This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.
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ISBN-13
978-0-8218-4062-7 (9780821840627)
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Schweitzer Klassifikation
Invited lectures: Deformation quantization: A mini-lecture by M. Bordemann Examples of noncommutative instantons by G. Landi Topological quantum field theories, strings and orbifolds by E. Lupercio and B. Uribe Non-formal deformation quantization of Frechet-Poisson algebras: The Heisenberg Lie algebra case by H. Omori, Y. Maeda, N. Miyazaki, and A. Yoshioka Anomalies and noncommutative index theory by D. Perrot Contributed talks: N-flat connections by M. Angel and R. Diaz Dirac equation in a black hole background by A. Caceres Homological matrices by E. Castillo and R. Diaz On some qualitative properties of stratified flows by A. Giniatoulline and O. Zapata Property (T) and tensor products by irreducible finite dimensional representations for $SL_n(\mathbb{R})n\geq3$ by M. P. Gomez-Aparicio Painleve VI equation from invariant instantons by R. M. Manasliski Quantum statistical mechanics and class field theory by J. Plazas Uniqueness of Kashiwara's quantization of complex contact manifolds by P. Polesello K-theoretic gap labeling for quasicrystals by F. Ypma.
