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- Alain Connes

Discipline name
H-index
Citations
Publications
World Ranking
National Ranking

Mathematics
H-index
88
Citations
36,666
241
World Ranking
41
National Ranking
4

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

2004 - Member of the European Academy of Sciences

1997 - Member of the National Academy of Sciences

1989 - Fellow of the American Academy of Arts and Sciences

1982 - Academie des sciences, France

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.

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

- 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.

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

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.

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

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

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.

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

- 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.

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)**

2290 Citations

Noncommutative Geometry and Matrix Theory: Compactification on Tori

Alain Connes;Michael R. Douglas;Michael R. Douglas;Albert Schwarz;Albert Schwarz;Albert Schwarz.

Journal of High Energy Physics **(1997)**

1820 Citations

Non-Commutative Geometry

Alain Connes.

**(1988)**

1418 Citations

Hopf Algebras, Renormalization and Noncommutative Geometry

Alain Connes;Dirk Kreimer.

Communications in Mathematical Physics **(1998)**

988 Citations

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

Alain Connes.

Communications in Mathematical Physics **(1996)**

858 Citations

The Spectral action principle

Ali H. Chamseddine;Alain Connes.

Communications in Mathematical Physics **(1997)**

747 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)**

731 Citations

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

Paul Baum;Alain Connes;Nigel Higson.

**(2004)**

694 Citations

Noncommutative Geometry, Quantum Fields and Motives

Alain Connes;Matilde Marcolli.

**(2007)**

617 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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