• Corpus ID: 117049854

Lectures on Arithmetic Noncommutative Geometry

@article{Marcolli2004LecturesOA,
  title={Lectures on Arithmetic Noncommutative Geometry},
  author={Matilde Marcolli},
  journal={arXiv: Quantum Algebra},
  year={2004}
}
  • M. Marcolli
  • Published 27 September 2004
  • Mathematics
  • arXiv: Quantum Algebra
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. 
View PDF on arXiv
8 Citations
Background Citations
1
Methods Citations
2

Figures from this paper

8 Citations

Citation Type

Citation Type

Moduli of complex curves and noncommutative geometry I: Riemann surfaces and dimension groups
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
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
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
We review the recent progress in the study of cyclic cohomology in the presence of Hopf symmetry
Matrix Model and Elliptic Curve
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
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
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…
Quantum statistical mechanics of Shimura varieties

References

SHOWING 1-10 OF 137 REFERENCES
An Introduction to Noncommutative Spaces and Their Geometries
Noncommutative Spaces and Algebras of Functions.- Projective Systems of Noncommutative Lattices.- Modules as Bundles.- A Few Elements of K-Theory.- The Spectral Calculus.- Noncommutative Differential…
Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
Abstract. We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric…
PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVES
In this paper we obtain explicit formulas for the values at the center of the critical strip of Dirichlet series connected with weight 2 parabolic forms of the group Γ0(N). In particular, these…
Non-commutative Differential Geometry
This chapter is an exposition, without any proof or detail, of some topics in Non-Commutative Differential Geometry (NCDG), which involve the cyclic theory.
Theta functions, modular invariance, and strings
We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure…
Noncommutative geometry, dynamics, and ∞-adic Arakelov geometry
Abstract In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the “closed fibers at infinity”. Manin described the…
Noncommutative Geometry and Matrix Theory: Compactification on Tori
We study toroidal compactification of Matrix theory, using ideas and results of noncommutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification…
A Short survey of noncommutative geometry
We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalization and the…
Geometry from the spectral point of view
In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A. H. D.) of an algebraA represented in a Hilbert spaceH with selfadjoint operatorD.…
Noncommutative two-tori with real multiplication as noncommutative projective varieties
...
1
2
3
4
5
...