Current focus: scientific machine learning (specifically, practical existence theory for multi-level deep neural networks applied to boundary-value problems for partial differential equations)
Other interests: symbolic dynamics, ergodic theory, information theory, coding theory, combinatorics on words, synchronization of finite automata.
Please note that until August 2024 I worked and published under the name Sophie MacDonald.
“Encoding subshifts through sliding block codes”. Ergodic Theory and Dynamical Systems 44 (6) 2023, pp. 1609—1628. DOI, arXiv
“The road problem and homomorphisms of directed graphs”. Theoretical Computer Science 968 (113981) 2023, pp. 1—20. DOI, arXiv
“Conformal measures and the Dobrushin-Lanford-Ruelle equations”, with Luísa Borsato. Proceedings of the American Mathematical Society 149 (10) 2021, pp. 4355—4369. DOI, arXiv
"A Dobrushin-Lanford-Ruelle theorem for irreducible sofic shifts". 2020, with Luísa Borsato. Not submitted for publication. arXiv
Title TBD. Mathematics of Machine Learning session, CMS Winter Meeting, Toronto, Sunday 7 December 2025.
"A multi-stage method for overcoming spectral bias in a function estimation problem motivated by physics-informed neural networks." CANSSI/INCASS Postdoc Day, Concordia, 9 September 2025.
"Encodings as embeddings and vice versa." LG&TBQ2, Montréal, 3 June 2025.
“Subset problems in combinatorial number theory from coding problems in symbolic dynamics.” 25 July 2024. Mini-Conference in Symbolic Dynamics, UBC Vancouver. Video link (MathTube)