2026 Alain Connes: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	91	68	57	5	5	259	38703

Research.com Recognitions

2026 - Research.com Mathematics in France Leader Award
2025 - Research.com Mathematics in France Leader Award
2023 - 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 - 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

Overview

Alain Connes is affiliated with the Collège de France in France and specializes in Mathematics, with a focus on subfields such as Mathematical Physics, Geometry and Topology, Statistical and Nonlinear Physics, Algebra and Number Theory, and Applied Mathematics.

Their research encompasses a variety of topics. Notable areas of focus include:

Homotopy and Cohomology in Algebraic Topology
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Advanced Operator Algebra Research
Noncommutative and Quantum Gravity Theories
Spectral Theory in Mathematical Physics
Algebraic Geometry and Number Theory

Frequent co-authors of Alain Connes include:

Caterina Consani
Walter D. van Suijlekom
Henri Moscovici
Ali H. Chamseddine
Ryszard Nest

Alain Connes has published extensively in several academic venues, notably:

arXiv (Cornell University)
Notices of the American Mathematical Society
Communications in Mathematical Physics
L'Enseignement Mathématique
Annals of Functional Analysis

Selected recent papers include:

Spectral Truncations in Noncommutative Geometry and Operator Systems, 2020, Communications in Mathematical Physics
The UV prolate spectrum matches the zeros of zeta, 2022, Proceedings of the National Academy of Sciences
Noncommutativity and physics: a non-technical review, 2023, The European Physical Journal Special Topics
Spectral triples and ζ-cycles, 2023, L'Enseignement Mathématique
On absolute algebraic geometry the affine case, 2021, Advances in Mathematics

Awards received by Alain Connes include:

Member of the European Academy of Sciences, 2004
CNRS Gold Medal, French National Centre for Scientific Research, 2004, Mathematics
Member of the National Academy of Sciences, 1997
Fellow of the American Academy of Arts and Sciences, 1989
Fields Medal of International Mathematical Union (IMU), 1982, for contributions to the theory of operator algebras including the classification and structure theorem of factors of type III and applications of C*-algebras to foliations and differential geometry
Academie des sciences, France, 1982
Ampère Prize (Prix Ampère de l'Électricité de France), French Academy of Sciences, 1980

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

2920
Citations
Non-commutative differential geometry

Alain Connes;Alain Connes

2446
Citations
Non-Commutative Geometry

Alain Connes

1522
Citations
Hopf Algebras, Renormalization and Noncommutative Geometry

Alain Connes;Dirk Kreimer

1237
Citations
Classification of Injective Factors Cases II 1 , II ∞ , III λ , λ 1

Unknown

1044
Citations
Gravity coupled with matter and the foundation of non-commutative geometry

Alain Connes

990
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

951
Citations
The Spectral action principle

Ali H. Chamseddine;Alain Connes

866
Citations
Particle models and noncommutative geometry

Alain Connes;John Lott

825
Citations
Classifying Space for Proper Actions and K-Theory of Group C*-algebras

Paul Baum;Alain Connes;Nigel Higson

735
Citations
Une classification des facteurs de type ${ m III}$

Alain Connes

720
Citations
Gravity coupled with matter and foundation of non-commutative geometry

A. Connes

713
Citations
Noncommutative Geometry, Quantum Fields and Motives

Alain Connes;Matilde Marcolli

712
Citations
An amenable equivalence relation is generated by a single transformation

A. Connes;J. Feldman;B. Weiss

666
Citations
Noncommutative geometry and reality

Alain Connes

646
Citations
The Local Index Formula in Noncommutative Geometry

Alain Connes;Henri Moscovici

630
Citations
Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory

J B Bost;Alain Connes

550
Citations
Sur la theorie non commutative de l’integration

Alain Connes

549
Citations
Gravity and the standard model with neutrino mixing

A H Chamseddine;A Connes;M Marcolli

522
Citations
The action functional in non-commutative geometry

A. Connes

520
Citations
Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group

Alain Connes;Dirk Kreimer

491
Citations

Frequent Co-Authors

Matilde Marcolli California Institute of Technology

Jean-Pierre Changeux Institut Pasteur

Michel Dubois-Violette Université Paris Cité

Dirk Kreimer Humboldt-Universität zu Berlin

Albert S. Schwarz University of California, Davis

Shahn Majid Queen Mary University of London

Roger Penrose University of Oxford

Fedor Sukochev University of New South Wales

Vaughan F. R. Jones Vanderbilt University

Thibault Damour Institut des Hautes Études Scientifiques

External Links

Wikipedia of Alain Connes Personal website of Alain Connes Google Scholar page

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