Dissertation Topics Titles 2021-22
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
Homotopy Type Theory - Prof K Kremnitzer
Integrated Information Theory - Prof K Kremnitzer
Enumerating finite groups - Prof N Nikolov
Hyperquiver Representations - Prof V Nanda
Analysis
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
Geometry, Number Theory and Topology
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
Logic
Topics in O-minimality - Prof J Pila
Mathematical Methods and Applications
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
Mathematical Physics
The classification of 2d conformal field theories - Prof A Henriques
Scattering Theory - Prof L Mason
Numerical Analysis and Data Science
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
Stochastics, Discrete Mathematics and Information
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
History of Mathematics
Students wishing to do a dissertation based on the History of Mathematics are asked to contact Brigitte Stenhouse 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 Brigitte Stenhouse 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.
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