Alain Connes

Geometry and Topology · 2000–2015

A researcher in the Science corpus: 21 papers; trusts 16 researchers and is trusted by 53 researchers here, as inferred from the citation graph.

Subfields

• Geometry and Topology — 35 citations into it; #889 of 7,422 by trust here, #726 by citations
• Mathematical Physics — 34 citations into it; #304 of 8,562 by trust here, #267 by citations
• Algebra and Number Theory — 18 citations into it; #219 of 2,864 by trust here, #222 by citations
• Discrete Mathematics and Combinatorics — 11 citations into it; #1,507 of 2,017 by trust here, #1,382 by citations
• Computational Theory and Mathematics — 7 citations into it; #2,466 of 12,182 by trust here, #2,419 by citations

Whom Alain Connes trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. R. Meyer
2. H. Moscovici
3. Sorin Popa
4. A. Chamseddine
5. Matilde Marcolli
6. C. Consani
7. Philippe Biane
8. David A. Cox
9. C. Soulé
10. Kenley Jung

Who trusts Alain Connes overall

1. Farzad Fathizadeh
2. Masoud Khalkhali
3. Sorin Popa
4. H. Moscovici
5. J. Bellissard
6. Matilde Marcolli
7. Joseph Keir
8. James M. Borger
9. Jeffrey C. Lagarias
10. Marius Junge

Papers from Alain Connes's perspective

Ordered by how strongly the researchers Alain Connes trusts endorse each paper. Same corpus, a different order for every researcher.

1. The Gauss-Bonnet Theorem for Noncommutative Two Tori With a General Conformal Structure
2. On a representation of the idele class group related to primes and zeros of L-functions
3. On a class of type $II_1$ factors with Betti numbers invariants
4. Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry
5. Cyclic Cohomology and Hopf Algebra Symmetry
6. Observables in effective gravity
7. The Baum-Connes Conjecture via Localization of Categories
8. Modular Hecke Algebras and their Hopf Symmetry
9. Noncommutative two-tori with real multiplication as noncommutative projective varieties
10. Convergence of Bogoliubov’s Method of Renormalization in Momentum Space

Their papers

• Classifying Space for Proper Actions and K-Theory of Group C*-algebras (2004) — 614 citations
• The Gauss-Bonnet Theorem for the noncommutative two torus (2009) — 126 citations
• Geometry of the Arithmetic Site (2015) — 49 citations
• The Arithmetic Site (2014) — 56 citations
• The hyperring of adèle classes (2011) — 115 citations
• Modular Curvature for Noncommutative Two-Tori (2011) — 140 citations
• On the notion of geometry over (2010) — 51 citations
• Schemes over 𝔽1 and zeta functions (2009) — 75 citations
• On the spectral characterization of manifolds (2008) — 301 citations
• Fun with $\F_1$ (2008) — 55 citations
• Noncommutative Geometry, Quantum Fields and Motives (2007) — 644 citations
• Why the Standard Model (2007) — 150 citations
• Gravity and the standard model with neutrino mixing (2006) — 466 citations
• Type III and spectral triples (2006) — 135 citations
• Noncommutative geometry and the standard model with neutrino mixing (2006) — 155 citations
• L 2-homology for von Neumann algebras (2003) — 99 citations
• Modular Hecke Algebras and their Hopf Symmetry (2003) — 75 citations
• Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry (2001) — 72 citations
• Cyclic Cohomology and Hopf Algebra Symmetry (2000) — 123 citations
• A Short survey of noncommutative geometry (2000) — 208 citations