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Noncommutative Line Bundles and Gerbes
We introduce noncommutative line bundles and gerbes within the framework of deformation quantization. The Seiberg-Witten map is used to construct the...
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Secondary Characteristic Classes of Lie Algebroids
We show how the intrinsic characteristic classes of Lie algebroids can be seen as characteristic classes of representations. We present two...
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Local Models for Manifolds with Symplectic Connections of Ricci Type*
We show that any symplectic manifold (Mω) of dimension 2n(n≥ 2) admitting a symplectic connection of Ricci type can locally be constructed by a...
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Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces
I give an introduction to Euclidean quantum field theory from the point of view of statistical physics, with emphasis both on Feynman graphs and on...
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An Infinite Family of Isospectral Pairs Topological Aspects
We give some basic properties of the isospectral pairs (Γ,Γ) of two bipartite graphs Γ and Γ. Then we present a systematic method of constructing an...
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Some Noncommutative Spheres
Noncommutative geometry provides us various means to deal with noncommutative phenomena in mathematics, and C*-algebras (and von Neumann algebras)...
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From Quantum Tori to Quantum Homogeneous Spaces
We construct dual objects for quantum complex projective spaces as quantum homogeneous spaces of quantum unitary groups, in which the deformation...
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Index Theorems and Noncommutative Topology
These lecture notes are mainly devoted to a K-theory proof of the Atiyah-Singer index theorem. Some applications of the K-theory to noncommutative...
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6 Fundamental “Uncertainty” in Science
The conference on “Uncertainty and Surprise” was concerned with our fundamental inability to predict future events. How can we restructure...
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17 Uncertainty as Certaint
I am trying to make money in the biotech industry from complexity science. And I am doing it with inspiration that I picked up on the edge of...
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2 Surprises in a Half Century
Ilya Prigogine participated early in the organization of our meeting and was invited to give a keynote address. Due to poor health he...
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9 A View from the Inside: The Task of Managing Uncertainty and Surprise
Let me shift the flow of the day a little bit, because I am not here to present a theory, or prove a theory. Actually, I come here with questions....
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Physical Properties
In Chap. 5 we studied solutions describing stationary counter-rotating dust disks in terms of hyperelliptic functions. As an example of this approach...
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4 The Evolutionary Complexity of Social Economic Systems: The Inevitability of Uncertainty and Surprise
In order to improve our quality of life and the successful functioning of our organisations and social institutions, or to mitigate some anticipated...
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7 The Complementary Nature of Coordination Dynamics: Toward a Science of the In-Between
My take-off point in this brief essay is the following comment from the introductory material that all the participants received for the conference...
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1 Uncertainty and Surprise: An Introduction
Much of the traditional scientific and applied scientific work in the social and natural sciences has been built on the supposition that the...
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Chiral Anomalies and Topology
When a field theory has a symmetry, global or local like in gauge theories, in the tree or classical approximation formal manipulations lead to...
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Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method
We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e....
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Index
Abstract not available
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