Lectures Notes & Downloads

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Here you can find lecture notes from previous schools, as well as additional notes prepared by students. Links to the proceedings (1999-2011) are displayed below.

2011 

Geometric, Algebraic and Topological Methods for Quantum Field Theory

Proceedings of the 2011 Villa de Leyva Summer School.
Edited by: Alexander Cardona, Carolina Neira-Jiménez, Hernán Ocampo, Sylvie Paycha and Andrés F. Reyes-Lega.

These volume was published with World Scientific and covers topics such as spectral geometry and index theory, noncommutative models and the standrard model, algebraic geometry and Feynman periods, generalized geometries and string theory, differential geometry and gravity and conformal field theory and integrability. If you are interested in this volume, you may find it either in the publisher's website (WS) or in Amazon.

  Contents:
  1. Spectral Geometry (B. Iochum).
  2. Index Theory for non-compact G-manifolds (M. Braverman and L. Cano).
  3. Generalized Euler Characteristics, Graph Hypersurfaces, and Feynman Periods(P. Aluffi).
  4. Gravitation Theory and Chern-Simon Forms (J. Zanelli).
  5. Noncommutative Geometry Models for Particle Physics (M. Marcolli).
  6. Noncommutative Spacetimes and Quantum Physics (A.P. Balachandran).
  7. Integrability and the AdS/CFT Correspondence (M. Staudacher).
  8. Compactifications of String Theory and Generalized Geometry (M. Graña and H. Triendl).
  9. Grupoids and Poisson Sigma Models with Boundary (A. Cattaneo and I. Contrearas).
  10. A Survey on Orbifold String Topology (A. Ángel).
  11. Grothendieck Ring Class of Banana and Flower Graphs (P. Morales-Almazán)
  12. On the Geometry Underlying a Real Lie Algebra Representation (R. Vargas Le-Bert)

2009 

Geometric and Topological Methods for Quantum Field Theory

Proceedings of the 2009 Villa de Leyva Summer School.
Edited by: Alexander Cardona, Iván Contreras and Andrés F. Reyes-Lega.

These volume was published with Cambridge University Press and covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric- aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. If you are interested in this volume, you may find it either in the publisher's website (CUP) or in Amazon.

  Contents:
  1. A brief introduction to Dirac manifolds (Henrique Bursztyn).
  2. Differential geometry of holomorphic vector bundles on a curve (Florent Schaffhauser).
  3. Paths towards an extension of Chern–Weil calculus to a class of infinite dimensional vector bundles (Sylvie Paycha).
  4. Introduction to Feynman integrals (Stefan Weinzierl).
  5. Iterated integrals in quantum field theory (Francis Brown).
  6. Geometric Issues in Quantum Field Theory and String Theory (Luis J. Boya).
  7. Geometric Aspects of the Standard Model and the Mysteries of Matter (Florian Scheck).
  8. Absence of singular continuous spectrum for some geometric Laplacians (Leonardo A. Cano García).
  9. Models for formal groupoids (Iván Contreras).
  10. Elliptic PDE's and Smoothness of Weakly Einstein Metrics of Hölder Regularity (Andrés Vargas).
  11. Regularized traces and the Index formula for manifolds with boundary (Alexander Cardona and César Del Corral)
Deadline for registration: November 30, 2022