My research is in
descriptive set theory, infinite combinatorics and applications to topology, analysis, model theory, graph theory, computability and theoretical computer science.

In which circumstances can you colour a graph with few colours such that no adjacent vertices are assigned the same colour? We study this problem in the context of graphs of a specified complexity such as open, closed or Borel as a subset of the plane. The study of such graphs led Todorcevic to devise the open colouring axiom. We aim to understand graphs and hypergraphs of finite and infinite dimension on large spaces that appear naturally in set theory and model theory.

I previously worked at the School of Mathematics at the Universty of Bristol and currently I am a Research Fellow at the School of Computer Science at the University of Auckland. Here are my research and teaching statements.

- Generalized Polish spaces at regular uncountable cardinals

with Claudio Agostini and Luca Motto Ros, 42 pages,*Journal of the London Mathematical Society*108, 5 (2023), 1886-1929 - Coarse groups, and the isomorphism problem for oligomorphic groups

with Andre Nies and Katrin Tent,*Journal of Mathematical Logic 22, 1 (2022), 2150029, 26 pages* -
Lebesgue's density theorem and definable selectors for ideals

with Sandra Müller, David Schrittesser and Thilo Weinert,*Israel Journal of Mathematics 249 (2022), 501–551* - How to have more things by forgetting how to count them

with Asaf Karagila,*Proceedings of the Royal Society A, Volume 476, Issue 2239 (2020), 1-12* - The Hurewicz dichotomy for generalized Baire spaces

with Luca Motto Ros and Philipp Lücke,*Israel Journal of Mathematics 216, 2 (2016), 973-1022* - Continuous images of closed sets in generalised Baire spaces

with Philipp Lücke,*Israel Journal of Mathematics 209, 1 (2015), 421-461* - Wadge-like reducibilities in arbitrary quasi-Polish spaces

with Luca Motto Ros and Victor Selivanov,*Mathematical Structures in Computer Science 25 , 8 (2015), 1705-1754*

- Between Ramsey and measurable cardinals

with Victoria Gitman, 33 pages, submitted - The open dihypergraph dichotomy on generalized Baire spaces and its applications

with Dorottya Sziraki, 128 pages, submitted - Forcing over choiceless models and generic absoluteness

with Daisuke Ikegami, 28 pages, submitted - Countable ranks at the first and second projective levels

with Merlin Carl and Philip Welch, 30 pages, submitted