Durring the Fall Semester of 2011 at Harvard University Mike Hopkins taught a course on equivvariant homotopy theory and the Kervaire invariant one problem. These are my course notes. There is more material on the course website. 

• Lecture notes on Equivaraint Homotopy Theory. 

During the Fall semester of 2007 there was an unusual event at the UC Berkeley mathematics department. For various reasons three professors decided independently to run classes on various aspects of quantum field theory. Two of the professors (Reshetikhin and Teichner) decided to integrate their classes together. This web page is a compilation of lecture notes and links that students may find useful throughout the semester. Each of the course web pages will contain more links and more information specific to each course. 

All lecture notes and course material linked by this website are for personal use only. Do not distribute.

Anton Geraschenko has a conglomerate of all his course notes listed in chronological order:   PDF     Source

• Conformal Field Theory and Topological Quantum Field Theory, taught by Nicolai Reshetikhin
  • Lecture notes by Chris Schommer-Pries:   PDF
  • Lecture notes by Anton Geraschenko:   Public: PDF   Private: PDF
  • Paper deriving the Euler-Lagrange equations in a coordinate-free manner: PDF
• Super Symmetric Field Theories and Generalized Cohomology, taught by Peter Teichner
  • Lecture notes by Chris Schommer-Pries:   PDF
  • Lecture notes by Anton Geraschenko:   PDF
  • Homework:   HW1   HW2   HW3   HW4   HW5  
  • Projects:   PDF
  • References:
    • Graeme Segal, The definition of conformal field theory, Proceedings of the 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal, edited by U. Tillmann, Cambridge University Press 2004, p. 421-577.
    • Stephan Stolz and Peter Teichner, What is an elliptic object? same volume, p. 247-343.
    • Juan A. Navarro Gonzalez and Juan B. Sancho de Salas, Smooth Differentiable Spaces. Lecture Notes in Mathematics, 1824. Springer-Verlag, Berlin, 2003. xiv+188 pp.
• Richard Borcherd's seminar/mini-course on Quantum Field Theory.
  • Notes by Chris Schommer-Pries:   PDF
  • Notes by Anton Geraschenko:   Public: PDF   Private:
• Topological Conformal Field Theory Seminar run by Peter Teichner
  • Notes by Chris Schommer-Pries:   PDF
  • Papers by Kevin Costello:
    • A dual view on the ribbon graph decomposition of moduli space,
    • Topological conformal field theories and Calabi-Yau categories,
    • Topological conformal field theories and Gauge theories,
    • Renormalisation and the Batalin-Vilkovisky formalism.
      
• Topology Colloquium and Student Topology Seminar talks on QFT.
  • Notes by Chris Schommer-Pries:   to appear. (Some of these are in the TCFT notes above).
  • Bruce Driver has some lecture notes on path integrals on his website.
    • Path Integrals over Euclidean Spaces
    • Path Integrals over a Manifold