__NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

s to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class="wikitable sortable" , - ! Year !! Winner !! Citation , - , 2022 , ,

Søren Galatius Søren Galatius (born 1 August 1976) is a Danish mathematician who works as a professor of mathematics at the University of Copenhagen. He works in algebraic topology, where one of his most important results concerns the homology of the automor ...

and

Oscar Randal-Williams Oscar Randal-Williams is a British mathematician and professor at the University of Cambridge, working in topology. He studied mathematics at the University of Oxford (MMath 2006, DPhil 2009), where he wrote his doctoral thesis ''Stable moduli sp ...

John Pardon John Vincent Pardon (born June 1989) is an American mathematician who works on geometry and topology. He is primarily known for having solved Gromov's problem on distortion of knots, for which he was awarded the 2012 Morgan Prize. He is currentl ...

, , "for their profound contributions to the understanding of high dimensional manifolds and their diffeomorphism groups; they have transformed and reinvigorated the subject."

"in recognition of his wide-ranging and transformative work in geometry and topology, particularly his groundbreaking achievements in symplectic topology." , - , 2021 , , Bhargav Bhatt , , "For his groundbreaking achievements in commutative algebra, arithmetic algebraic geometry, and topology in the p-adic setting." , - , 2020 , , not awarded , - , 2019 , , Wei Zhang

Tristan Buckmaster, Philip Isett and Vlad Vicol , , "In recognition of his ground-breaking work in arithmetic geometry and arithmetic aspects of automorphic forms."

"In recognition of the profound contributions that each of them has made to the analysis of partial differential equations, particularly the Navier-Stokes and Euler equations." , - , 2018 , , not awarded , - , 2017 , , Aleksandr Logunov and Eugenia Malinnikova

Jason Miller and Scott Sheffield

Maryna Viazovska Maryna Sergiivna Viazovska ( uk, Марина Сергіївна Вязовська, ; born 2 December 1984) is a Ukrainian mathematician known for her work in sphere packing. She is full professor and Chair of Number Theory at the Institute of M ...

, , "In recognition of their introduction of a novel geometric combinatorial method to study doubling properties of solutions to elliptic eigenvalue problems."

"In recognition of their groundbreaking and conceptually novel work on the geometry of the Gaussian free field and its application to the solution of open problems in the theory of two-dimensional random structures."

"In recognition of her groundbreaking work on sphere-packing problems in eight and twenty-four dimensions." , - , 2016 , , Mark Gross and

Bernd Siebert Bernd Siebert (born 5 March 1964 in Berlin-Wilmersdorf) is a German mathematician who researches in algebraic geometry. Life Siebert studied mathematics starting 1984 at the University of Erlangen. In 1986, he changed to the University of B ...

Geordie Williamson Geordie Williamson (born 1981 in Bowral, Australia) is an Australian mathematician at the University of Sydney. He became the youngest living Fellow of the Royal Society when he was elected in 2018 at the age of 36. Education Educated at Che ...

, , "In recognition of their groundbreaking contributions to the understanding of

mirror symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D ther ...

, in joint work generally known as the ‘Gross-Siebert Program’"

"In recognition of his groundbreaking work in

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

and related fields" , - , 2015 , ,

Larry Guth Lawrence David Guth (born 1977) is a professor of mathematics at the Massachusetts Institute of Technology. Education and career Guth graduated from Yale in 2000, with BS in mathematics. In 2005, he got his PhD in mathematics from the Massach ...

and

Nets Katz Nets Hawk Katz is the IBM Professor of Mathematics at the California Institute of Technology. He was a professor of Mathematics at Indiana University Bloomington until March 2013. Katz earned a B.A. in mathematics from Rice University in 1990 at t ...

, , "For their solution of the Erdős distance problem and for other joint and separate contributions to combinatorial

incidence geometry In mathematics, incidence geometry is the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles, continuity, betweenness, and incidence. An ''incide ...

" , - , 2014 , ,

Maryam Mirzakhani Maryam Mirzakhani ( fa, مریم میرزاخانی, ; 12 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ...

Peter Scholze Peter Scholze (; born 11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018. He ha ...

, , "For her many and significant contributions to geometry and

ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...

, in particular to the proof of an analogue of Ratner's theorem on unipotent flows for moduli of flat surfaces"

"For his many and significant contributions to

arithmetic algebraic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

, particularly in the development and applications of the theory of perfectoid spaces" , - , 2013 , ,

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, enumerativ ...

, , "For his recent outstanding work in

enumerative geometry In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory. History The problem of Apollonius is one of the earliest examp ...

, specifically for his proof in a large class of cases of the MNOP conjecture that he formulated with Maulik, Okounkov and Nekrasov" , - , 2012 , ,

Jeremy Kahn Jeremy Adam Kahn (born October 26, 1969) is an American mathematician. He works on hyperbolic geometry, Riemann surfaces and complex dynamics. Education Kahn grew up in New York City and attended Hunter College High School. He was a child prod ...

and

Vladimir Markovic Vladimir Marković is a Professor of Mathematics at University of Oxford. He was previously the John D. MacArthur Professor at the California Institute of Technology (2013–2020) and Sadleirian Professor of Pure Mathematics at the University of ...

, , "For their work in

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P ...

" , - , 2011 , , Yves Benoist and Jean-François Quint

Jonathan Pila Jonathan Solomon Pila (born 1962) FRS One or more of the preceding sentences incorporates text from the royalsociety.org website where: is an Australian mathematician at the University of Oxford. Education Pila earned his bachelor's degree at ...

, , "For their spectacular work on stationary measures and orbit closures for actions of non-abelian groups on

homogeneous spaces In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group ''G'' is a non-empty manifold or topological space ''X'' on which ''G'' acts transitively. The elements of ...

"For his resolution of the André-Oort Conjecture in the case of products of modular curves" , - , 2010 , , not awarded , - , 2009 , ,

Jean-Loup Waldspurger Jean-Loup Waldspurger (born July 2, 1953) is a French mathematician working on the Langlands program and related areas. He proved Waldspurger's theorem, the Waldspurger formula, and the local Gan–Gross–Prasad conjecture for orthogonal group ...

Ian Agol Ian Agol (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds. Education and career Agol graduated with B.S. in mathematics from the California Institute of Technology in 1992 and ...

Danny Calegari Danny Matthew Cornelius Calegari is a mathematician who is currently a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory. Educ ...

and

David Gabai David Gabai is an American mathematician and the Hughes-Rogers Professor of Mathematics at Princeton University. Focused on low-dimensional topology and hyperbolic geometry, he is a leading researcher in those subjects. Biography David Ga ...

, , "For his work in p-adic harmonic analysis, particularly his contributions to the transfer conjecture and the fundamental lemma"

"For their solutions of the

Marden Tameness Conjecture Marden may refer to: Places Australia * Marden, South Australia, a suburb of Adelaide England * Marden, Herefordshire * Marden, Kent ** Marden Airfield ** Marden railway station * Marden, Tyne and Wear * Marden, West Sussex ** East Marden ** N ...

, and, by implication through the work of Thurston and Canary, of the

Ahlfors Measure Conjecture In mathematics, the Ahlfors conjecture, now a theorem, states that the limit set of a finitely-generated Kleinian group is either the whole Riemann sphere, or has measure 0. The conjecture was introduced by , who proved it in the case that the Kl ...

" , - , 2008 , ,

Clifford Taubes Clifford Henry Taubes (born February 21, 1954) is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional topology. His brother is the journalist Gary Taube ...

Claire Voisin Claire Voisin (born 4 March 1962) is a French mathematician known for her work in algebraic geometry. She is a member of the French Academy of Sciences and holds the chair of Algebraic Geometry at the Collège de France. Work She is noted for ...

, , "For his proof of the Weinstein conjecture in dimension three"

"For her disproof of the Kodaira conjecture" , - , 2007 , , Alex Eskin

Christopher Hacon Christopher Derek Hacon (born 14 February 1970) is a mathematician with British, Italian and US nationalities. He is currently distinguished professor of mathematics at the University of Utah where he holds a Presidential Endowed Chair. His res ...

and

James McKernan James McKernan (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at MIT from 2007 until 2013. Education McKernan was educated at the Campion School, Hornchurch, and Tr ...

Michael Harris and Richard Taylor , , "For his work on rational billiards and

geometric group theory Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such group (mathematics), groups and topology, topological and geometry, geometric pro ...

, in particular, his crucial contribution to joint work with David Fisher and Kevin Whyte establishing the quasi-isometric rigidity of sol"

"For their work in advancing our understanding of the

birational geometry In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational ...

algebraic varieties Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. ...

in dimension greater than three, in particular, for their inductive proof of the existence of

flips Flip, FLIP, or flips may refer to: People * Flip (nickname), a list of people * Lil' Flip (born 1981), American rapper * Flip Simmons, Australian actor and musician * Flip Wilson, American comedian Arts and entertainment Fictional characters * ...

"For their work on local and global Galois representations, partly in collaboration with Clozel and Shepherd-Barron, culminating in the solution of the Sato-Tate conjecture for

elliptic curves In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If t ...

with non-integral j-invariants" , - , 2006 , , not awarded , - , 2005 , ,

Manjul Bhargava Manjul Bhargava (born 8 August 1974) is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds A ...

Nils Dencker , , "For his discovery of new composition laws for

quadratic forms In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to ...

, and for his work on the average size of ideal class groups"

"For his complete resolution of a conjecture made by F. Treves and L. Nirenberg in 1970" , - , 2004 , , Ben Green

Gérard Laumon and

Ngô Bảo Châu Ngô Bảo Châu (, born June 28, 1972) is a Vietnamese-French mathematician at the University of Chicago, best known for proving the fundamental lemma for automorphic forms (proposed by Robert Langlands and Diana Shelstad). He is the first ...

, , "For his joint work with

Terry Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes ...

arithmetic progressions An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common differ ...

prime numbers A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

"For their proof of the Fundamental Lemma for unitary groups" , - , 2003 , , Richard S. Hamilton

Terence Tao , , "For his discovery of the

Ricci Flow In the mathematical fields of differential geometry and geometric analysis, the Ricci flow ( , ), sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be ana ...

Equation and its development into one of the most powerful tools of

geometric analysis Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of ...

"For his ground-breaking work in analysis, notably his optimal restriction theorems in Fourier analysis, his work on the wave map equation, his global existence theorems for KdV type equations, as well as significant work in quite distant areas of mathematics" , - , 2002 , ,

Oded Schramm Oded Schramm ( he, עודד שרם; December 10, 1961 – September 1, 2008) was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory ...

Manindra Agrawal Manindra Agrawal (born 20 May 1966) is a professor at the Department of Computer Science and Engineering and the Deputy Director at the Indian Institute of Technology, Kanpur. He was also the recipient of the first Infosys Prize for Mathematics ...

, , "For his work in combining analytic power with geometric insight in the field of

random walks In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...

percolation Percolation (from Latin ''percolare'', "to filter" or "trickle through"), in physics, chemistry and materials science, refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applicatio ...

, and

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

in general, especially for formulating stochastic Loewner evolution"

"For finding an algorithm that solves a modern version of a problem going back to the ancient Chinese and Greeks about how one can determine whether a number is prime in a time that increases polynomially with the size of the number" , - , 2001 , ,

Edward Witten Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, q ...

Stanislav Smirnov Stanislav Konstantinovich Smirnov (russian: Станисла́в Константи́нович Cмирно́в; born 3 September 1970) is a Russian mathematician currently working at the University of Geneva. He was awarded the Fields Medal in ...

, , "For a lifetime of achievement, especially for pointing the way to unify apparently disparate fields of mathematics and to discover their elegant simplicity through links with the physical world"

"For establishing the existence of the scaling limit of two-dimensional

, and for verifying

John Cardy John Lawrence Cardy FRS (born 19 March 1947, England)Guggenheim Foundation: Annual Report 1985. is a British-American theoretical physicist at the University of California, Berkeley. He is best known for his work in theoretical condensed matter ...

's conjectured relation" , - , 2000 , ,

Alain Connes Alain Connes (; born 1 April 1947) is a French mathematician, and a theoretical physicist, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the , , Ohio State University and Vand ...

Laurent Lafforgue Laurent Lafforgue (; born 6 November 1966) is a French mathematician. He has made outstanding contributions to Langlands' program in the fields of number theory and analysis, and in particular proved the Langlands conjectures for the automorphism ...

, , "For revolutionizing the field of

operator algebras In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study ...

, for inventing modern non-commutative geometry, and for discovering that these ideas appear everywhere, including the foundations of theoretical physics"

"For his work on the

Langlands program In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by , it seeks to relate Galois groups in algebraic num ...

" , - , 1999 , ,

Andrew Wiles Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awar ...

, , "For his role in the development of

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

External links

Official web page2014 Clay Research Awards2017 Clay Research Awards2019 Clay Research Awards2021 Clay Research Award2022 Clay Research Award
Mathematics awards Awards established in 1999 Research awards 1999 establishments in England

See also

External links