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Mathematics

D-Index
54
Citations
21477
World Ranking
813
National Ranking
61

Research.com Recognitions

  • 2020 - Wolf Prize in Mathematics for their contributions to differential geometry and topology.
  • 2013 - Fellow of the American Mathematical Society
  • 2000 - Member of the National Academy of Sciences
  • 1993 - Member of Academia Europaea
  • 1986 - Fellow of the Royal Society, United Kingdom
  • 1986 - Fields Medal of International Mathematical Union (IMU) Received medal primarily for his work on topology of four-manifolds, especially for showing that there is a differential structure on euclidian four-space which is different from the usual structure.

Overview

Simon Donaldson is affiliated with Imperial College London in the United Kingdom. Their research primarily spans the field of Mathematics, with a focus on several subfields including Geometry and Topology, Mathematical Physics, and Applied Mathematics. Other areas of interest include Nuclear and High Energy Physics, as well as Statistical and Nonlinear Physics.

The scientist's work covers key topics such as:

  • Geometric Analysis and Curvature Flows
  • Geometry and complex manifolds
  • Homotopy and Cohomology in Algebraic Topology
  • Geometric and Algebraic Topology
  • Advanced Algebra and Geometry
  • Numerical methods in inverse problems
  • Advanced Operator Algebra Research

Simon Donaldson has published frequently in several venues, including:

  • arXiv (Cornell University)
  • Bulletin of the American Mathematical Society
  • The Quarterly Journal of Mathematics
  • Notices of the American Mathematical Society
  • International Journal of Mathematics

Recent selected publications highlight their contributions with full titles, publication years, and venues as follows:

  • "Atiyah's work on holomorphic vector bundles and gauge theories," 2021, Bulletin of the American Mathematical Society
  • "Deformations Of Multivalued Harmonic Functions," 2021, The Quarterly Journal of Mathematics
  • "Isadore M. Singer (1924-2021) In Memoriam Part 1: Scientific Works," 2022, Notices of the American Mathematical Society
  • "Introduction to the Atiyah issue," 2021, Bulletin of the American Mathematical Society
  • "The ADHM construction of Yang-Mills instantons," 2022, arXiv (Cornell University)

Frequent co-authors who have collaborated on multiple publications include:

  • Fabian Lehmann
  • Robert L. Bryant
  • Jean-Michel Bismut
  • Jeff Cheeger
  • Phillip Griffiths

Throughout their career, Simon Donaldson has received various distinctions and memberships in prestigious organizations. These include:

  • Wolf Prize in Mathematics (2020) for contributions to differential geometry and topology
  • Fellow of the American Mathematical Society (2013)
  • Member of the National Academy of Sciences (2000)
  • Member of Academia Europaea (1993)
  • Fields Medal of International Mathematical Union (IMU) (1986), awarded primarily for work on the topology of four-manifolds, notably on differential structures on Euclidean four-space
  • Fellow of the Royal Society, United Kingdom (1986)

Best Publications

  • The Geometry of Four-Manifolds

    Simon K. Donaldson;P. B. Kronheimer

  • Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles

    S. K. Donaldson

  • An application of gauge theory to four-dimensional topology

    Simon K. Donaldson

  • Scalar Curvature and Projective Embeddings, I

    S.K. Donaldson

  • Scalar Curvature and Stability of Toric Varieties

    S. K. Donaldson

  • Polynomial invariants for smooth four-manifolds

    S.K. Donaldson

  • A new proof of a theorem of Narasimhan and Seshadri

    S. K. Donaldson

  • Twisted harmonic maps and the self-duality equations

    S. K. Donaldson

  • The orientation of Yang-Mills moduli spaces and 4-manifold topology

    S. K. Donaldson

  • Symplectic submanifolds and almost-complex geometry

    S. K. Donaldson

  • Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities

    Xiuxiong Chen;Simon Donaldson;Song Sun

  • Infinite determinants, stable bundles and curvature

    S. K. Donaldson

  • Gauge theory in higher dimensions, II

    S.K. Donaldson;R.P. Thomas

  • Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2 and completion of the main proof

    Xiuxiong Chen;Simon Donaldson;Song Sun

  • Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2

    Xiuxiong Chen;Simon Donaldson;Song Sun

  • Lefschetz pencils on symplectic manifolds

    S. K. Donaldson

  • Instantons and geometric invariant theory

    S. K. Donaldson;S. K. Donaldson

  • Nahm's equations and the classification of monopoles

    S. K. Donaldson;S. K. Donaldson

  • Irrationality and the $h$-cobordism conjecture

    S. K. Donaldson

  • Lower bounds on the Calabi functional

    S.K. Donaldson

  • Geometry of four-manifolds

    Simon K. Donaldson

Frequent Co-Authors

Xiuxiong Chen
Xiuxiong Chen Stony Brook University
Edward Witten
Edward Witten Institute for Advanced Study
Mikhael Gromov
Mikhael Gromov Institut des Hautes Études Scientifiques
Michael Atiyah
Michael Atiyah University of Edinburgh
Yakov Eliashberg
Yakov Eliashberg Stanford University

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