Search Results

Hugo Duminil-Copin,

France

For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four.

James Maynard,

United Kingdom of Great Britain and Northern Ireland

For contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation.解析的整数論に貢献し，素数の構造理解とディオファントス近似の理解に大きな進歩をもたらした[22]。

June Huh,

United States of America

For bringing the ideas of Hodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture.

Maryna Viazovska,

Ukraine

For the proof that theE8{\displaystyle E_{8}}lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis.球充填問題を8次元と24次元で解決したことや，フーリエ解析における極値および補間問題への更なる貢献が評価[22]。

Maryna Viazovska,

Ukraine

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Akshay Venkatesh,

Australia

For his synthesis ofanalytic number theory, homogeneous dynamics,topology, andrepresentation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects.

Alessio Figalli,

Italy

For contributions to the theory ofoptimal transportand its applications inpartial differential equations,metric geometryandprobability.

Caucher Birkar,

United Kingdom of Great Britain and Northern Ireland

For the proof of the boundedness ofFano varietiesand for contributions to theminimal model program.

Peter Scholze,

Germany

For transformingarithmetic algebraic geometryoverp-adic fieldsthrough his introduction ofperfectoid spaces, with application toGalois representations, and for the development of newcohomology theories.

Artur Avila,

Brazil

for his profound contributions todynamical systemstheory have changed the face of the field, using the powerful idea of renormalization as a unifying principle.

Manjul Bhargava,

Canada

for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank ofelliptic curves.

Martin Hairer,

Austria

for his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations.

Maryam Mirzakhani,

Iran (Islamic Republic of)

for her outstanding contributions to the dynamics and geometry ofRiemann surfacesand theirmoduli spaces.

Cédric Villani,

France

For his proofs of nonlinear Landau damping and convergence to equilibrium for theBoltzmann equation.

Elon Lindenstrauss,

Israel

For his results on measure rigidity inergodic theory, and their applications tonumber theory.

Ngô Bảo Châu,

Viet Nam

For his proof of the Fundamental Lemma in the theory ofautomorphic formsthrough the introduction of new algebro-geometric methods.

Stanislav Smirnov,

Russian Federation

For the proof of conformal invariance ofpercolationand the planarIsing modelinstatistical physics.

Andrei Okounkov,

Russian Federation

for his contributions bridgingprobability,representation theoryandalgebraic geometry

Grigori Perelman,

Russian Federation

for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of theRicci flow

Terence Tao,

Australia

for his contributions topartial differential equations,combinatorics,harmonic analysisand additive number theory

Wendelin Werner,

France

for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensionalBrownian motion, andconformal field theory

Laurent Lafforgue,

France

Laurent Lafforgue has been awarded the Fields Medal for his proof of theLanglands correspondencefor thefull linear groupsGLr(r≥1) overfunction fields.

Vladimir Voevodsky,

Russian Federation

he defined and developed motivic cohomology and the A1-homotopy theory ofalgebraic varieties; he proved theMilnor conjectureson theK-theoryof fields

Curtis T. Mcmullen,

United States of America

He has made important contributions to various branches of the theory ofdynamical systems, such as the algorithmic study of polynomial equations, the study of the distribution of the points of a lattice of aLie group,hyperbolic geometry,holomorphic dynamicsand the renormalization of maps of the interval.

Maxim Kontsevich,

Russian Federation

contributions to four problems of geometry

Richard E. Borcherds,

United Kingdom of Great Britain and Northern Ireland

for his work on the introduction of vertex algebras, the proof of the Moonshine conjecture and for his discovery of a new class of automorphic infinite products

William Timothy Gowers,

United Kingdom of Great Britain and Northern Ireland

William Timothy Gowers has provided important contributions tofunctional analysis, making extensive use of methods fromcombination theory. These two fields apparently have little to do with each other, and a significant achievement of Gowers has been to combine these fruitfully.

Efim Zelmanov,

Russian Federation

For his solution to the restricted Burnside problem.

Jean Bourgain, 1954年 - 2018年）

Belgium

Bourgain's work touches on several central topics of mathematical analysis: the geometry ofBanach spaces, convexity in high dimensions,harmonic analysis,ergodic theory, and finally, nonlinearpartial differential equationsfrommathematical physics.

Jean-Christophe Yoccoz,

France

proving stability properties - dynamic stability, such as that sought for the solar system, orstructural stability, meaning persistence under parameter changes of the global properties of the system.