Spinors in Geometry and Physics

Math 425 and Physics 498C

S.B. Bradlow and R.G. Leigh

Termpapers

Guidelines:

1. Select a topic. Either choose from the list below, or make one up yourself. If you choose a topic yourself, you must okay it with either Rob or Steve first.

2. Let us know by Friday November 14 of your choice.

3. The writeup should be (roughly) 7-10 TeXed pages. Due by the end of the semester.

List of Possible Topics: (more to be added)

Spin_C structures and almost complex manifolds
(Gilkey, Michelson and Lawson, Morgan)

Spin_C structures and Seiberg-Witten equations
(Gilkey, Michelson and Lawson, Morgan)

Harmonic spinors
(Hitchin, Adv. Math.14, 1974, 1-55)

Algebraic structures on Clifford algebras/spaces of spinors
(Reese Harvey)

Applications to geometry and Lie groups
(e.g., vector fields on spheres, low dimensional Lie groups, triality for spin(8) )
(Michelson and Lawson)

The index of the Dirac operator and index theorems
(Gilkey, Michelson-Lawson, John Roe, `Elliptic Operators, Topology and Asymptotic Methods')

Four dimensional geometry: self-duality, positive spin bundles and twistors
(Atiyah, Hitchin and Singer, `Self-duality in four dimensional Riemannian geometry', Proc. R. Soc. Lond. A 362, 1978 (425-461))

Witten's proof of the positive mass conjecture

Anything in chapter IV of Michelson and Lawson

Zero Modes of Dirac operators on Calabi-Yau manifolds

Supersymmetry algebras

Spin and statistics in various dimensions

Instanton moduli space and fermion zero modes