58 citations · 133 across the 7 of their papers we have counts for
7 papers
Towards the fractional quantum Hall effect: a noncommutative geometry perspective
Matilde Marcolli, Varghese Mathai
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of e…
KMS states and complex multiplication
Alain Connes, Matilde Marcolli, Niranjan Ramachandran
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 e…
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…