Number Theory: Galois Representations,
Modular Forms, p-adic Hodge Theory
Research:
Preprints:
Serre weights for quaternion algebras (with Toby Gee)
Submitted for publication. (pdf)
Serre weights for mod p Hilbert modular forms: the totally ramified case (with Toby Gee)
Submitted for publication. (pdf)
Published papers:
Poids de l'inertie modérée de certaines
représentations cristallines (avec
Xavier
Caruso)
Journal de Théorie des Nombres de Bordeaux, to appear. (pdf)
Polygones de Hodge, de Newton et de l'inertie
modérée des
répresentations semi-stables (avec
Xavier
Caruso)
Mathematische Annalen343 (2009), no. 4, 773-789.
(pdf)
Polynomials, meanders, and paths in the lattice of
noncrossing partitions
Transactions of the A.M.S361 (2009), 3083-3107. (pdfps)
Solutions to x3=y2 in
PSL(2,Fq), 3-page appendix to "Generalised
knot groups distinguish the square and granny knots" by Christopher
Tuffley
Journal of Knot Theory and its Ramifications18
(2009), no. 8, 1129-1157. (pdf)
Breuil modules for Raynaud schemes
Journal of
Number Theory128 (2008), 2939-2950. (pdfdvi)
Harmonic algebraic curves and noncrossing partitions (with
Jeremy Martin and Ted
Singer).
Discrete and Computational Geometry37 (2007),
267-286.
(pdfps)
Modularity of some potentially Barsotti-Tate Galois
representations.
Compositio Mathematica140 (2004), no. 1, 31-63.
(pdfps)
The maximum number of points on a curve of genus 4 over
F8 is 25
(with an appendix by
Kristin Lauter).
Canadian Journal of Mathematics55 (2003), no.2,
331-352.
(pdfps). Some examples accompanying the paper:
(pdfps)
A note on the symmetric powers of the standard representation of
Sn
(with Richard P. Stanley).
Electronic Journal of Combinatorics7 (2000), R06, 8
pages.
(pdfps)
Books edited:
p-adic Geometry: Lectures from the 2007 Arizona Winter School
(co-edited with Dinesh Thakur)
University Lecture Series 45, American Mathematical Society,
Providence, RI, 2008. 203 pp.
Thesis:
Modularity of some potentially Barsotti-Tate Galois
representations, Ph.D. thesis, Harvard, 2001. Advisor: Richard Taylor.
(pdfps)
(Note: don't read this. Instead, read the Compositio paper with the
same title.)
Expository:
The Mathematics of Gauss. Ongoing project.
(pdfps)
Cohomology on Grothendieck Topologies (with Andrew Archibald). (pdfps) Warning: this paper still requires some revision.
A site-theoretic characterization of points in a topological space (with Andrew Archibald and Pete Clark).
(pdfps)
Associated Primes and Primary Decomposition. Clarifies differences among the treatments of this
subject by Atiyah-MacDonald, Bourbaki, and Matsumura. (pdfps)
Noncommutative Algebra for Part III of Serre's Linear Representations of Finite Groups. Harvard
University minor thesis. (pdfps)
Problem solving:
From January 1998 to December 2001, I edited the Challenge Board problems section of
Crux Mathematicorum with Mathematical Mayhem.
Those volumes are still subscribers-only content at the Crux website, so I cannot post them all,
but here are two sample columns:
Russell Mann and I wrote the problems for the 2001 Konhauser Problemfest. Here are the problems,
together with a brief history of the Konhauser Problemfest by Stan Wagon of Macalester College:
(pdfps)