Matilde Marcolli

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It has become increasingly evident, starting from the seminal paper of Bost and Connes [3] and continuing with several more recent developments ([8], [10], [12], [13], [22], [24]), that there is a rich interplay between quantum statistical mechanics and arithmetic. In the case of number fields, the symmetries and equilibrium states of the Bost–Connes system(More)
In this paper we show that the Breitenlohner-Maison prescription for treating the presence of chiral symmetry in Dimensional Regularization fits remarkably well with the framework of noncommutative geometry. In fact, it corresponds to taking the cup product of spectral triples, with a specific spectral triple Xz whose dimension spectrum is a single complex(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 into account some congruence properties of successive convergents. This result has an application to the Mixmaster Universe model in general relativity. We then(More)
3 Morse-Bott theory 30 3.1 Framed moduli space . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Gradient flow lines . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Relative Morse Index . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4 Decay estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5 Transversality of(More)
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 spectral realization of zeros of L-functions. The analogue in characteristic zero of the action of the Frobenius on -adic cohomology is the action of the scaling group on the cyclic(More)