429 citations · 1.5k across the 138 of their papers we have counts for
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From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
Alain Connes, Matilde Marcolli
We establish a precise relation between Galois theory in its motivic form with the mathematical theory of perturbative renormalization (in the minimal subtraction scheme with dimen…
Lectures on Arithmetic Noncommutative Geometry
Matilde Marcolli
This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt Univer…
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…
Archimedean cohomology revisited
Caterina Consani, Matilde Marcolli
Archimedean cohomology provides a cohomological interpretation for the calculation of the local L-factors at archimedean places as zeta regularized determinant of a log of Frobeniu…
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…