures - Prof D Sejdinovic

Mirror Descent and Statistical Robustness - Prof P Rebeschini

Multi-Locus Phase-type Distributions in Population Genetics - Dr A Biddanda

Polygenic scores - Prof R Davies

Protein folding interfaces template the formation of the native state - Dr D Nissley

Quasistationary distributions for Markov processes - Prof D Steinsaltz

Random Recursive Trees - Prof C Goldschmidt

Urn models and applications - Prof M Winkel

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

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

 Selective inference - Dr R Lewis

 Selective Inference and its application - Dr O Crook

 Separation results for methods based on implicit regularization - Prof P Rebeschini

 Theoretical properties of denoising diffusion models - Dr G Deligiannidis

 Topics in Computational Biology - Prof J Hein

 Urn models and applications - Prof M Winkel

 BBM and beta genealogies

 Categorical probability and statistics - Prof R  Cornish

 Genealogival threading of ancient and modern DNA and age estimation for ancient DNA samples - Prof S Myers

 Inference for the (conditional) average treatment effect - Prof R Evans

 Instrumental Variable Estimation with Weak Instruments - Prof F Windmeijer

 New models for analysis of rank data - Prof G Nicholls

 Randomisation strategies for multiple testing and post-selection inference - Prof D Steinsaltz

Understanding the link between mobility, wastewater and SARS-CoV-2 transmission - Prof C Donnelly

 Applications of Machine Learning to Drug Discovery - Prof G M Morris