# Research

Summer Research Projects 2017

Student Name |
Project Title |
Supervisor |

Letizia Angeli | Feynman-Kac models for large deviation conditioning problme | Stefan Grosskinskey |

Eleanor Archer | Resistance and Random Walks on loop trees | David Croydon |

Luke Hatcher | A phase field model for domain formation for small displacements of a spherical membrane | Charlie Elliott |

Philip Herbert | Small deformations of energy minimising biomembrances by adhesion to particles | Charlie Elliott |

Shannon Horrigan | Phase transition in Deleaunay Potts Models R2 with tile interactions | Stefan Adams |

Zak Lawrence | Spectral approximation of an Ab Initio Energy | Christoph Ortner |

Stephen Pidgeon | Large deviations for (1+1) dimensional Laplacian models | Stefan Adams |

Georgios Vasdekis | Non reversible Markov processes and zig-sag | Gareth Roberts |

Quirin Vogel | Surface tension of stochastic gradient models | Stefan Adams |

### Summer Research Projects 2016

Student Name |
Project Title |
Supervisor |

Georgios Andriopoulos | "Near" Local time continuity for G-W Trees | David Croydon |

Maciej Buze | Atomistic models for crystal defects | Christoph Ortner |

Lewis Church | Numerical approximation of a Stefan Problem on an evolving surface | Charlie Elliott |

Matthew Collins | Asymptotic methods for Phase Field Models | Andreas Dedner |

Matthew Dickson | Equivalence of Ensembles of Mean Field Boston Gases | Stefan Adams |

William Fitzgerald | The supermum of Dyson Brownian Motion | Jon Warren |

Matthew Galton | Central limit theorums for slowing fixing dynamical systems | Ian Melbourne |

John Herman | Stochastic Duality of Markov Processes with Applications | Vassili Kolokoltsov |

Katharina Hopf | Stable formation of singularity for a classial chemotaxis model | Jose Rodrigo |

Ifan Johnston | Psudo-differntial operators on bounded domains generating Markov processes | Vassili Kolokoltsov |

Kamil Kosiba | Oscillation and concentration pheomena in sequences of functions | Filip Rindler |

Barinder Matharu | Central limit theorems for the linear random walk on the torus | Ian Melbourne |

Jesse Pritchard | Preliminary parameter studies of Rayleigh-Benard convection | James Sprittles |

David Woodford | Lamperti transforms fo self similar Markov process | Larbi Alili |

### Summer Research Projects 2015

Student Name |
Project Title |
Supervisor |

Theodoris Assiotis |
Orthogonal Polynomials, Non Colliding Diffusions and Extended Kernels | Neil O'Connell |

Neil Chada | Reduced Basis-EnKF Method for Inverse Problems | Andrew Stuart |

Lloyd Connellan | Transparent Boundary conditins applied to Atmospheric problems | Andreas Dedner |

Adam Nix | Mathematical Computation in Cell Biology | Charles Elliott |

Wojciech Ozanski | Monge-Ampere equation and the 2D Navier Stokes equations | James Robinson |

Pavlos Tsatsoulis | Solutions to the Stochastic Quantisation Equatiions | Hendrik Weber |

Curtis Wilson | Decay Estimates for Minimiser of Lattice Energy of Multilattices with Point Defects | Christoph Ortner |

### Summer Research Projects 2014

## Student Name |
## Project Title |
## Supervisor |

Adam Bowditch | Biased Random Walks on subcritical Galton-Watson Trees Conditioned to Survive | David Croydon |

Qiaochu Chen | Particle Filtering and Parameter Inference for the CIR Model | Gareth Roberts |

Oliver Dunbar | Knot energies in the numerical detection and prevention of self-intersecting moving membranes | Bjorn Sinner |

Jake Dunn | Stability Problems in AdS Spacetimes | Mario Micallef/ Claude Warnick |

Matthew Egginton | Solutions of the Boltzmann Equation corresponding to an Invariant Manifold of Molecular Dynamics | Florian Theil |

Rodolfo Gameros Leal | Traffic in Poissonian Line Networks | Wilfrid Kendall |

Yulong Lu | A Bayesian Level Set Method for Geometric Inverse Problems | Andrew Stuart |

Jamie Lukins | On the Asymptotic Density of an Infinite System of Coalescing Random Walks | Roger Tribe |

Annagloria Santello | Corruption as an evolutionary theoretic game | Vassili Kolokoltsov |

Jack Skipper | Besov Spaces and Parabolic Systems | James Robinson |

John Sylvester | The cover cost of a random walk on a random graph | Agelos Georgakopulos |

Luke Williams | Aspects of Symmetry Breaking in Equilibrium Statistical Mechanics | Florian Theil |

### Summer Research Projects 2013

## Student Name |
## Project Title |
## Supervisor |

Matthew Dunlop | The support theorum | Andrew Stuart |

Adam Griffin | Convergence to Equilibrium in Granular Media and Related Equations | Simon Spencer |

Graham Hobbs | Monge Gauge with Point Particles | Charlie Elliott |

Jere Koskela | The Spatial Lamda-Fleming-Viot Process: Modelling and Inference in Population Genetics | Dario Spano |

Benjamin Lees | Probabilistic representations of qantum spin systems | Daniel Ueltschi |

Jorge Lindley | Enstrophy and Temperatrue Gradient Production for Vortices in Stratified Flow | Robert Kerr |

Felipe Medina Aguayo | The Pseudo-Marginal approach to MCMC | Gareth Roberts |

Fazian Nazar | Electronic Structure of Defects in the Thomas-Fermi-von-Weisz acker Model of Crystals | Christoph Ortner |

David O'Connor | Surface Cahn-Hilliard Equation | Bjorn Stinner |

Huan Wu | Atomistic-to-contium coupling | Christoph Ortner |

Summer Research Projects 2012

## Student Name |
## Project Title |
## Supervisor |

Maha Al Harji |
Spatial Modelling and Simulation of Ran-driven Nuclear Transport |
Markus Kirklionis |

Amal Alphonse |
Cell Motility: Modelling and Analysis |
Charlie Elliott |

Simon Bignold |
Density Functional Theory: The Classical Hard-Core Gas |
Christoph Ortner |

Tessa Colledge |
Free Energy and Large Deviations for 1-Dimensional Pinning Models |
Stefan Adams |

Owen Daniel |
Phase Transitions in the Random Stirring Process on Infinite Graphs |
Stefan Adams |

Barnaby Garrod |
The Infinitesimal Pairwise Immigration model |
Roger Tribe |

Alexander Kister |
Loop-Erased Random Walks and Schramm-Loewner-Evolutions |
Stefan Adams |

Chin Lun |
Eigenvalues of a Hermitian matrix of Brownian motions with drift |
Jon Warren |

Yuchen Pei |
RSK Correspondence and Pitman's Theorem |
Neil O'Connell |

Abhisek Shukla |
The Bayesian Approach to Inverse Problems |
Andrew Stuart |

Matthew Thorpe |
Multi Target Tracking as Applied to Telecommunications |
Florian Theil |

## Summer Research Projects 2011

## Student Name |
## Project Title |
## Supervisor |

Don Praveen Amarasinghe | A Mathematical Foundation for Density Functional Theory- A Statistical Mechanics Approach. | Stefan Adams |

Aylwin Andrew | First Passage Times for Levy Processes | Llarbi Alili |

Charles Brett | Inverse Problems Including Interfaces and Free Boundaries | Charlie Elliott |

Michael Eyres | What are the Possible Conformal Invariance Principles for Voronoi Percolations? | Stefan Adams |

Adam Hall | Pharmacokinetic and Pharmcodynamic Modelling of the Anti-Malarial Drug Artemisinin | John Aston |

Andrew Lam | Surface Phase-Field Methods. | Bjorn Stinner |

Pravin Madhavan | Discontinuous Galerkin Methods for Surface Partial Differential Equations | Andreas Dedner |

David McCormick | Limit States for the Euler Equations and Magnetohydrodynamics | James Robinson |

Chris Pettitt | A Review of Computational Methods in Population Genetics | Dario Spano |

Michael Scott | Stochastic Partial Differential Equations on an Evolving Surface | Martin Hairer |

Maria Veretennikova | Control Fractional Dynamics with Applications to Games and Finances | Vassili Kolokoltsov |