A short survey of noncommutative geometry

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 Riemann-Hilbert problem. We discuss at length two issues. The first is the relevance of the paradigm of geometric space, based on spectral considerations, which is central in the theory. As a simple illust...

A Survey of Noncommutative Geometry Methods for Group Algebras

In this survey we shall report about a K-theoretic approach to study group algebras. Following the example of the group of affine transformations of the straight line, the method consists of: 1. Construction of irreducible group representations (orbit method, category O ), 2. Decomposition of the group algebra into a sequence of repeated extensions, and finally 3. Computation of the extension i...

a structural survey of the polish posters

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Cosmological perturbations and short distance physics from noncommutative geometry

We investigate the possible effects on the evolution of perturbations in the inflationary epoch due to short distance physics. We introduce a suitable non local action for the inflaton field, suggested by Noncommutative Geometry, and obtained by adopting a generalized star product on a Friedmann-Robertson-Walker background. In particular, we study how the presence of a length scale where spacet...

Noncommutative geometry