Guidelines

• Your paper should present, in an expository way, a topic related to but not covered in the course.
• Your paper should be about 10-20 typewritten (preferrably TeX'ed) pages.
• A short paper showing you have understood a topic thoroughly is the best.
• Try to make your treatment as concrete as possible -- include examples as well as theory. The more focused the better.

Some Possible Topics/References

• "Unbounded Operators" - Rudin, Ch. 13; Reed-Simon, Ch. VIII; Riesz-Nagy, Chap. VIII
• "Unitary Group Representations in Physics, Probability and Number Theory" (G. Mackey)
• "Fourier Analysis, Self-Adjointness" (Reed and Simon, vol. II)
• "Linear Operators", vols. I,II,III (Dunford and Schwartz)
• "Banach Algebras and Several Complex Variables" (Wermer)
• "Singular Integrals..." (E. Stein)
• "Lectures on Physics, vol. 3" (R. Feynman)
• "Ergodic Theory" (Cornfeld, Fomin and Sinai)
• "Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces" (Bedford, Keane, Series)
• "Harmonic Analysis on Symmetric Spaces" (A. Terras)
• "Divergent Series" (G. Hardy) (Tauberian theorems)
• "Bounded Analytic Functions" (J. Garnett) (BMO and H^1)
• "La Propriete T de Kazhdan" (de la Harpe, Valette)
• "Discrete Groups, Expanding Graphs and Invariant Measures" (Lubotzky)
• "Principles of Algebraic Geometry", Chapter 0 (Griffiths and Harris) (Laplacian on manifolds, Hodge theory)
• "Spin Geometry" (Lawson and Michelson) (Index theory)

Due Date

• Papers are due by the last day of class: Thursday, 6 May 1999.