Research
I am on the mathematics faculty of Colorado State University.
In May 2000, I completed my dissertation,
"Formal Patching and Deformation of Wildly Ramified Covers of Curves"
at the University of Pennsylvania under the supervision of Professor D. Harbater.
After this, I spent three years as an assistant professor at Columbia University.
My research is in the area of arithmetic geometry and Galois theory, with the
main focus on curves and Jacobians in characteristic p.
I like to study moduli spaces of curves or abelian varieties with a group action.
I often focus on wild ramification or the p-torsion of Jacobians.
The main techniques I use are Galois theory, semi-stable reduction, deformation, and formal patching.
My research is currently supported by NSF grant DMS 07-01303.
Research activity during the period 7/2004-6/2007 was supported
in part by NSF grant DMS 04-00461.
My preprints are available here as pdf files.
pdf
Equiramified deformations of covers in positive characteristic, in preparation.
pdf
The p-rank stratification of Artin-Schreier curves (with Hui June Zhu), submitted.
pdf
Monodromy of the p-rank strata of the moduli space of curves (with Jeff Achter), to appear in
International Mathematics Research Notices.
pdf
The p-torsion of curves with large p-rank,
accepted pending revision to International Journal of Number Theory.
pdf
Curves of given p-rank with trivial automorphism group (with Jeff Achter and Darren Glass),
to appear in Michigan J. Math.
pdf
A short guide to p-torsion of abelian varieties in characteristic p,
to appear in
Computational Arithmetic Geometry, Contemporary Mathematics Series, AMS.
2007
Hyperelliptic curves with a-number 1 in small characteristic (with Arsen Elkin),
Albanian Journal of Math, 1, issue 4, 245-252.
2007
The integral monodromy of hyperelliptic and trielliptic curves (with Jeff Achter),
Math. Annalen, 338 (2007) (1):187-206.
2006
Wildly ramified covers with large genus, J. Number Theory, 119 (2006) 2:194-209.
2005
Hyperelliptic curves with prescribed p-torsion (with Darren Glass) Manuscripta, 117 (2005) 3:299-317.
2005
Questions on p-torsion of hyperelliptic curves (with Darren Glass)
in Problems from the 2004 Leiden Workshop,
Rendiconti del Seminario Matematico, 113 (2005) 145-149.
2005
On the moduli space of Klein four covers of the projective line (with Darren Glass)
in Computational Aspects of Algebraic Curves, ed. T. Shaska,
Lecture Notes Series in Computing, 13 (2005).
2005
Jacobians of quotients of Artin-Schreier curves,
in Recent progress in arithmetic and algebraic geometry, CONM. 386 (2005) 145-156.
2003
Rigidity, reduction, and ramification (with Irene Bouw),
Math. Annalen. 326 (2003) 4: 802-824.
2003
Conductors of wildly ramified covers III,
Pacific J.Math. 221 (2003) 1:163-182.
2002
Conductors of wildly ramified covers II,
C.R. Acad Sci. Paris, Ser. I 335 (2002) 484-487.
2002
Conductors of wildly ramified covers I,
C.R. Acad Sci. Paris, Ser. I 335 (2002) 481-484.
2002
Families of wildly ramified covers of curves,
Amer. J. Math. 124 (2002), 4:737-768.
2000
Construction of covers with formal and rigid geometry,
in Courbes semi-stables et groupe fondamental en geometrie algebrique, Progr. Math. 187 (2000) 157-167.
Papers advised:
In summer 2002, Jeff Achter and I were faculty advisors for a
VIGRE undergraduate research project:
A new construction of maximal curves, by A. Ebin, D. Hur, A. Katz and V. Shchogolev,
in Recent progress in arithmetic and algebraic geometry, CONM.
386 (2005) 35-45.
pdf
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