Richard Thomas studies moduli problems in algebraic geometry, and ‘mirror symmetry’ — a phenomenon in pure mathematics predicted by string theory in theoretical physics. Together with Simon Donaldson FRS, he defined the Donaldson–Thomas (DT) invariants of Calabi–Yau 3-folds, now a major topic in geometry and the mathematics of string theory.
For the special case of curve counting, the more recent Pandharipande–Thomas (PT) stable pair invariants further refine the DT invariants. With Martijn Kool and Vivek Shende, he used the PT invariants to prove the Göttsche conjecture — a classical algebro-geometric problem going back more than a century. He has translated ideas from symplectic geometry through mirror symmetry to produce group actions on derived categories with applications to knot theory.
Richard has been awarded a London Mathematical Society Whitehead Prize, a Philip Leverhulme Prize, a Royal Society Wolfson Research Merit Award, and was an invited speaker at the International Congress of Mathematicians in 2010.