Connes is currently Professor at the Collège de France, IHÉS, in France, as well as at Ohio State University and Vanderbilt University. Connes’ work focuses on algebra, or what is known as “operator algebra,” an important area in functional analysis. Born in France, Connes received his undergraduate degree in Mathematics from the prestigious École normale supérieure in Paris and his Ph.D. from the University Pierre et Marie Curie.

Among other notables, Connes was a member of Bourbaki, a group of predominantly French mathematicians who formed after the First World War in response to the loss of so many mathematicians in the wake of the war. The Bourbaki group (a pseudonym—there was no person “Bourbaki”) consisted of world-class mathematicians who contributed to mathematics by taking up the task of writing major new texts. Connes is also known for fundamental work in mathematics, such as the Connes embedding problem, a problem in algebra. He is also known for the Baum-Connes conjecture and has made important contributions to differential geometry.

Connes was awarded the Fields Medal in 1982. He is a member of the French Academy of Sciences as well as the US National Academy of Sciences (and others, including Danish, Norwegian, and Russian).

**Featured in Top Influential Mathematicians Today**

According to Wikipedia, Alain Connes is a French mathematician, and a theoretical physicist, known for his contributions to the study of operator algebras and noncommutative geometry. He is a Professor at the Collège de France, IHÉS, Ohio State University and Vanderbilt University. He was awarded the Fields Medal in 1982.

- Noncommutative geometry
- Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Non-commutative differential geometry
- Gravity coupled with matter and the foundation of non-commutative geometry
- Classification of Injective Factors Cases II 1 , II ∞ , III λ , λ 1
- Hopf Algebras, Renormalization and Noncommutative Geometry
- Non-Commutative Geometry
- Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem
- The Spectral Action Principle
- An amenable equivalence relation is generated by a single transformation
- Classifying Space for Proper Actions and K-Theory of Group C*-algebras
- Noncommutative geometry and reality
- Particle models and noncommutative geometry
- Noncommutative Geometry, Quantum Fields and Motives
- Gravity and the standard model with neutrino mixing
- Hopf Algebras, Cyclic Cohomology and the Transverse Index Theorem
- Renormalization in quantum field theory and the Riemann-Hilbert problem
- Noncommutative Manifolds, the Instanton Algebra¶and Isospectral Deformations
- CYCLIC COHOMOLOGY, THE NOVIKOV CONJECTURE AND HYPERBOLIC GROUPS
- Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group
- The Longitudinal Index Theorem for Foliations
- Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
- An analogue of the thom isomorphism for crossed products of a C∗ algebra by an action of R
- Kac Algebras and Duality of Locally Compact Groups
- Sur la theorie non commutative de l’integration
- A survey of foliations and operator algebras
- Compact metric spaces, Fredholm modules, and hyperfiniteness
- Outer conjugacy classes of automorphisms of factors
- Noncommutative Finite-Dimensional Manifolds. I. Spherical Manifolds and Related Examples
- The action functional in non-commutative geometry
- Von Neumann algebra automorphisms and time-thermodynamics relation in general covariant quantum theories
- Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
- On the spectral characterization of manifolds
- Yang-Mills for noncommutative two-tori
- The Local Index Formula in Noncommutative Geometry
- Dynamical entropy ofC* algebras and von Neumann algebras
- Property T for von Neumann Algebras
- THE FLOW OF WEIGHTS ON FACTORS OF TYPE III Part1
- Almost periodic states and factors of type III1
- Cyclic cohomology and the transverse fundamental class of a foliation
- Geometry from the spectral point of view
- A Short survey of noncommutative geometry
- Entropy for automorphisms of II1 von neumann algebras
- Entire cyclic cohomology of Banach algebras and characters of θ-summable Fredholm modules
- On the spatial theory of von Neumann algebras
- CHERN CHARACTER FOR DISCRETE GROUPS
- Noncommutative geometry and the standard model with neutrino mixing
- Why the Standard Model
- Closed star products and cyclic cohomology
- Property T and asymptotically invariant sequences
- Noncommutative Geometry Year 2000
- Cyclic Cohomology and Hopf Algebra Symmetry
- Dynamical Entropy of C* Algebras and yon Neumann Algebras
- On the cohomology of operator algebras
- CYCLIC COHOMOLOGY, QUANTUM GROUP SYMMETRIES AND THE LOCAL INDEX FORMULA FOR SUq(2)
- Cyclic Cohomology and Hopf Algebras
- Beyond the spectral standard model: emergence of Pati-Salam unification
- Modular Curvature for Noncommutative Two-Tori
- Type III and spectral triples
- Rankin-Cohen Brackets and the Hopf Algebra of Transverse Geometry
- THE METRIC ASPECT OF NONCOMMUTATIVE GEOMETRY
- The Gauss-Bonnet Theorem for the noncommutative two torus
- The L2-index theorem for homogeneous spaces of Lie groups
- Resilience of the spectral standard model
- Schemes over 𝔽1 and zeta functions
- Quantum fields and motives
- From Physics to Number theory via Noncommutative Geometry
- Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
- A Factor Not Anti-Isomorphic to Itself
- L 2-homology for von Neumann algebras
- Conversations on mind, matter, and mathematics
- A walk in the noncommutative garden
- Group cohomology with lipschitz control and higher signatures
- Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function
- The hyperring of adèle classes
- Homogeneity of the state space of factors of type III1
- Conceptual explanation for the algebra in the noncommutative approach to the standard model.
- Caract6re multiplicatif d'un module de Fredholm
- Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry
- Inner fluctuations in noncommutative geometry without the first order condition
- Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory
- Modular Hecke Algebras and their Hopf Symmetry
- Inner fluctuations of the spectral action
- KMS states and complex multiplication
- Moduli Space and Structure of Noncommutative 3-Spheres
- Noncommutative geometry and motives: The thermodynamics of endomotives
- Quasiconformal mappings, operators on hilbert space, and local formulae for characteristic classes☆
- The Uncanny Precision of the Spectral Action
- Yang–Mills Algebra
- Insertion and Elimination: the Doubly Infinite Lie Algebra of Feynman Graphs
- Scale invariance in the spectral action
- Operator Algebras and Applications: K-theory for discrete groups
- From Physics to Number Theory via Noncommutative Geometry. Part I: Quantum Statistical Mechanics of Q-lattices
- Non-commutative geometry and physics
- A ${\text{II}}_1 $ factor with two nonconjugate Cartan subalgebras
- Approximately transitive flows and ITPFI factors
- Measure space automorphisms, the normalizers of their full groups, and approximate finiteness
- Fun with $\F_1$
- On the notion of geometry over
- Renormalization and motivic Galois theory
- From monoids to hyperstructures: in search of an absolute arithmetic
- Non-Commutative Di erential Geometry
- The Arithmetic Site
- Quanta of geometry: noncommutative aspects.
- Transgression and the Chern character of finite-dimensional K-cycles
- Geometry and the quantum: basics
- Grand unification in the spectral Pati-Salam model
- C*algebras and differential geometry
- Quantum gravity boundary terms from the spectral action of noncommutative space.
- Characteristic one, entropy and the absolute point
- Geometry of the Arithmetic Site
- On hyperfinite factors of type III0 and Krieger's factors
- Noncommutative Geometry and Physics
- On the Chern character of θ summable Fredholm modules
- Quantized calculus and applications
- The von Neumann algebra of a foliation
- Yang-Mills and Some Related Algebras
- Hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks
- a Unitary Invariant in Riemannian Geometry
- Leafwise Homotopy Equivalence and Rational Pontrjagin Classes
- On the notion of geometry over $\F_1$
- Triangle of Thoughts
- Background independent geometry and Hopf cyclic cohomology
- Noncommutative Finite Dimensional Manifolds II: Moduli Space and Structure of Noncommutative 3-Spheres
- The Weil Proof and the Geometry of the Adèles Class Space
- Spectral action for Robertson-Walker metrics
- A Universal Action Formula
- Operator algebras, unitary representations, enveloping algebras, and invariant theory : actes du colloque en l'honneur de Jacques Dixmier
- The term a_4 in the heat kernel expansion of noncommutative tori
- Noncommutative Differential Geometry and the Structure of Space Time
- Universal Thickening of the Field of Real Numbers
- Characteristic 1 , entropy and the absolute point
- Cyclic Cohomology, Noncommutative Geometry and Quantum Group Symmetries
- Noncommutative Geometry and the Riemann Zeta Function
- KMS states and complex multiplication. (Part II)
- Introduction to non commutative differential geometry
- The local index formula in noncommutative geometry
- A new proof of Morley's theorem
- THE WITT CONSTRUCTION IN CHARACTERISTIC ONE AND QUANTIZATION
- Embeddings ofU(1)-current algebras in non-commutative algebras of classical statistical mechanics
- On the arithmetic of the BC-system
- Cyclic homology, Serre's local factors and the -operations
- ON THE SPECTRAL CHARACTERIZATION
- THE MODULAR THEORY
- A Property of Parallelograms Inscribed in Ellipses
- Causality, quantum theory and cosmology
- Homological algebra in characteristic one
- Q-lattices: Quantum statistical mechanics and Galois theory
- A Factor not Anti-Imsomorphic to itself
- The universal thickening of the eld of real numbers
- A Dress for SM the Beggar
- 1 2 M ay 2 00 7 Quantum Gravity Boundary Terms from Spectral Action
- Trace formula on the Adele Class Space and Weil Positivity
- Noncommutative geometric spaces with boundary: Spectral action
- Geometry and the Quantum
- Trace theorem for quasi-Fuchsian groups
- SP ACE-TIME FROM THE SPECTRAL POINT OF VIEW
- The Scaling Site
- Cyclic Cohomology, Hopf Algebras and the Modular Theory
- On Space and Time
- Absolute algebra and Segal's Γ-rings: Au dessous de Spec(Z)‾
- Spectral truncations in noncommutative geometry and operator systems
- Classification of automorphisms of hyperfinite factors of type ${\text{II}}_1$ and ${\text{II}}_\infty$ and application to type ${\text{III}}$ factors
- Entropy and the Spectral Action
- Projective geometry in characteristic one and the epicyclic category
- Geometry of the scaling site
- Non commutative finite dimensional manifolds II. Moduli space and structure of non commutative 3-spheres
- Diameters of state spaces of type III factors
- Conformal trace theorem for Julia sets of quadratic polynomials
- The $L^2$-index theorem for homogeneous spaces
- Matrix Vieta Theorem Revisited
- From Local Perturbation Theory to Hopf and Lie Algebras of Feynman Graphs
- An Essay on the Riemann Hypothesis
- A construction of approximately finite-dimensional non-ITPFI factors
- Lessons from Quantum Field Theory
- Cyclic structures and the topos of simplicial sets
- Noncommutative Geometry, the Spectral Standpoint
- Cyclic Cohomology and Hopf Symmetry
- Noncom m utativeGeom etry and M atrix Theory: Com pactication on Tori
- Errata: ``The flow of weights on factors of type ${\rm III}$''
- Gabor Analysis, Noncommutative Tori and Feichtinger's Algebra
- The hyperring of ad\`ele classes
- Absolute algebra and Segal's Gamma sets
- Cyclic homology, Serre's local factors and the $\lambda$-operations
- ASPHERICAL GRAVITATIONAL MONOPOLES
- Symétries quantiques : Les Houches, session LXIV, 1 août - 8 septembre 1995 = Quantum symmetries
- On the hierarchy of W. Krieger
- A VIEW OF MATHEMATICS
- On the Foundations of Noncommutative Geometry
- Noncommutative geometry, arithmetic, and related topics : proceedings of the Twenty-first Meeting of the Japan-U.S. Mathematics Institute
- On Absolute Algebraic Geometry, the affine case
- The Dynamical Entropy of Quantum Systems
- The Riemann-Roch strategy, Complex lift of the Scaling Site
- Where physics meets metaphysics
- Renormalization and Galois Theories
- THE INSTANTON ALGEBRA AND ISOSPECTRAL DEFORMATIONS
- On Feynman graphs as elements of a Hopf algebra
- Transgressions of the Godbillon-Vey Class and Rademacher functions
- On the fine structure of spacetime
- The Scaling Hamiltonian
- Noncommutative Geometry and Global Analysis
- Morse Inequalities for Foliations
- BUILDING COSMOLOGICAL MODELS VIA NONCOMMUTATIVE GEOMETRY
- Quanta of Geometry
- The cyclic and epicyclic sites
- Non-commutative Geometry and the Spectral Model of Space-time
- LOCAL HOCHSCHILD HOMOLOGY OF HILBERT-SCHMIDT OPERATORS ON SIMPLICIAL SPACES
- Weil positivity and trace formula the archimedean place
- Institute for Mathematical Physics Trace Formula in Noncommutative Geometry and the Zeros of the Riemann Zeta Function Trace Formula in Noncommutative Geometry and the Zeros of the Riemann Zeta Function
- On Space and Time: Preface
- Quasi-inner functions and local factors
- Noncommutative Geometry: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000
- Editorial (dedication of this issue to Huzihiro Araki)
- Noncommutative Geometry for Symmetric Non-Self-Adjoint Operators
- Noncommunicative differential geometry
- BIRS Workshop on Noncommutative Geometry
- $\overline{Spec\mathbb Z}$ and the Gromov norm
- Local area-preserving algebras for two-dimensional surfaces
- Quantum fields, noncommutative spaces, and motives
- Renomalization and the Riemann-Hilbert problem
- Segal's Gamma rings and universal arithmetic
- K1-INJECTIVITY FOR PROPERLY INFINITE C ∗-ALGEBRAS
- On Space and Time edited by Shahn Majid
- The nature of time
- The Group Property of the Invariant $S$ of von Neumann Algebras.
- O A ] 2 0 Se p 20 03 L 2-HOMOLOGY FOR VON NEUMANN ALGEBRAS
- On an idea of Michael Atiyah
- Almost Periodic States and Factors of Type III, A. CONNES
- ANOMALIES, DIMENSIONAL REGULARIZATION AND NONCOMMUTATIVE GEOMETRY: UNFINISHED DRAFT
- Uffe Haagerup–In Memoriam
- The BC-system and L-functions
- Spectral Triples and Zeta-Cycles
- Noncom m utativeG eom etry and M atrix Theory : Com pacti cation on Tori
- Motivic rhythms
- The dark Universe
- The Carlitz group of the rationals September 11 , 2018
- Endomotives, thermodynamics, and the Weil explicit formula
- Non-commutative Geometry, Index Theory and Mathematical Physics
- Noncommutative geometry and particle physics , after
- Addendum: Discussions at the Dead Sea
- Book Reviews
- Renormalization and the Riemann-Hilbert correspondence
- SERIJA III www.math.hr/glasnik
- The End of an Era
- Q A ] 1 6 D ec 2 00 3 Modular Hecke Algebras and their Hopf Symmetry
- Sir Michael Atiyah, a Knight Mathematician A tribute to Michael Atiyah, an inspiration and a friend
- Preface to the tenth Takagi Lectures
- Standard Model, Gravity, Neutrino Mixing, Ncg 2007 Joint with A.chamseddine and A.connes
- [Werner's syndrome].
- LECTURE 1. STATEMENT OF CONNES’ EMBEDDING CONJECTURE
- N ov 2 00 8 The Uncanny Precision of the Spectral Action
- Noncommutative geometry and global analysis : conference in honor of Henri Moscovici, June 29-July 4, 2009, Bonn, Germany
- S ep 2 01 4 Quanta of Geometry
- An essay on the Riemann Hypothesis 3 function fields as done
- Number theory / Algebraic geometry The Arithmetic Site ✩ Le Site arithmétique
- Iteration of the exterior power on representation rings
- How Noncommutative Geometry looks at Arithmetic
- J an 2 00 3 Modular Hecke Algebras and their Hopf Symmetry
- Classification of injective factors Cases II,, IIL, IIIH, X ? 1
- A Property of Parallelograms Inscribed in Ellipses Author ( s ) :
- Dynamical Entropy of C * Algebras and yon
- Spherical isotropy representations . Non-commutative differential geometry . Transformation de fourier et majoration de sommes exponentielles . Corrections to, Metaplectic forms
- Periods ( and why the fundamental theorem of calculus conjec-turely is a fundamental theorem )
- 2 8 Se p 20 03 Modular Hecke Algebras and their Hopf Symmetry
- Around Wilson's theorem
- Quantum statistical mechanics and Galois symmetries
- The Carlitz group of the rationals.
- ec 2 00 5 Scale Invariance in the Spectral Action
- A Lecture on Noncommutative Geometry
- Dedicated to Henri Moscovici, with admiration and friendship
- The Riemann zeta function and noncommutative geometry
- L-HOMOLOGY FOR VON NEUMANN ALGEBRAS
- Fe b 20 15 Quanta of Geometry : Noncommutative Aspects
- Space and Time in the Foundations of Mathematics, or some challenges in the interactions with other sciences1
- 2 3 M ay 2 00 5 Background independent geometry and Hopf cyclic cohomology
- 1 SPECTRAL TRIPLES and ζ-CYCLES
- What is New Today in a Mathematician ’ s Work ? Conversation between

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