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We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary… (More)

Quantum fields, noncommutative spaces, and motives The Riemann zeta function and noncommutative geometry Quantum statistical mechanics and Galois symmetries Endomotives, thermodynamics, and the Weil… (More)

We give here a comprehensive treatment of the mathematical theory of per-turbative renormalization (in the minimal subtraction scheme with dimensional regularization), in the framework of the… (More)

One of the many remarkable properties of conformal field theory in two dimensions is its connection to algebraic geometry. Since every compact Riemann surface is a projective algebraic curve, many… (More)

Abstract
In Arakelov theory a completion of an arithmetic surface is
achieved by enlarging the group of divisors by formal linear
combinations of the “closed fibers at infinity”. Manin described
the… (More)

We investigate the nature of divergences in quantum field theory, showing that they are organized in the structure of a certain `` motivic Galois group'', which is uniquely determined and universal… (More)

- Matilde Marcolli
- 2009

AbstractWe compare two different models of noncommutative geometry of the cyclotomic tower, both based on an arithmetic algebra of functions of roots of unity and an action by endomorphisms, the… (More)

We consider representations of Cuntz–Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these… (More)

Abstract.We construct a quantum statistical mechanical system which generalizes the Bost–Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the explicit… (More)

Abstract. Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss-Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take… (More)