The geometric Breuil-Mézard conjecture for two-dimensional potentially Barsotti-Tate Galois representations (with Ana Caraiani, Matthew Emerton, and Toby Gee) Preprint. Submitted. (pdf)
Local geometry of moduli stacks of two-dimensional Galois representations (with Ana Caraiani, Matthew Emerton, and Toby Gee) To appear, Proceedings of the International Colloquium on 'Arithmetic Geometry', TIFR Mumbai, Jan. 6-10, 2020 (pdf)
General Serre weight conjectures (with Toby Gee and Florian Herzig) J. Eur. Math. Soc.20 (2018), no. 12, 2859-2949 (pdf)
Potentially crystalline lifts of certain prescribed types (with Toby Gee, Florian Herzig, and Tong Liu) Documenta Math.22 (2017) 397-422 (pdf)
Serre weights for locally reducible two-dimensional Galois representations (with Fred Diamond) J. Inst. Math. Jussieu, 14 (2015), no. 3, 639-672. (pdf)
Lattices in the cohomology of Shimura curves (with Matthew Emerton and Toby Gee) Invent. math.200 (2015), no. 1, 1-96. (pdf)
The weight part of Serre's conjecture for GL(2) (with Toby Gee and Tong Liu) Forum of Mathematics, Pi3 (2015), e2 (52 pages). (pdf)
The Buzzard-Diamond-Jarvis conjecture for unitary groups (with Toby Gee and Tong Liu) J. Amer. Math. Soc.27 (2014), no. 2, 389-435. (pdf)
Crystalline extensions and the weight part of Serre's conjecture (with Toby Gee and Tong Liu) Algebra & Number Theory6-7 (2012), 1537-1559. (pdf)
Serre weights for mod p Hilbert modular forms: the totally ramified case (with Toby Gee) J. Reine Angew. Math.660 (2011), 1-26. (pdf)
Poids de l'inertie modérée de certaines représentations cristallines (with Xavier Caruso) Journal de Théorie des Nombres de Bordeaux22 (2010), 79-96. (pdf)
Polygones de Hodge, de Newton et de l'inertie modérée des
répresentations semi-stables (with 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. (pdf)
Breuil modules for Raynaud schemes Journal of Number Theory128 (2008), 2939-2950. (pdf)
Harmonic algebraic curves and noncrossing partitions (with Jeremy Martin and Ted Singer) Discrete and Computational Geometry37 (2007), 267-286. (pdf)
Modularity of some potentially Barsotti-Tate Galois representations. Compositio Mathematica140 (2004), no. 1, 31-63. (pdf)
The maximum number of points on a curve of genus 4 over F_{8} is 25 (with an appendix by Kristin Lauter) Canadian Journal of Mathematics55 (2003), no.2, 331-352. (pdf) Some examples accompanying the paper: (pdf)
A note on the symmetric powers of the standard representation of S_{n} (with Richard P. Stanley) Electronic Journal of Combinatorics7 (2000), R06, 8
pages. (pdf)
Other publications:
Solutions to x^{3}=y^{2} in PSL(2,F_{q}), 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)
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, advised by Richard Taylor (pdf) (Note: don't read this. Instead, read the Compositio paper with the
same title.)
Unpublished:
Moduli stacks of two-dimensional Galois representations (with Ana Caraiani, Matthew Emerton, and Toby Gee) Original combined version of the three papers above by the same authors (pdf)
To my chagrin, the Springer GTM Test has
surely been read more than all of the above papers combined.