Dissertation Topics Titles 2020-21
Mathematical Institute
For current students please see the full proposals here.
Algebra
The Virasoro Algebra - Andre Henriques
Symmetric Tensor Rank - Anna Seigal and Jared Tanner
D-modules and the Beilinson-Bernstein localisation - Clemens Koppensteiner
Construction of Non-Liftable Varieties in Positive Characteristic - Damian Roessler
Representation theory of quivers - Fabian Haiden
Representation type of finite-dimensional algebras - Karin Erdmann
Homotopy Type Theory - Kobi Kremnizer
Relative Algebraic Geometry - Kobi Kremnizer
Crystal graphs and the representation theory of the symmetric group - Kevin McGerty
Generalised Character Theory - Lukas Brantner
Derived deformation rings - Lukas Brantner
Analysis
Homogenization of partial differential equations - Benjamin Fehrman
Mean value inequalities for second order elliptic equations - Luc Nguyen
Operator spaces and completely bounded- Stuart White
von Neumann Algebras - Stuart White
Application of the conformal method in the hyperbolic PDE - Qian Wang
Hausdorff dimension, fractals and multifractals - Dmitry Belyaev
Minimal surfaces - Melanie Rupflin
Geometry, Number Theory and Topology
Ribbon knotoids - Agnese Barbensi and Ulrike Tillmann
Persistent homology of knotted proteins - Agnese Barbensi, Heather Harrington and Ulrike Tillmann
Explicit Coleman Integration and its Application - Alan Lauder
Prime Numbers in Residue Classes - Ben Green
Symplectic Topology - Fabian Haiden
Poisson Geometry and Symplectic Groupoids - Francis Bischoff
The Riemann Hypothesis- James Maynard
Geometry and Topology of Black Holes - Jason Lotay
Twisted topological K-theory - Markus Upmeier
Local Fields and the Hasse Principle - Victor Flynn
Graded rings and projective varieties - Balasz Szendroi
Milnor—Wood inequality - Andrew Dancer
Algebraic fundamental group - Martin Gallauer
Asymptotic dimension and boundaries of hyperbolic groups - Panos Papazoglou
Logic
Satisfiability algorithms for guarded logics - Michael Benedikt
Mathematical Methods and Applications
Traveling wave solutions for the thin film - Andreas Muench
Advanced machine learning methods for drug discovery for Alzheimer’s disease - Andrey Kormilitzin and Noel Buckley
Geometry and mechanics of seashells - Derek Moulton
Modelling the formation of laccoliths - Ian Hewitt
Modelling of ice shelves - Ian Hewitt and MIchael McPhail
Mathematical modelling of hydrogels - Matthew Hennessy
Dynamics on hypergraphs - Renaud Lambiotte
Mathematics at the nanoscale: moving beyond Fourier law of conduction - Matthew Hennessy
Tensor and matrix eigenvalue perturbation theory - Yuji Nakatsukasa
Mathematical Physics
Quantum circuit optimisation with the ZX-calculus - Aleks Kissinger
Deformation Quantisation - Christopher Beem
Kontsevich Deformation Quantization - Erik Panzer
Numerical Analysis and Data Science
Complexity of Optimization Problems - Coralia Cartis
Compressed sensing, matrix completion, and related low complexity sampling models - Jared Tanner
Approximation of functions in a square, cube, and hypercube - Nick Trefethen
C ∞ but nowhere analytic functions - Nick Trefethen
Eigenvalue avoided crossings - Nick Trefethen
Lightning PDE solvers - Nick Trefethen
Numerical conformal mapping - Nick Trefethen
Pseudospectra of random matrices - Nick Trefethen
Solving ODEs in Chebfun - Nick Trefethen
The field of values and Crouzeix’s conjecture - Nick Trefethen
Stochastics, Discrete Mathematics and Information
Random fractals and branching processes - Ben Hambly
Proposal - Spin glass theory and its applications - Mo Dick Wong
Convergence of finite Markov chains on abelian groups- Zhongmin Qian
Heat kernel estimates for second order parabolic equations- Zhongmin Qian
Probability concentration inequalities - Zhongmin Qian
Integrated Information Theory - Kobi Kremnizer
History of Mathematics
Students interested in taking a history of mathematics dissertation can find further information about the application process here.
Department of Statistics
Applications of Machine Learning to Drug Discovery - Garrett M Morris
Contrastive Learning and new computational tools for Bayesian inference - Geoff Nicholls
Edge-exchangeable random graph models - Francois Caron
Estimating exponential random graph models - Gesine Reinert
Generating random trees - Alessandra Caraceni
Identification and estimation of causal effects using instrumental variables - Frank Windmeijer
Levy processes - Matthias Winkel
Miracles and Applications of Mirror Descent - Patrick Rebeschini
Random recursive trees - Christina Goldschmidt
Recombination in Covid-19 - Jotun Hein
Some Martingales associated to Branching random walks - Julien Berestycki
Stable Matchings - James Martin
The critical window for random graphs - Dominic Yeo
Random graphs and the multiplicative coalescent - Dominic Yeo
Time series prediction and classification via generative adversarial networks - Mihai Cucuringu
Understanding the link between mobility and SARS-CoV-2 transmission - Christl Donnelly
X in Algebraic Statistics (where X is the actual topic selected) - Robin Evans
Stochastic models and statistical analysis of the human sex ratio at birth - David Steinsaltz