** **## Final Papers

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** 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)

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** Due Date **

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