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My research focuses on Multilevel Monte Carlo Methods for Uncertainty Quantification. Specifically, I work on PDEs with random coefficients, where we aim to quantify how the uncertainty in the input propagates through the model and affects the output. This problem arises in modelling groundwater pollution, which can happen either through accidental spills or leakages from underground carbon storage or nuclear fuel repositories.
My research is motivated by the ways insurance claims are estimated. Suppose claims amounts are independently distributed and follow a Pareto distribution, with the total number of claims following a Poisson distribution. Then the total claim amount is a compound distribution and can be easily estimated. I aim to explore the case where we remove the assumption of independence by the way of copulas and other computational methods for claims estimation.
My research focuses on the theory and applications of dynamical systems that feature multiple timescales, such as the Koper model from chemical kinetics and the Hodgkin-Huxley equations from mathematical neuroscience. In parallel, I also look into the existence and stability of travelling waves in reaction-diffusion equations with cut-off functions.
My mathematical research is motivated by the need to handle energetic materials (materials with large stores of chemical energy) with care. I develop models to describe a sample's thermo-mechanical response to a given low-energy mechanical insult, focusing on the physics underlying the material's behaviour, so as to inform safety principles. When analysing the models, I tend to opt for pen-and-paper techniques, such as matched asymptotics and PDE methods.
Conor Osborne •
Bernhard Heinzelreiter •
Elliot Addy •
David Varro •
Yiran Zhu •
Joshua Fogg •
Karolína Benková •
Teresa Klatzer •
Monse Guedes Ayala •
Kaitlyn Louth •
Matthew McCormack •
Peiqi Li •