My research field is mathematical logic, in particular set theory, large cardinals, descriptive set theory and applications to analysis, model theory, graph theory, computability and theoretical computer science.
I work on the EPSRC project ‘‘Graphs on generalised Baire spaces’’ with Prof. Philip Welch at the University of Bristol. 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. These spaces appear naturally in set theory and model theory.
Asymmetric cut and choose games accepted for Bulletin of Symbolic Logic - February 2, 2023