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. In his spare time, Dáire enjoys yoga, listening to music, reading, and learning languages (or at least trying to).

My current project (with Avi) is on the ergodicity of non-Markovian systems in infinite dimensions. This involves investigating the existence and uniqueness of invariant measures and associated convergence rates in a dynamical systems framework. A motivation is to study the ergodicity of SPDEs driving by fractional Brownian motion such as the 2D stochastic Navier-Stokes equation with fractional noise.

Last year (with James) I was working on numerical methods for SDEs, in particular, the development of higher order solvers for underdamped Langevin dynamics (ULD). The project involved showing third order convergence of a method for Langevin MCMC. Such solvers are of great interest to those in machine learning communities due to the ergodicity of ULD, offering an efficient method for sampling from a target distribution.

I am funded in connection with Maths4DL.