Math 276, Topics in Topology
Fall 2007, Tu/Th 11-12:30 in 70 Evans

Chris' centralized website of notes (etc.) for this QFT semester at Berkeley. One of those course is this:

Super symmetric field theories and generalized cohomology.

Homework 1 , due Sept. 11 in class.
Homework 2 , due Sept. 25 in class.
Homework 3 , due Oct. 9 in class.
Homework 4 , due Oct. 23 in class.
Homework 5 , due Nov. 20 in class.
This is the last homework, spin structures are discussed in projects 11 and 12 (and will be taken up again in the fall 2008 course).

---

Projects as of Nov. 26. The paper versions are due Thursday, Dec. 6 in class. The mini conference will be after that.

---

We'll explain how to extend Graeme Segal's definition of a QFT over a manifold X in various directions, most significantly to super symmetric QFT's. We then show how these behave for d-dimensional space-time when d=0,1,2. It turns out that d=0 leads to closed differential forms on X, d=1 to interesting geometric representatives for elements in the K-theory of X, K(X), and that 2-dimensional susy QFT's give integral modular forms. If time permits, we'll show how open-closed theories are related to locality for these generalized cohomology theories. This will require an introduction into higher category theory.

The class will start with some basics on super geometry and super symmetric classical field theory. We'll be coordinating this introduction with Kolya Reshetikhin's course on Conformal Field Theory and Topological Quantum Field Theory , MWF 1-2 in 9 Evans. The two courses will build on each other and we strongly recommend to participate in both. There will be notes available weekly.

---

References include:
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

Notes from a previous class , for personal use only, do not distribute!

---

For your iPod: Lectures on elliptic cohomology at the Kavli Institute for Theoretical Physics

Topological Modular Forms, Mike Hopkins

Generalized Cohomology and Supersymmetric Field Theories, Part 1, Peter Teichner

Generalized Cohomology and Supersymmetric Field Theories, Part 2, Stephan Stolz

For the whole program, see Mathematical Structures in String Theory (Aug 1 - Dec 16, 2005)