Patrick is a pure mathematician specialising in algebraic geometry. His current research is focussed on developing tools for turning complicated algebraic geometry questions into a combination of simple algebraic geometry questions, and combinatorial (or tropical) questions. More precisely, he is interested in developing tools of logarithmic geometry to prove theorems about coherent sheaves and their moduli.

Between finishing his PhD at the University of Cambridge and joining Peterhouse, Patrick spent 6 months as an LMS early career research fellow at the University of Sheffield.