**Noncommutative Geometry, Quantum Fields and Motives**

by Alain Connes, Matilde Marcolli

**Publisher**: American Mathematical Society 2007**ISBN/ASIN**: 0821842102**ISBN-13**: 9780821842102**Number of pages**: 705

**Description**:

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools.

Download or read it online for free here:

**Download link**

(6.4MB, PDF)

## Similar books

**Lectures on complex geometry, Calabi-Yau manifolds and toric geometry**

by

**Vincent Bouchard**-

**arXiv**

These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds.

(

**6371**views)

**Geometry and Topology in Electronic Structure Theory**

by

**Raffaele Resta**-

**University of Trieste**

From the table of contents: Introduction; Early discoveries; Berry-ology (geometry in nonrelativistic quantum mechanics); Manifestations of the Berry phase; Modern theory of polarization; Quantum metric and the theory of the insulating state.

(

**7228**views)

**Topology and Physics: A Historical Essay**

by

**C. Nash**-

**arXiv**

In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.

(

**10352**views)

**Differential Geometry in Physics**

by

**Gabriel Lugo**-

**University of North Carolina at Wilmington**

These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.

(

**14651**views)