Philipp Schlicht

I work at the School of Mathematics of the University of Bristol as an EPSRC Fellow on the project ''Graphs on generalised Baire spaces'' with Prof. Philip Welch. The project aims to understand the structure of large graphs that satisfy topological conditions. For instance, can you colour a graph with few colours such that no adjacent vertices are assigned the same colour? This problem is particularly interesting for graphs of a specified complexity, for instance for graphs on the real numbers that are open, closed or Borel (as a subset of the plane). This case has been studied in the 1980s and led Todorcevic to devise the so-called open colouring axiom.

In this project, we aim to understand graphs on larger spaces that appear naturally in set theory and model theory. We study open, Borel and more complex graphs and hypergraphs of finite and infinite dimensions. This is part of a recent area that has exciting connections with infinite combinatorics, deep set theoretic problems and classification problems in model theory.