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.