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The Clay Research Award is an annual award given by the Oxford-based
Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address is now in Denver, Colorado. CMI's sc ...
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"
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! Year !! Winner !! Citation
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, 2022 , , Søren Galatius and Oscar Randal-WilliamsJohn Pardon , , "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."
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, 2021 , , Bhargav Bhatt , , "For his groundbreaking achievements in commutative algebra, arithmetic algebraic geometry, and topology in the p-adic setting."
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, 2020 , , not awarded
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, 2019 , , Wei ZhangTristan 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."
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, 2018 , , not awarded
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, 2017 , , Aleksandr Logunov and Eugenia MalinnikovaJason Miller and Scott SheffieldMaryna Viazovska , , "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."
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, 2016 , , Mark Gross and Bernd SiebertGeordie Williamson , , "In recognition of their groundbreaking contributions to the understanding of mirror symmetry, in joint work generally known as the ‘Gross-Siebert Program’" "In recognition of his groundbreaking work in representation theory and related fields"
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, 2015 , , Larry Guth and Nets Katz , , "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 ''inciden ...
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 expr ...
, 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"
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, 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, enumerative ...
, , "For his recent outstanding work in enumerative geometry, specifically for his proof in a large class of cases of the MNOP conjecture that he formulated with Maulik, Okounkov and Nekrasov"
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, 2012 , , Jeremy Kahn 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 ...
Yves Benoist
Yves Benoist is a French mathematician, known for his work on group dynamics on homogeneous spaces. He is currently a Senior Researcher (Directeur de Recherche) of CNRS at the University of Paris-Sud.
In 1990 Benoist proved a longstanding open co ...
and
Jean-François Quint
Jean-François Quint is a French mathematician, specializing in dynamical systems theory for homogeneous spaces.
He studied at the École normale supérieure de Lyon and then received his Ph.D. from École Normale Supérieure (ENS) in Paris unde ...
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 ''G ...
modular curves
In number theory and algebraic geometry, a modular curve ''Y''(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular grou ...
fundamental lemma
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral c ...
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 Taub ...
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 he ...
, , "For his proof of the
Weinstein conjecture In mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows. More specifically, the conjecture claims that on a compact contact manifold, its Reeb vector field should carr ...
in dimension three" "For her disproof of the Kodaira conjecture"
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, 2007 , ,
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"
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, 2006 , , not awarded
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, 2005 , , Manjul BhargavaNils Dencker , , "For his discovery of new composition laws for quadratic forms, 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"
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, 2004 , , Ben Green
Gérard Laumon
Gérard Laumon (; born 1952) is a French mathematician, best known for his results in number theory, for which he was awarded the Clay Research Award.
Life and work
Laumon studied at the École Normale Supérieure and Paris-Sud 11 University, Or ...
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 ...
Fundamental Lemma
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral c ...
Terence 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 ...
, , "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 an ...
Equation and its development into one of the most powerful tools of geometric analysis" "For his ground-breaking work in analysis, notably his optimal restriction theorems in
Fourier analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph ...
, 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"
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, 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 , , "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 ...
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 ...
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"
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, 2001 , , Edward WittenStanislav Smirnov , , "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 percolation, and for verifying John Cardy's conjectured relation"
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, 2000 , , Alain ConnesLaurent Lafforgue , , "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 stud ...
, 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"
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, 1999 , , Andrew Wiles , , "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 integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...
"
See also
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List of mathematics awards
This list of mathematics awards is an index to articles about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, but awards may be open to mathematicians from around the wo ...