Project description
The project belongs to the following areas of Mathematics: Stochastic Analysis, Applied Probability, Statistics, Machine Learning and Numerical Analysis
State-of-the-art applications in molecular dynamics (e.g., simulations of constrained behaviour between bonds), biomedical imaging (e.g., predicting tumour trajectory), language models in Natural Language Processing (e.g., optimising over constrained matrices), and many more, demand development of scalable, efficient computational and statistical tools that exploit the geometry of parameter spaces. At the core of such development is the ability to sample from probability distributions on geometric spaces such as manifolds.
This project is devoted to the development of novel numerical methods for ergodic stochastic differential equations on manifolds (e.g., 3D rotations) and more general non-Euclidean spaces (e.g., stratified spaces) and their stochastic numerical analysis, with a view towards using them to sample from distributions on such spaces thus facilitating statistical inference and optimisation.
We require an enthusiastic graduate with a 1st class degree in Mathematics, preferably at MMath/MSc level (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). We are expecting that the successful applicant has a very good background in Probability, good computational skills and some knowledge of differential geometry.