Richard Paul Winsley Thomas is a British mathematician working in several areas of geometry. He is a professor at Imperial College London. He studies moduli problems in

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, and ‘ mirror symmetry’—a phenomenon in pure mathematics predicted by

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...

in theoretical physics.

Education

Thomas obtained his PhD on

gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups) ...

on Calabi–Yau manifolds in 1997 under the supervision of Simon Donaldson at the University of Oxford. Together with Donaldson, he defined the Donaldson–Thomas invariants of Calabi–Yau

3-fold In algebraic geometry, a 3-fold or threefold is a 3-dimensional algebraic variety. The Mori program In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a bira ...

s, now a major topic in geometry and the mathematics of string theory.

Career and research

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

differential Geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

, and

symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed differential form, closed, nondegenerate form, nondegenerate different ...

. 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 In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M , equipped with a closed nondegenerate differential 2-form \omega , called the symplectic form. The study of symplectic manifolds is called sympl ...

of a Calabi–Yau manifold. Together with

Rahul Pandharipande Rahul Pandharipande (born 1969) is a mathematician who is currently a professor of mathematics at the Swiss Federal Institute of Technology Zürich (ETH) working in algebraic geometry. His particular interests concern moduli spaces, enumerative ...

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 Daniel Huybrechts (9 November 1966) is a German mathematician, specializing in algebraic geometry. Education and career Huybrechts studied mathematics from 1985 at the Humboldt University of Berlin, where in 1989 he earned his Diplom with Diplo ...

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

In 2004, Thomas was awarded the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

's Whitehead Prize and the

Philip Leverhulme Prize The Philip Leverhulme Prize is awarded by the Leverhulme Trust to recognise the achievement of outstanding researchers whose work has already attracted international recognition and whose future career is exceptionally promising. The prize schem ...

, in 2010 the Royal Society Wolfson Research Merit Award. From the Whitehead prize citation: "Thomas has made seminal contributions across an unusually broad range of topics. Much of his work is related to mirror symmetry and Calabi–Yau geometry, and thus has an important bearing on exciting contemporary interactions with mathematical physics. ..This involved the combination of deep, original insights and sophisticated technical proofs that is characteristic of Thomas’s work." In 2010 he also was invited speaker for the algebraic geometry section at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Hyderabad, where he delivered a lecture on mirror symmetry. Thomas was elected a Fellow of the Royal Society (FRS) in 2015. His contributions to algebraic geometry led to his election to the 2018 class of fellows of the American Mathematical Society.

References

External links

* {{DEFAULTSORT:Thomas, Richard Living people 20th-century British mathematicians 21st-century British mathematicians Fellows of the Royal Society Fellows of the American Mathematical Society Alumni of the University of Oxford Academics of Imperial College London Algebraic geometers British string theorists Royal Society Wolfson Research Merit Award holders Year of birth missing (living people)