eBook ISBN:  9780821881132 
Product Code:  CONM/434.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821881132 
Product Code:  CONM/434.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 434; 2007; 255 ppMSC: Primary 53; 55; 58; 81
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.
ReadershipGraduate students and research mathematicians interested in topological and geometric method in quantum field theory.

Table of Contents

Invited Lectures [ MR 2348965 ]

Martin Bordemann — Deformation quantization: a minilecture [ MR 2349629 ]

Giovanni Landi — Examples of noncommutative instantons [ MR 2349630 ]

Ernesto Lupercio and Bernardo Uribe — Topological quantum field theories, strings and orbifolds [ MR 2349631 ]

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka — Nonformal deformation quantization of FréchetPoisson algebras: the Heisenberg and Lie algebra case [ MR 2349632 ]

Denis Perrot — Anomalies and noncommutative index theory [ MR 2349633 ]

Contributed talks [ MR 2348965 ]

Mauricio Ángel and Rafael Díaz — $N$flat connections [ MR 2349634 ]

Alejandro Cáceres — Dirac equation in a black hole background [ MR 2349635 ]

Edmundo Castillo and Rafael Díaz — Homological matrices [ MR 2349636 ]

Andrei Giniatoulline and Oswaldo Zapata — On some qualitative properties of stratified flows [ MR 2349637 ]

Maria Paula GomezAparicio — Property (T) and tensor products by irreducible finite dimensional representations for ${\rm SL}_n(\Bbb R)\ n\geq 3$ [ MR 2349638 ]

Richard Muñiz Manasliski — Painlevé VI equation from invariant instantons [ MR 2349639 ]

Jorge Plazas — Quantum statistical mechanics and class field theory [ MR 2349640 ]

Pietro Polesello — Uniqueness of Kashiwara’s quantization of complex contact manifolds [ MR 2349641 ]

Fonger Ypma — $K$theoretic gap labeling for quasicrystals [ MR 2349642 ]


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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.
Graduate students and research mathematicians interested in topological and geometric method in quantum field theory.

Invited Lectures [ MR 2348965 ]

Martin Bordemann — Deformation quantization: a minilecture [ MR 2349629 ]

Giovanni Landi — Examples of noncommutative instantons [ MR 2349630 ]

Ernesto Lupercio and Bernardo Uribe — Topological quantum field theories, strings and orbifolds [ MR 2349631 ]

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka — Nonformal deformation quantization of FréchetPoisson algebras: the Heisenberg and Lie algebra case [ MR 2349632 ]

Denis Perrot — Anomalies and noncommutative index theory [ MR 2349633 ]

Contributed talks [ MR 2348965 ]

Mauricio Ángel and Rafael Díaz — $N$flat connections [ MR 2349634 ]

Alejandro Cáceres — Dirac equation in a black hole background [ MR 2349635 ]

Edmundo Castillo and Rafael Díaz — Homological matrices [ MR 2349636 ]

Andrei Giniatoulline and Oswaldo Zapata — On some qualitative properties of stratified flows [ MR 2349637 ]

Maria Paula GomezAparicio — Property (T) and tensor products by irreducible finite dimensional representations for ${\rm SL}_n(\Bbb R)\ n\geq 3$ [ MR 2349638 ]

Richard Muñiz Manasliski — Painlevé VI equation from invariant instantons [ MR 2349639 ]

Jorge Plazas — Quantum statistical mechanics and class field theory [ MR 2349640 ]

Pietro Polesello — Uniqueness of Kashiwara’s quantization of complex contact manifolds [ MR 2349641 ]

Fonger Ypma — $K$theoretic gap labeling for quasicrystals [ MR 2349642 ]