D-Index & Metrics Best Publications
Mathematics
France
2023

D-Index & Metrics D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines.

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 82 Citations 33,565 232 World Ranking 82 National Ranking 5

Research.com Recognitions

Awards & Achievements

2023 - Research.com Mathematics in France Leader Award

2022 - Research.com Mathematics in France Leader Award

2004 - Member of the European Academy of Sciences

2004 - CNRS Gold Medal, French National Centre for Scientific Research Mathematics

1997 - Member of the National Academy of Sciences

1989 - Fellow of the American Academy of Arts and Sciences

1982 - Fields Medal of International Mathematical Union (IMU) Contributed to the theory of operator algebras, particularly the general classification and structure theorem of factors of type III, classification of automorphisms of the hyperfinite factor, classification of injective factors, and applications of the theory of C*-algebras to foliations and differential geometry in general.

1982 - Academie des sciences, France

1980 - Ampère Prize (Prix Ampère de l’Électricité de France), French Academy of Sciences

Overview

What is he best known for?

The fields of study he is best known for:

  • Pure mathematics
  • Algebra
  • Mathematical analysis

Alain Connes focuses on Pure mathematics, Noncommutative geometry, Spectral triple, Noncommutative quantum field theory and Mathematical physics. Pure mathematics and Discrete mathematics are commonly linked in his work. His Noncommutative geometry study incorporates themes from Operator algebra, Theoretical physics and Space, Mathematical analysis.

Alain Connes has included themes like Dirac operator, Standard Model and Riemannian geometry in his Spectral triple study. His Dirac operator study deals with Commutative property intersecting with Fredholm module. His Mathematical physics study combines topics in areas such as Hopf algebra, Riemann zeta function, Quantum mechanics and Homogeneous space.

His most cited work include:

  • Noncommutative Geometry and Matrix Theory: Compactification on Tori (1797 citations)
  • Non-Commutative Geometry (972 citations)
  • Non-commutative differential geometry (967 citations)

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

His scientific interests lie mostly in Pure mathematics, Noncommutative geometry, Algebra, Mathematical physics and Noncommutative quantum field theory. His Pure mathematics research is multidisciplinary, relying on both Discrete mathematics, Mathematical analysis and Group. His Noncommutative geometry research is multidisciplinary, incorporating elements of Dirac operator, Theoretical physics and Standard Model.

The Standard Model study combines topics in areas such as Higgs boson, Symmetry, Geometry and Feynman diagram. His work carried out in the field of Algebra brings together such families of science as Hopf algebra, Quantum group, Algebra representation and Quadratic algebra. The study incorporates disciplines such as Space, Riemann zeta function and Action in addition to Mathematical physics.

He most often published in these fields:

  • Pure mathematics (60.61%)
  • Noncommutative geometry (60.88%)
  • Algebra (26.17%)

What were the highlights of his more recent work (between 2013-2021)?

  • Pure mathematics (60.61%)
  • Noncommutative geometry (60.88%)
  • Semifield (10.19%)

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

Pure mathematics, Noncommutative geometry, Semifield, Dirac operator and Quotient are his primary areas of study. Alain Connes interconnects Space, Order and Character in the investigation of issues within Pure mathematics. His Noncommutative geometry research integrates issues from Structure, Theoretical physics, Quantum, Riemann hypothesis and Isometry group.

His research investigates the connection between Theoretical physics and topics such as Symmetry that intersect with issues in Scalar boson and Noncommutative quantum field theory. Alain Connes focuses mostly in the field of Dirac operator, narrowing it down to topics relating to Standard Model and, in certain cases, Feynman diagram and Quantization. His Quotient research is multidisciplinary, incorporating perspectives in Elliptic curve and Group.

Between 2013 and 2021, his most popular works were:

  • Modular curvature for noncommutative two-tori (102 citations)
  • Quanta of geometry: noncommutative aspects. (64 citations)
  • Quanta of geometry: noncommutative aspects. (64 citations)

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

  • Pure mathematics
  • Algebra
  • Geometry

Alain Connes spends much of his time researching Noncommutative geometry, Pure mathematics, Semifield, Dirac operator and Standard Model. His research integrates issues of Conformal geometry, Cyclic homology, Topos theory, Riemann hypothesis and Scalar curvature in his study of Noncommutative geometry. His work on Canonical decomposition as part of general Pure mathematics study is frequently linked to Context, therefore connecting diverse disciplines of science.

Within one scientific family, Alain Connes focuses on topics pertaining to Quotient under Semifield, and may sometimes address concerns connected to Theta function, Pointwise, Abelian group and Product. The various areas that he examines in his Dirac operator study include Noncommutative quantum field theory, Quantization, Feynman diagram, Pati–Salam model and Particle physics. His Standard Model study combines topics in areas such as Symmetry, Spontaneous symmetry breaking, Theoretical physics and Grand Unified 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.

Best Publications

Noncommutative Geometry and Matrix Theory: Compactification on Tori

Alain Connes;Michael R. Douglas;Michael R. Douglas;Albert S. Schwarz;Albert S. Schwarz;Albert S. Schwarz.
Journal of High Energy Physics (1998)

2804 Citations

Noncommutative geometry and Matrix theory

Alain Connes;Michael R. Douglas;Michael R. Douglas;Albert Schwarz;Albert Schwarz;Albert Schwarz.
Journal of High Energy Physics (1998)

2378 Citations

Non-commutative differential geometry

Alain Connes;Alain Connes.
Publications Mathématiques de l'IHÉS (1985)

2365 Citations

Non-Commutative Geometry

Alain Connes.
(1988)

1520 Citations

Hopf Algebras, Renormalization and Noncommutative Geometry

Alain Connes;Dirk Kreimer.
Communications in Mathematical Physics (1998)

1158 Citations

Gravity coupled with matter and the foundation of non-commutative geometry

Alain Connes.
Communications in Mathematical Physics (1996)

925 Citations

Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

Alain Connes;Dirk Kreimer.
Communications in Mathematical Physics (2000)

832 Citations

The Spectral action principle

Ali H. Chamseddine;Alain Connes.
Communications in Mathematical Physics (1997)

800 Citations

Particle models and noncommutative geometry

Alain Connes;John Lott.
Nuclear Physics B - Proceedings Supplements (1991)

768 Citations

Classifying Space for Proper Actions and K-Theory of Group C*-algebras

Paul Baum;Alain Connes;Nigel Higson.
(2004)

719 Citations

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