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Noncommutative geometry and motives: the thermodynamics of endomotives
Alain Connes, Caterina Consani, Matilde Marcolli
We combine aspects of the theory of motives in algebraic geometry with noncommutative geometry and the classification of factors to obtain a cohomological interpretation of the spe…
Scale Invariance in the Spectral Action
Ali H. Chamseddine, Alain Connes
The arbitrary mass scale in the spectral action for the Dirac operator in the spectral action is made dynamical by introducing a dilaton field. We evaluate all the low-energy terms…
Non commutative finite dimensional manifolds II. Moduli space and structure of non commutative 3-spheres
Alain Connes, Michel Dubois-Violette
This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic…
Transgressions of the Godbillon-Vey class and Rademacher functions
Alain Connes, Henri Moscovici
We construct, out of modular symbols, 1-traces that are invariant with respect to the actions of the Hopf algebra $\Hc_{1}$ on the crossed product $\Ac_{Q}$ of the algebra of modul…
Background independent geometry and Hopf cyclic cohomology
Alain Connes, Henri Moscovici
This is primarily a survey of the way in which Hopf cyclic cohomology has emerged and evolved, in close relationship with the application of the noncommutative local index formula…
Quantum fields and motives
Alain Connes, Matilde Marcolli
This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common un…