58 citations · 137 across the 11 of their papers we have counts for
5 papers · 1 filter
Renormalization and motivic Galois theory
Alain Connes, Matilde Marcolli
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 determi…
From Physics to Number Theory via Noncommutative Geometry. Part I: Quantum Statistical Mechanics of Q-lattices
Alain Connes, Matilde Marcolli
This is the first installment of a paper in three parts, where we use noncommutative geometry to study the space of commensurability classes of Q-lattices and we show that the arit…
Spectral triples from Mumford curves
Caterina Consani, Matilde Marcolli
We construct spectral triples associated to Schottky--Mumford curves, in such a way that the local Euler factor can be recovered from the zeta functions of such spectral triples. W…
Limiting modular symbols and the Lyapunov spectrum
Matilde Marcolli
This paper consists of variations upon the theme of limiting modular symbols. Topics covered are: an expression of limiting modular symbols as Birkhoff averages on level sets of th…
Continued fractions, modular symbols, and non-commutative geometry
Yuri I. Manin, Matilde Marcolli
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 t…