These are various course notes for courses and lectures I’ve attended. (Warning this is still under construction and some links are broken).

## Equivariant Homotopy Theory and Kervaire Invariant One Problem, Fall 2011

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.

## Chromatic Stable Homotopy Theory, Spring 2010

Durring the Spring Semester of 2010 at Harvard University Jacob Lurie taught a course on the chromatic picture of stable homotopy theory. The course description promised to begin with Quillen’s work on cohomology theories and formal group laws and culminate with the resolution of the Ravenel conjectures via the work of Devinatz-Hopkins-Smith.

The following lecture notes should be considered preliminary, and may contain errors or typos. Hopefully as the semester progresses these will be discovered and eliminated, but you can help speed along the process by letting me know of any errors you happen to discover. Your help is always appreciated.

- Lecture notes on Chromatic Homotopy. You can also have my TeX Files.

There are alternative lecture notes that Jacob is writing up which are available on the course website.

## Quantum Field Theory Lecture Notes, Fall 2007

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.

- Graeme Segal,

- 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
- 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.