# Lectures on Arithmetic Noncommutative Geometry

@article{Marcolli2004LecturesOA, title={Lectures on Arithmetic Noncommutative Geometry}, author={Matilde Marcolli}, journal={arXiv: Quantum Algebra}, year={2004} }

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 University in May 2004. It is meant as an overview of recent results illustrating the interplay between noncommutative geometry and arithmetic geometry/number theory.

## 8 Citations

Moduli of complex curves and noncommutative geometry I: Riemann surfaces and dimension groups

- Mathematics
- 2003

This paper is a brief account of the moduli of complex curves from the perspective of noncommutative geometry. We focus on the uniformization of Riemann surfaces by the ordered K-groups of a…

Three examples of noncommutative boundaries of Shimura varieties

- Mathematics
- 2004

We study the noncommutative modular curve (which was already studied by Connes, Manin and Marcolli), and the space of geodesics on the usual modular curve, from the viewpoint of algebraic groups,…

Modular Index Invariants of Mumford Curves

- Mathematics
- 2011

We continue an investigation initiated by Consani-Marcolli of the relation between the algebraic geometry of p-adic Mumford curves and the noncommutative geometry of graph C*-algebras associated to…

Introduction to Hopf-Cyclic Cohomology

- Mathematics
- 2006

We review the recent progress in the study of cyclic cohomology in the presence of Hopf symmetry

Matrix Model and Elliptic Curve

- Physics
- 2010

Solution to the reduced matrix model of IKKT type is studied with non-zero fermion fields. A suggestion is made that our universe is made of rational numbers rather than being a continuum. To…

Riemann Surfaces in Geometry and Topology

- Mathematics
- 2015

Riemann surfaces have long been one of the central objects of study in several areas of mathematics. One landmark in the theory of Riemann surfaces is the idea of uniformization, which allows one to…

On the Magnetic Current Density in the Maxwell Equations Based on the Noether Theorem

- Mathematics, Physics
- 2019

Despite the search for supersymmetry based on abelian and non-abelian Yang-Mills gauge field theory, the Maxwell equations, as the earliest gauge field theory, are non-symmetric because of the…

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