H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 73 Citations 49,587 137 World Ranking 94 National Ranking 1

Research.com Recognitions

Awards & Achievements

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

What is he best known for?

The fields of study he is best known for:

  • Quantum mechanics
  • Pure mathematics
  • Geometry

The scientist’s investigation covers issues in Pure mathematics, Mathematical analysis, Elliptic operator, Discrete mathematics and Index. His Pure mathematics study incorporates themes from Fundamental theorem of Riemannian geometry and Euclidean geometry. He interconnects Quantum electrodynamics, Instanton, Gauge group and Twistor theory in the investigation of issues within Euclidean geometry.

The study incorporates disciplines such as Equivariant map, Quantum cohomology and Cartan model in addition to Mathematical analysis. His work focuses on many connections between Elliptic operator and other disciplines, such as Semi-elliptic operator, that overlap with his field of interest in Operator theory. While the research belongs to areas of Discrete mathematics, Michael Atiyah spends his time largely on the problem of Fixed point, intersecting his research to questions surrounding Schauder fixed point theorem.

His most cited work include:

  • Introduction to Commutative Algebra (3179 citations)
  • Spectral asymmetry and Riemannian geometry. III (1969 citations)
  • The Yang-Mills equations over Riemann surfaces (1749 citations)

What are the main themes of his work throughout his whole career to date?

His primary scientific interests are in Pure mathematics, Algebra, Theoretical physics, Mathematical physics and Mathematical analysis. His study brings together the fields of Discrete mathematics and Pure mathematics. Much of his study explores Theoretical physics relationship to Magnetic monopole.

His Mathematical physics research focuses on Instanton in particular. Michael Atiyah frequently studies issues relating to Equivariant cohomology and Equivariant map. Michael Atiyah merges Elliptic operator with Index in his study.

He most often published in these fields:

  • Pure mathematics (32.82%)
  • Algebra (12.60%)
  • Theoretical physics (12.21%)

What were the highlights of his more recent work (between 2007-2021)?

  • Theoretical physics (12.21%)
  • Mathematical physics (9.92%)
  • Instanton (6.49%)

In recent papers he was focusing on the following fields of study:

His scientific interests lie mostly in Theoretical physics, Mathematical physics, Instanton, Dirac equation and Pure mathematics. His Theoretical physics research integrates issues from Electric charge, Quantum mechanics and Surface. The concepts of his Instanton study are interwoven with issues in Twistor space, Twistor theory, Cohomology, Holomorphic function and Space.

His Dirac equation study also includes

  • Dirac which is related to area like Time evolution, Geometric modeling, Spacetime, Spin-½ and Magnetic monopole,
  • Cosmological constant and related Differential equation and Differential. He merges many fields, such as Pure mathematics and Discrete valuation, in his writings. His Gravitation research is multidisciplinary, relying on both Mathematical analysis and Signature.

Between 2007 and 2021, his most popular works were:

  • The Geometry and Physics of Knots (125 citations)
  • The experience of mathematical beauty and its neural correlates (113 citations)
  • The experience of mathematical beauty and its neural correlates (113 citations)

In his most recent research, the most cited papers focused on:

  • Quantum mechanics
  • Geometry
  • Pure mathematics

The scientist’s investigation covers issues in Mathematical physics, Neuroscience, Functional magnetic resonance imaging, Pure mathematics and Instanton. His work carried out in the field of Mathematical physics brings together such families of science as Fiber bundle, Singularity, Curvature, Signature and Gravitation. In general Neuroscience study, his work on Sensory system often relates to the realm of Neural correlates of consciousness, thereby connecting several areas of interest.

His Functional magnetic resonance imaging study combines topics in areas such as Frontal lobe, Neuroesthetics, Cortex and Human brain. His Pure mathematics study frequently draws connections to other fields, such as String. His biological study spans a wide range of topics, including Space, Einstein, Gravitational singularity and Twistor theory.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

Introduction to Commutative Algebra

Michael Atiyah.
(1969)

4849 Citations

The Yang-Mills equations over Riemann surfaces

Michael Francis Atiyah;Raoul Bott.
Philosophical Transactions of the Royal Society A (1982)

3013 Citations

Spectral asymmetry and Riemannian geometry. III

M. F. Atiyah;V. K. Patodi;I. M. Singer.
Mathematical Proceedings of the Cambridge Philosophical Society (1975)

2635 Citations

Selfduality in Four-Dimensional Riemannian Geometry

Michael Francis Atiyah;Nigel James Hitchin;I. M. Singer.
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (1978)

1896 Citations

Construction of Instantons

M.F. Atiyah;Nigel J. Hitchin;V.G. Drinfeld;Yu.I. Manin.
Physics Letters A (1978)

1770 Citations

THE INDEX OF ELLIPTIC OPERATORS

Michael F. Atiyah.
(1997)

1691 Citations

The moment map and equivariant cohomology

M.F. Atiyah;M.F. Atiyah;R. Bott;R. Bott.
Topology (1984)

1540 Citations

Convexity and Commuting Hamiltonians

M. F. Atiyah.
Bulletin of The London Mathematical Society (1982)

1225 Citations

Vector Bundles Over an Elliptic Curve

M. F. Atiyah.
Proceedings of The London Mathematical Society (1957)

1224 Citations

The Index of elliptic operators. 1

M.F. Atiyah;I.M. Singer.
Annals of Mathematics (1968)

1208 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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