Expository papers

An introduction to cobordism theory
(ps
pdf)
My minor thesis, written under the supervision of Raoul Bott and Franklin
Peterson. Nothing terribly original here, although I think that,
as these things go, it's a fairly painless introduction to the subject.

The BanachTarski paradox
(ps
pdf)
An extraexplicit exposition of this wellknown result.
The highlight, from a purely visual standpoint, is pages 10 and 11.

The inflationrestriction sequence: an introduction to spectral
sequences
(ps
pdf)
A quick introduction to spectral sequences. My most popular paper, for some
reason. I suspect that it's the pictures.
 The modular curves X_{0}(11) and X_{1}(11)
(ps)
An introduction to modular curves focused on
the motivating problem of analyzing rational 11torsion on elliptic curves.
It originated in some notes of Matthew Emerton and some computations of
Keith Conrad and Robert Pollack, and ostensibly had some connection to the
1999 Park City Mathematics Institute.

Lfunctions and cyclotomic units
(ps
pdf)
A writeup of a lecture on Euler systems
I gave at the 2001 Arizona Winter School.

The Euler system of Heegner points
(ps
pdf)
An exposition of Kolyvagin's work on the conjecture of Birch and
SwinnertonDyer, inspired by a student project I supervised at the 2001
Arizona Winter School.

Lectures on the Dirichlet class number formula for imaginary quadratic fields
(ps
pdf)
A writeup of some lectures I gave at the Ross program in the summer of 2004.
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