Dissertation Topics 2019-20

Mathematical Institute

Please note the following topics are only open to Part C Maths, Maths & Phil, Maths & CompSci and OMMS students. You should be able to access any of the undergraduate courses referenced under the pre-requisites by clicking on the unit name. You will also be able to access the courses at https://courses.maths.ox.ac.uk/overview/undergraduate.

Logic

PDF icon 'Aspects of Stone duality for Boolean algebras' - Prof. Hilary Priestley

PDF icon 'Satisfiability algorithms for guarded logics' - Prof. Michael Benedikt

PDF icon 'The Scott Topology' - Prof. Hilary Priestley

 

Algebra

PDF icon 'Crystal graphs and the representation theory of the symmetric group' - Prof. Kevin McGerty

PDF icon 'D-modules' - Clemens Koppensteiner

PDF icon 'Derived Categories and Koszul Duality' - Dr Jack Kelly

PDF icon 'Profinite Groups' - Prof. Nikolay Nikolov

PDF icon 'Spherical Buildings for Classical Groups'- Dr Marcelo De Martino

 

Geometry

PDF icon 'Graded rings and projective varieties' - Prof. Balazs Szendroi

PDF icon 'Grothendieck ring of varieties' - Dr Martin Gallauer

PDF icon 'Hodge Theory' - Prof. Damian Rössler

PDF icon 'Spinors and Dirac operators' - Dr Markus Upmeier

PDF icon 'Weighted projective spaces and sheaves thereon' - Dr Adam Gyenge

 

Number Theory

PDF icon 'Additive combinatorics over finite fields' - Prof. Ben Green

PDF icon 'Berkovich spaces' - Dr Federico Bambozzi

PDF icon 'Complex multiplication' - Dr Netan Dogra

PDF icon 'Goldbach's Conjecture' - Prof. James Maynard

PDF icon 'Number Theory and Random Matrices' - Prof. Jon Keating

PDF icon 'Number of solutions to equations over finite fields' - Prof. Alan Lauder

PDF icon 'Torsion points on curves' - Dr Netan Dogra

 

Topology and Algebra

PDF icon 'Generalised Character Theory' - Dr Lukas Brantner

PDF icon Modular tensor categories - Dr Andre Henriques

PDF icon 'Random Groups' - Dr David Hume

 

Analysis

PDF icon 'Application of the conformal method in the hyperbolic PDE' - Prof. Qian Wang

PDF icon 'C*-algebras' - Prof. Stuart White

PDF icon 'Coefficient problems for univalent maps' - Prof. Dmitry Belyaev

PDF icon 'Geometric variational problems' - Prof. Melanie Rupflin

PDF icon 'Hausdorff dimension, fractals and multifractals' - Prof. Dmitry Belyaev

PDF icon 'Homogenization of partial differential equations' - Dr Benjamin Fehrman

PDF icon 'Loewner and Schramm-Loewner Evolution' - Prof. Dmitry Belyaev

PDF icon 'Mean value in equalities for second ordered elliptic equations' - Prof. Luc Nguyen

PDF icon 'Spectral approximation of strain-limiting nonlinear elastic models' - Prof. Endre Süli

PDF icon 'Study of the Strichartz estimates for wave equations' - Prof. Qian Wang

 

Mathematical Methods and Applications

PDF icon 'Elastocapillarity: Dynamics and Statics' - Prof. Dominic Vella

PDF icon 'Maslow’s hammers to investigate pattern formation' - Dr Priya Subramanian

PDF icon 'Mathematical Modelling of Filtration' - Dr Ian Griffiths

PDF icon 'Mathematical modelling of food blenders' - Dr Ian Griffiths and Prof. Colin Please

PDF icon 'Mathematical modelling of hydrogels' - Dr Matthew Hennessy 

PDF icon 'Mathematical modelling of tumour angiogenesis' - Prof. Helen Byrne and Prof. Philip Maini

PDF icon 'Mathematics at the nanoscale: moving beyond Fourier's law of conduction' - Dr Matthew Hennessy

PDF icon 'Modelling Collective Cell Motion' - Prof. Ruth Baker and Prof. Philip Maini

PDF icon 'Multi-scale dynamics of surface quasi-geostrophic flows' - Dr Vassilios Dallas

PDF icon 'Network science measures of data describing spatial network models' - Dr Heather Harrington and Bernadette Stolz

PDF icon 'Nonlinear Dynamics in Population Ecology' - Dr Andrew Krause

PDF icon 'Non-linear dynamics on networks' - Dr Renaud Lambiotte

PDF icon 'Reversals of zonal jets in 2D turbulence' - Dr Vassilios Dallas

PDF icon 'The effect of population heterogeneity on the risk of an infectious disease epidemic' - Dr Robin Thompson and William Hart

PDF icon 'Transition to turbulence scenario in pipe flows' - Dr Vassilios Dallas

 

Numerical Analysis

PDF icon 'Approximation of functions by composite polynomials' - Prof. Yuji Nakatsukasa

PDF icon 'Complexity of Optimization Problems' - Prof. Coralia Cartis

PDF icon 'Efficient Exemplar selection for Representation Learning' - Dr Vinayak Abrol

PDF icon 'Multilevel Radial Basis Function Approximation of PDEs' - Dr Kathryn Gillow

PDF icon 'Numerical algorithms related to Chebfun' - Prof Nick Trefethen

PDF icon 'Numerical computation with rational functions' - Prof Nick Trefethen

PDF icon 'Tensor and matrix eigenvalue perturbation theory' - Prof. Yuji Nakatsukasa

 

Mathematical Physics

PDF icon 'Numerical analysis of conformal field theories' - Prof. Christopher Beem

PDF icon 'Scattering Theory' - Prof. Lionel Mason

 

Stochastics, Discrete Mathematics and Information 

PDF icon 'Diffusion on fractals' - Prof. Ben Hambly 

PDF icon 'Discrete mathematics for the modern world' - Dr Ebrahim Patel

PDF icon 'Homogenization of partial differential equations' - Dr Benjamin Fehrman

PDF icon 'Particle systems and Stefan problems' - Prof. Ben Hambly

PDF icon 'String graphs' - Prof. Alex Scott

 

History of Mathematics

Students interested in taking a history of mathematics dissertation can find further information about the application process here.

 

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 acadadmin@maths.ox.ac.uk for more information.

 

PDF icon 'Applications of Machine Learning to Drug Discovery' - Prof. Garrett Morris

PDF icon 'Casual Mediation' - Prof. Robin Evans

PDF icon 'Evaluation of outbreak detection algorithms' - Prof. Christl Donnelly

PDF icon 'How long does it take to shuffle a deck of cards?' - Dr Alessandra Caraceni

PDF icon 'Implicit Bias of Learning Algorithms' - Prof. Patrick Rebeschini

PDF icon 'Levy Processes' - Prof. Matthias Winkel

PDF icon 'Linkage disequilibrium in genomic data: models and inference' - Prof. Pier Palamara

PDF icon 'Load balancing in queueing networks' - Prof. James Martin

PDF icon 'Local convergence of random graphs' - Dr Robin Stephenson

PDF icon 'New approaches to Approximate Bayesian Computation New Markov Chain Monte Carlo methods' - Prof. Geoff Nicholls 

PDF icon 'Optimization and generalization of deep neural networks' - Prof. George Deligiannidis

PDF icon 'Products of random matrices and population ecology' - Prof. David Steinsaltz 

PDF icon 'Quasi-Stationary distributions and selection principle' - Prof. Julien Berestycki

PDF icon 'Random graphs and the multiplicative coalescent' - Dr Dominic Yeo

PDF icon 'Ruin probabilities in a network of insurance agents and objects' - Prof. Gesine Reinert

PDF icon 'Statistics of Ramachandran Plots' - Prof. Jotun Hein

PDF icon Time series embeddings via graph neural networks - Prof. Mihai Cucuringu