Lecture Notes / Downloads

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.


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.

  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. 10. Elliptic PDE’s and Smoothness of Weakly Einstein Metrics of Hölder Regularity (Andrés Vargas).
  11. 11. Regularized traces and the Index formula for manifolds with boundary Alexander Cardona and César Del Corral