Dáire O’Kane

PhD Student, University of Bath

Dáire graduated from the University of Edinburgh in 2023 with an MMath Mathematics degree. He mainly studied analysis, algebra and stochastic analysis. His masters dissertation was in Gaussian analysis, exploring the properties of Gaussian measures in infinite dimensions and their role in constructive quantum field theory.

Dáire is completing a PhD project in stochastic analysis. On the applied side, this includes investigating higher order numerical methods for stochastic differential equations relevant to data science such as the underdamped Langevin equation (ULD). Due to its ergodic properties, ULD is popular for sampling methods in machine learning such as Langevin MCMC. On the purer side, this involves studying the ergodicity of stochastic equations in infinite dimensions, particular those driven by non-Markovian noise. A motivating example is the 2D stochastic Navier-Stokes equation with fractional noise.