Below is a list of my research papers and other publications. Click on the link for a short abstract, or on (pdf)
to download a copy, if available.
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(pdf)
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Kisin modules, Wach modules, and p-divisible groups
over abelian extensions of Qp
In preparation.
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(pdf)
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Hida families for GL2 and p-adic Hodge theory
In preparation.
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(pdf)
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Trace morphisms in rigid cohomology and applications
to companion forms
In preparation.
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(pdf)
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Canonical Extensions of Néron Models of
Jacobians.
Algebra & Number Theory
Vol. 4, No. 2 (2010)
pp. 111-150
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(pdf)
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Canonical Integral Structures
on the de Rham Cohomology of Curves.
Annales de l'Institut Fourier
59
no. 6 (2009),
pp. 2255-2300.
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(pdf)
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Modular Curves and Ramanujan's Continued Fraction.
(With Brian Conrad)
Journal für die reine und angewandte Mathematik (Crelle's Journal)
597 (2006),
pp. 27-104.
Erratum to Appendix D.
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My Ph.D. Thesis, written at the University of Michigan under the supervision of
Brian Conrad
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(pdf)
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Compatibilities, correspondences, and integral structures
in p-adic cohomology
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(pdf)
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On the Transformation of Infinite Series (2000)
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(pdf)
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University of Michigan Undergraduate Math Club
How to compute 45 million digits of \pi (April. 16, 2009)
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(pdf)
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Number Theory Learning Seminar "Serre's Conjecture"
Serre's Conjectures
(Nov. 30, 2005; revised Nov 26., 2009)
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(pdf)
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VIGRE Number Theory Working Group "CM Abelian Varieties Seminar"
Abelian Varieties (Dec. 17, 2004)
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(pdf)
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Preliminary Exam Special Topic
Isogeny Invariance of the BSD Formula (Aug. 10, 2004)
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(pdf)
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VIGRE Number Theory Working Group "Mazur Seminar"
Finiteness of Mordell-Weil, with K. Klosin (March 9, 2004)
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(pdf)
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University of Michigan Undergraduate Math Club
Divergent Series (Feb. 05, 2004)
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(pdf)
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VIGRE Number Theory Working Group "Mazur Seminar"
Universal Families and Ruling out Small Primes (Sept. 16, 2003)
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Some MAGMA and
PARI
programs I have written to compute various things of interest.
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(txt)
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Pari script: Computing 45 million digits of \pi (April 16, 2009)
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(txt)
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Magma script: Serre's invariants for icosahedral mod 2 Galois representations (Dec 2, 2005)
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My undergraduate thesis, advised by Noam Elkies,
written to fulfill the honors requirement of concentrating in math at Harvard.
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(pdf)
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Riemann Surfaces and Modular Function Field Extensions. (April 1, 2002)
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