I recently completed my PhD at the University of Oxford under the supervision of Emmanuel Breuillard and also mentored by Péter Varjú. During the first two years of my doctoral studies, I was based at the University of Cambridge as part of the CCIMI cohort. Prior to my doctorate, I earned a master’s degree in mathematics from ETH Zürich in 2020.
My research focuses on random walks on Lie groups, particularly self-similar measures, and recently also on mathematical aspects of machine learning.
Image Copyright: Maria O'Leary, Institute for Advanced Study.
Research
Optimal Initialization in Depth: Lyapunov Initialization and Limit Theorems for Deep Leaky ReLU Networks (with Tassilo Schwarz and Samuel Kittle). (arxiv)
Permutation-Invariant Spectral Learning via Dyson Diffusion (with Tassilo Schwarz et al.). (arxiv)
On absolute continuity of inhomogeneous and contracting on average self-similar measures (with Samuel Kittle). (arxiv)
Dimension of contracting on average self-similar measures (with Samuel Kittle). (arxiv)
Entropy theory for random walks on Lie groups (with Samuel Kittle). Journal of Theoretical Probability 2025. (arxiv, journal)
Polynomial tail decay for stationary measures (with Samuel Kittle). To appear Proceedings of the AMS. (arxiv)
Local limit theorem for random walks on symmetric spaces. Journal d'Analyse Mathématique 2025. (arxiv, journal)
Effective density of non-degenerate random walks on homogeneous spaces (with Wooyeon Kim). IMRN 2024. (arxiv, journal)
Theses:
Topic in Random Walks on Lie Groups. PhD Thesis. (205 pages, pdf)
