Before joining Imperial College, he was member of the
Institute for Advanced Study in
Princeton, New Jersey, and affiliated with
Harvard University and the University of Oxford. He was made professor of pure mathematics in 2005. Thomas has made contributions to
algebraic geometry,
differential geometry, and
symplectic geometry. His doctoral thesis, which introduced the invariants that later became known as Donaldson–Thomas invariants, was published in the
Journal of Differential Geometry as `A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations'. Motivated by
homological mirror symmetry, he produced
braid group actions on
derived categories of
coherent sheaves in joint work with
Paul Seidel. With
Shing-Tung Yau he formulated a conjecture (now known as the Thomas–Yau conjecture) concerning the existence of a special Lagrangian in the Hamiltonian deformation class of a fixed
Lagrangian submanifold of a
Calabi–Yau manifold. Together with
Rahul Pandharipande he formulated a refinement of the Donaldson–Thomas invariants for the special case of curve counting, the Pandharipande–Thomas (PT) stable pair 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. With Davesh Maulik and Pandharipande he proved the Katz–Klemm–Vafa (KKV) conjecture, establishing links between the
Gromov–Witten theory of
K3 surfaces and
modular forms. His collaboration with
Daniel Huybrechts led to contributions to the deformation theory of complexes. With Nick Addington he established a compatibility result for two rationality conjectures on cubic fourfolds. He coauthored a book on mirror symmetry. Thomas also wrote expository notes on derived categories, curve counting, and homological projective duality. He appeared in the documentary film 'Thinking space' by Heidi Morstang. Thomas has played an important part in promoting geometry in the UK, encouraging younger mathematicians, and in bringing more geometry to Imperial college: "[...] There was little geometry in Imperial then, but now, thanks largely to the drive of my colleague Richard Thomas, we have one of the main centres for research in this area." -
Simon Donaldson ==Awards and honours==