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Mathematics
UK
2022

D-Index & Metrics

Mathematics

D-Index
85
Citations
56111
World Ranking
102
National Ranking
7

Research.com Recognitions

  • 2022 - Research.com Mathematics in United Kingdom Leader Award
  • 2008 - President's Medal of the IOP, Institute of Physics
  • 2004 - Abel Prize For their discovery and proof of the index theorem, bringing together topology, geometry and analysis, and their outstanding role in building new bridges between mathematics and theoretical physics.
  • 1978 - Member of the National Academy of Sciences
  • 1966 - Fields Medal of International Mathematical Union (IMU) Did joint work with Hirzebruch in K-theory; proved jointly with Singer the index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the 'Lefschetz formula'.

Overview

Michael Atiyah was affiliated with the University of Edinburgh in the United Kingdom. Their research contributions spanned several fields, primarily centered on mathematics and materials science, with notable focus on geometry and topology, nuclear and high energy physics, computational theory and mathematics, polymers and plastics, and materials chemistry.

The scientist's recent publications included the following papers:

  • "Anyon Networks from Geometric Models of Matter" (2021) published in The Quarterly Journal of Mathematics
  • "New Subclasses of Bi-univalent Functions Associated with Quasi-subordination" (2025) published in the Journal of Al-Qadisiyah for Computer Science and Mathematics

Frequent collaborators throughout the career included Matilde Marcolli, Saad Raheem Bakheet, and Muhammed Salih Muhammed.

The primary venues for publishing research were:

  • The Quarterly Journal of Mathematics
  • Journal of Al-Qadisiyah for Computer Science and Mathematics

Main areas of study in their work included:

  • Mathematics
  • Materials Science

Significant subfields explored include:

  • Geometry and Topology
  • Nuclear and High Energy Physics
  • Computational Theory and Mathematics
  • Polymers and Plastics
  • Materials Chemistry

The scientific topics addressed involved:

  • Black Holes and Theoretical Physics
  • Algebraic Structures and Combinatorial Models
  • Topological and Geometric Data Analysis
  • Analytic and Geometric Function Theory
  • Polymer Synthesis and Characterization
  • X-ray Diffraction in Crystallography

Atiyah was recognized with several awards over the course of their career including the Fields Medal from the International Mathematical Union in 1966 for joint work on K-theory and the index theorem of elliptic operators, the Abel Prize in 2004 for contributions to bringing together topology, geometry, and analysis, a membership in the National Academy of Sciences in 1978, and the President's Medal of the Institute of Physics in 2008.

Best Publications

  • Introduction to Commutative Algebra

    Michael Atiyah

  • Spectral asymmetry and Riemannian geometry. III

    M. F. Atiyah;V. K. Patodi;I. M. Singer

  • The Yang-Mills equations over Riemann surfaces

    Michael Francis Atiyah;Raoul Bott

  • Self-duality in four-dimensional Riemannian geometry

    Michael Francis Atiyah;Nigel James Hitchin;I. M. Singer

  • Construction of Instantons

    M.F. Atiyah;Nigel J. Hitchin;V.G. Drinfeld;Yu.I. Manin

  • THE INDEX OF ELLIPTIC OPERATORS

    Michael F. Atiyah

  • The moment map and equivariant cohomology

    M.F. Atiyah;M.F. Atiyah;R. Bott;R. Bott

  • Vector Bundles Over an Elliptic Curve

    M. F. Atiyah

  • Convexity and Commuting Hamiltonians

    M. F. Atiyah

  • The Index of elliptic operators. 1

    M.F. Atiyah;I.M. Singer

  • The Geometry and Dynamics of Magnetic Monopoles

    Michael Francis Atiyah;Nigel J Hitchin

  • Topological quantum field theories

    Michael F. Atiyah

  • Complex analytic connections in fibre bundles

    M. F. Atiyah

  • The Index of elliptic operators. 3.

    Unknown

  • On the heat equation and the index theorem

    M. Atiyah;R. Bott;V. K. Patodi;V. K. Patodi

  • The index of elliptic operators on compact manifolds

    M. F. Atiyah;I. M. Singer

  • Vector bundles and homogeneous spaces

    Michael Francis Atiyah;Friedrich Hirzebruch

  • A Lefschetz Fixed Point Formula for Elliptic Complexes: I

    M. F. Atiyah;R. Bott

  • The Index of Elliptic Operators: IV

    M.F. Atiyah;I.M. Singer

  • The Geometry and Physics of Knots

    Michael Francis Atiyah

  • Spectral Asymmetry and Riemannian Geometry

    M. F. Atiyah;V. K. Patodi;I. M. Singer

Frequent Co-Authors

Nigel Hitchin
Nigel Hitchin University of Oxford
Raoul Bott
Raoul Bott Harvard University
Friedrich Hirzebruch
Friedrich Hirzebruch Max Planck Institute for Mathematics
Graeme B. Segal
Graeme B. Segal University of Oxford
Paul Sutcliffe
Paul Sutcliffe Durham University
Alan Bundy
Alan Bundy University of Edinburgh
Edward Witten
Edward Witten Institute for Advanced Study
Semir Zeki
Semir Zeki University College London
Gregory W. Moore
Gregory W. Moore Rutgers, The State University of New Jersey

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