Quantization, Geometry and Noncommutative Structures in Mathematics and Physics

Quantization, Geometry and Noncommutative Structures in Mathematics and Physics (A. Cardona, H. Ocampo, P. Morales, S. Paycha, A.F. Reyes Lega (Eds.)).- General Overview (Alexander Cardona, Sylvie Paycha and Andrés F. Reyes Lega).- Introduction.- Poisson Geometry and Classical Dynamics.- Geometric and Deformation Quantization.- Noncommutative Geometry and Quantum Groups.- Deformation Quantization and Group Actions (Simone Gutt).- What do we mean by quantization?.- Deformation Quantization.- Fedosov's star products on a symplectic manifold.- Classification of Poisson deformations and star products.- Star products on Poisson manifolds and formality.- Group actions in deformation quantization.- Reduction in deformation quantization.- Some remarks about convergence.- . Principal fiber bundles in non-commutative geometry (Christian Kassel).- Introduction.- Review of principal fiber bundles.- Basic ideas of non-commutative geometry.- From groups to Hopf algebras.- Quantum groups associated with SL2(C).- Group actions in non-commutative geometry.- Hopf Galois extensions.- Flat deformations of Hopf algebras.- An Introduction to Nichols Algebras (Nicolás Andruskiewitsch).- Preliminaries.- Braided tensor categories.- Nichols algebras.- Classes of Nichols algebras.- Quantum Field Theory in Curved Space-Time (Andrés F. Reyes Lega).- Introduction.- Quantum Field Theory in Minkowski Space-Time.- Quantum Field Theory in Curved Space-Time.- Cosmology.- An Introduction to Pure Spinor Superstring Theory (Nathan Berkovits and Humberto Gomez).- Introduction.- Particle and Superparticle.- Pure Spinor Superstring.- Appendix.- Introduction to Elliptic Fibrations (Mboyo Esole).- Introduction.- Elliptic curves over C.- Elliptic fibrations.- Kodaira-Néron classification of singular fibers.- Miranda models.- Batalin-Vilkovisky formalism as a theory of integration for polyvectors (Pierre J. Clavier and Viet Dang Nguyen).- Motivations and program.- BV integral.- Gauge fixing.- Master equations.- Conclusion.- Split Chern-Simons theory in the BV-BFV formalism (Alberto S. Cattaneo, Pavel Mnev, and Konstantin Wernli).- Introduction.- Overview of the BV and BV-BFV formalisms.- Chern-Simons theory as a BF-like theory.- Split Chern-Simons theory on the solid torus.- Conclusions and outlook.- Weighted direct product of spectral triples (Kevin Falk).- Introduction and motivation. -Weighted direct product of spectral triples.- Example of weighted direct product with Toeplitz operators.- Index.