My research interests lie in semigroup theory, infinite combinatorics, model theory and theoretical computer science. At present, I am studying monoids lying between the automorphism group and endomorphism monoid of first order structures, with a particular emphasis on homomorphism-homogeneity. I plan to investigate more connections between model theory and semigroup theory; in particular, looking at partial map monoids related to first-order structures. In addition, I am looking at classification results for homomorphism-homogeneous structures.
I am an active referee.
Publications and preprints
- Two Fraïssé-style results for homomorphism-homogeneous relational structures, to appear in Discrete Mathematics, arXiv preprint 1812.01934v2.
- Permutation monoids and MB-homogeneity of graphs and relational structures (joint with David Evans and Robert Gray), European Journal of Combinatorics, Volume 78, May 2019, pp163-189.