I work in the research area of model theory - a branch of the field of mathematical logic that studies the interplay between mathematical structures (such as graphs, orders, groups, and rings) and first-order logic. I study homogeneous structures in the sense of Fraïssé theory and their automorphism groups which are Polish groups when endowed with the pointwise convergence topology. The study of homogeneous structures meets with other areas in mathematics such as combinatorics, permutation group theory, and descriptive set theory. We say a first-order structure is homogeneous if it is countable, and every isomorphism between any two of its finitely generated substructures extends to an automorphism of the whole structure. Examples of homogeneous structures include the rationals as a linear order, the Erdős–Rényi graph, and Philip Hall’s locally finite universal group.
Model Theory conferences [link]
Map of first-order theories [link]
A two-sorted theory of nilpotent Lie algebras (with Christian d'Elbee, Isabel Muller, and Nick Ramsey), 2025. [Journal of Symbolic Logic | arXiv]
Model-theoretic properties of nilpotent groups and Lie algebras (with Christian d'Elbee, Isabel Muller, and Nick Ramsey), 2025. [Journal of Algebra | arXiv]
Bowtie-free graphs and generic automorphisms, 2023. [Mathematical Logic Quarterly | arXiv]
On the automorphism group of the universal homogeneous meet-tree (with Itay Kaplan and Tomasz Rzepecki), 2021. [Journal of Symbolic Logic | arXiv]
Coherent extension of partial automorphisms, free amalgamation, and automorphism groups (with Slawomir Solecki), 2019. [Journal of Symbolic Logic | arXiv]
Title: Automorphism Groups of Homogeneous Structures. [Thesis]
Supervisor: Prof Dugald Macpherson
Institution: University of Leeds [website]
Keywords: Extension property for partial automorphisms (EPPA), homogeneous structure, omega-categorical theory, ample generics, free amalgamation, bowtie-free graphs, Philip Hall's universal group, weak amalgamation property, Fraïssé's Theorem.