H-Index & Metrics Top Publications
Isadore Manuel Singer

Isadore Manuel Singer

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 34 Citations 20,397 58 World Ranking 1591 National Ranking 672

Research.com Recognitions

Awards & Achievements

2013 - Fellow of the American Mathematical Society

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.

2000 - Steele Prize for Lifetime Achievement

1983 - US President's National Medal of Science "For his inspired revival of differential geometry and its connections to analysis; for his contribution to the discovery and applications of the index theorem for differential operators; and for his leadership in using geometric and topological methods in connection with theoretical physics.", Presented by President Reagan at a White House Ceremony on February 27, 1985.

1975 - Fellow of John Simon Guggenheim Memorial Foundation

1968 - Fellow of John Simon Guggenheim Memorial Foundation

1968 - Member of the National Academy of Sciences

1959 - Fellow of Alfred P. Sloan Foundation

1959 - Fellow of the American Academy of Arts and Sciences

Overview

What is he best known for?

The fields of study he is best known for:

  • Pure mathematics
  • Mathematical analysis
  • Quantum mechanics

Pure mathematics, Mathematical analysis, Riemannian geometry, Fundamental theorem of Riemannian geometry and Index are his primary areas of study. Analytic torsion is the focus of his Pure mathematics research. Isadore Manuel Singer combines subjects such as Curvature of Riemannian manifolds, Topology, Information geometry and Spectral geometry with his study of Riemannian geometry.

His Topology research includes themes of Eigenvalues and eigenvectors, Combinatorics and Laplace operator. The various areas that Isadore Manuel Singer examines in his Information geometry study include Penrose transform, Twistor space, Twistor theory, Gauge group and Euclidean geometry. His biological study spans a wide range of topics, including Riemannian manifold, Surface, Boundary and Gaussian curvature, Curvature.

His most cited work include:

  • Spectral asymmetry and Riemannian geometry. III (1969 citations)
  • Selfduality in Four-Dimensional Riemannian Geometry (1312 citations)
  • R-Torsion and the Laplacian on Riemannian manifolds (936 citations)

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

His primary scientific interests are in Pure mathematics, Mathematical physics, Mathematical analysis, Algebra and Elliptic operator. His study connects Signature and Pure mathematics. His work deals with themes such as Boundary and Fundamental theorem of Riemannian geometry, which intersect with Mathematical analysis.

His Elliptic operator study also includes fields such as

  • Semi-elliptic operator and related Operator theory,
  • Class which intersects with area such as Twisted K-theory. His study focuses on the intersection of Instanton and fields such as Yang–Mills theory with connections in the field of Supersymmetric gauge theory. His work carried out in the field of Riemannian manifold brings together such families of science as Riemannian geometry, Differential, Line bundle and Kervaire invariant.

He most often published in these fields:

  • Pure mathematics (47.37%)
  • Mathematical physics (15.79%)
  • Mathematical analysis (15.79%)

What were the highlights of his more recent work (between 2000-2016)?

  • Pure mathematics (47.37%)
  • Elliptic operator (14.47%)
  • Riemannian manifold (6.58%)

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

Isadore Manuel Singer focuses on Pure mathematics, Elliptic operator, Riemannian manifold, Riemann surface and Invariant. His studies deal with areas such as Mapping class group and Group, Algebra as well as Pure mathematics. The study incorporates disciplines such as Vector bundle and Mirror symmetry in addition to Algebra.

His work blends Elliptic operator and Index studies together. His Riemannian manifold study combines topics from a wide range of disciplines, such as Differential, Line bundle and Kervaire invariant. His Differential research incorporates elements of Geometry, Section, Riemannian geometry and Differential topology.

Between 2000 and 2016, his most popular works were:

  • Quadratic functions in geometry, topology, and M-theory (307 citations)
  • Vertex Operators in Mathematics and Physics (264 citations)
  • The index of projective families of elliptic operators (55 citations)

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

  • Pure mathematics
  • Mathematical analysis
  • Quantum mechanics

The scientist’s investigation covers issues in Pure mathematics, Atiyah–Singer index theorem, Kervaire invariant, Differential and Riemannian manifold. Borrowing concepts from Torsion subgroup, Isadore Manuel Singer weaves in ideas under Pure mathematics. He has included themes like Complex projective space, Projective space, Projective line, Clifford analysis and Algebra in his Atiyah–Singer index theorem study.

His work in the fields of Twisted K-theory overlaps with other areas such as Index. The concepts of his Differential study are interwoven with issues in Geometry and topology, Geometry, Section, Riemannian geometry and Differential topology. His Riemannian manifold study is concerned with the larger field of Topology.

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

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

R-Torsion and the Laplacian on Riemannian manifolds

D.B. Ray;I.M. Singer.
Advances in Mathematics (1971)

1511 Citations

Curvature and the Eigenvalues of the Laplacian

H. P. McKean;I. M. Singer.
Journal of Differential Geometry (1967)

1216 Citations

The Index of elliptic operators. 1

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

1208 Citations

Some remarks on the Gribov ambiguity

I. M. Singer;I. M. Singer.
Communications in Mathematical Physics (1978)

949 Citations

Analytic torsion for complex manifolds

D.B. Ray;I.M. Singer.
Annals of Mathematics (1973)

698 Citations

The index of elliptic operators on compact manifolds

M. F. Atiyah;I. M. Singer.
Bulletin of the American Mathematical Society (1963)

692 Citations

The Index of Elliptic Operators: IV

M.F. Atiyah;I.M. Singer.
Annals of Mathematics (1971)

588 Citations

Chern-Simons perturbation theory. II

Scott Axelrod;I. M. Singer.
Journal of Differential Geometry (1994)

578 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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