Richard Paul Winsley Thomas is a British mathematician working in several areas of

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

. He is a professor at

Imperial College London Imperial College London, also known as Imperial, is a Public university, public research university in London, England. Its history began with Prince Albert of Saxe-Coburg and Gotha, Prince Albert, husband of Queen Victoria, who envisioned a Al ...

. He studies moduli problems in

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, and ‘

mirror symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a Reflection (mathematics), reflection. That is, a figure which does not change upon undergoing a reflection has reflecti ...

’—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 intera ...

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

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 under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...

Calabi–Yau manifold In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has certain properties, such as Ricci flatness, yielding applications in theoretical physics. P ...

s in 1997 under the supervision of

Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth function, smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähl ...

at the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

. In his dissertation research with Donaldson, he defined the Donaldson–Thomas invariants of Calabi–Yau 3-folds, 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 The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

, and affiliated with

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

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 Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

, 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, nondegenerate 2-form. Symplectic geometry has its origins in the ...

. His doctoral thesis, which introduced the invariants that later became known as Donaldson–Thomas invariants, was published in the

Journal of Differential Geometry The ''Journal of Differential Geometry'' is a peer-reviewed scientific journal of mathematics published by International Press on behalf of Lehigh University in 3 volumes of 3 issues each per year. The journal publishes an annual supplement in book ...

as `A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations'. Motivated by

homological mirror symmetry Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory. History In an addre ...

, he produced

braid group In mathematics, the braid group on strands (denoted B_n), also known as the Artin braid group, is the group whose elements are equivalence classes of Braid theory, -braids (e.g. under ambient isotopy), and whose group operation is composition of ...

actions on

derived categories In mathematics, the derived category ''D''(''A'') of an abelian category ''A'' is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on ''A''. The construction proce ...

coherent sheaves In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with refer ...

in joint work with

Paul Seidel Paul Seidel (born 30 December 1970) is a Swiss-Italian mathematician specializing in homological mirror symmetry. He is a faculty member at the Massachusetts Institute of Technology. Career Seidel attended Heidelberg University, where he receive ...

. With

Shing-Tung Yau Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician. He is the director of the Yau Mathematical Sciences Center at Tsinghua University and professor emeritus at Harvard University. Until 2022, Yau was the William Caspar ...

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 sy ...

of a

. 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 surface In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with а trivial canonical bundle and irregularity of a surface, irregularity zero. An (algebraic) K3 surface over any field (mathematics), field ...

s and

modular forms In mathematics, a modular form is a holomorphic function on the Upper half-plane#Complex plane, complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the Group action (mathematics), group action of the ...

. 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." -

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 society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

Whitehead Prize The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whitehe ...

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 sche ...

, in 2010 the

Royal Society Wolfson Research Merit Award The Royal Society Wolfson Fellowship, known as the Royal Society Wolfson Research Merit Award until 2020, is a 5 years fellowship awarded by the Royal Society since 2000. The scheme is described by the Royal Society as providing ''long-term flexib ...

. 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 IMU Abacus Medal (known before ...

Hyderabad Hyderabad is the capital and largest city of the Indian state of Telangana. It occupies on the Deccan Plateau along the banks of the Musi River (India), Musi River, in the northern part of Southern India. With an average altitude of , much ...

, 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

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

s of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. For 2025 he was awarded the

Oswald Veblen Prize in Geometry __NOTOC__ The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was funded in 1961 in memory of Oswald Veblen and first issued in 1964. The Veblen Prize is n ...

, shared with Soheyla Feyzbakhsh.Oswald Veblen Prize in Geometry 2025
/ref>

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)