edited by Alexander Cardona (Université Blaise Pascal, Clermont-Ferrand, France & Universidad de Los Andes, Bogotá, Colombia) , Sylvie Paycha (Université Blaise Pascal, Clermont-Ferrand, France) , & Hernan Ocampo (Universidad del Valle, Cali, Colombia)

This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.

• Noncommutative Geometry:
  • Hopf Algebras in Noncommutative Geometry (J C Várilly)
  • The Noncommutative Geometry of Aperiodic Solids (J Bellissard)
  • Noncommutative Geometry and Abstract Integration Theory (M-T Benameur)
• Topological Field Theory:
  • Introduction to Quantum Invariants of 3-Manifolds, Topological Quantum Field Theories and Modular Categories (C Blanchet)
  • An Introduction to Donaldson–Witten Theory (M Mariño)
• Supergravity and String Theory:
  • (Super)-Gravities Beyond 4 Dimensions (J Zanelli)
  • Introductory Lectures on String Theory and the AdS/CFT Correspondence (A Pankiewicz & S Theisen)
• Short Communications:
  • Group Contractions and Its Consequences Upon Representations of Different Spatial Symmetry Groups (M Ayala-Sánchez & R W Haase)
  • Phase Anomalies as Trace Anomalies in Chern–Simons Theory (A Cardona)
  • Deligne Cohomology for Orbifolds, Discrete Torsion and B-Fields (E Lupercio & B Uribe)