Preprints and Publications

In each section, items are arranged in reverse chronological order. Some papers can be downloaded directly from this web site by clicking on the indicated formats; "arXiv" denotes a link to the arXiv e-print server, while "journal" denotes as precise a link as I could find to the published paper, or at least its journal.

Note that arXiv versions are preprints, and may differ from published papers. If you wish to cite an unpublished paper of mine, please use an arXiv citation (by date or version number) if possible, as the location and/or structure of this web site may change over time.

If you were looking for something on this page and can't find it anymore, it may be on a subsidiary page; see the contents.

Word from our sponsor: for information about financial support, see this list and the acknowledgments sections of individual articles.

This file last modified Friday, 05-Sep-2008 16:32:50 EDT.

Contents
Books
Preprints
Research publications (includes accepted papers)
Key to format types

On separate pages:

Overflow (includes dissertation)
Talks and presentations
Advised projects
Description of the semistable reduction project (but the papers themselves appear here)

Books

Formats	Title and Citation
AMS bookstore, AWS home page	p-adic Geometry: Lectures from the 2007 Arizona Winter School (with David Savitt, Dinesh Thakur, Matt Baker, Brian Conrad, Samit Dasgupta, and Jeremy Teitelbaum), University Lecture Series 45, American Mathematical Society, to appear (expected September 2008). These are somewhat edited from the original AWS notes, which are available from the AWS home page.
review, Amazon, errata, amusing photo	The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary (with Bjorn Poonen and Ravi Vakil), Mathematical Association of America (Washington), 2002. I am now compiling an errata list for this book; see link at left. There is a longer review in the September 2004 issue of Math Horizons.
website	Geometry Unbound, e-book. I have decided to release this project as an open-source e-book. See the website for more details.

Preprints

Papers accepted for publication are listed under Research publications.

This section now includes works in progress; these appear at the top of the list. Please let me know if you are trying to read one of these, so I can help with clarifications and corrections. Also, be advised that anything listed as work in progress is unstable, so results are subject to being added, deleted, or moved. For stable work only, refer to my arXiv listings.

Formats Title (work in progress)

tex, dvi, pdf, ps Good formal structures for flat meromorphic connections, I: Surfaces, unstable draft (version of 5 Sep 08).

pdf p-adic differential equations, draft (version of 29 Jul 08).
This is a book in progress, based on notes from the course 18.787 (Topics in Number Theory, MIT, fall 2007). This version corrects a few typos from, and adds a few remarks to, the 8 Feb 08 version.
For the original course web page, see here.

Formats	Title (work in progress)
tex, dvi, pdf, ps	Good formal structures for flat meromorphic connections, I: Surfaces, unstable draft (version of 5 Sep 08).
pdf	p-adic differential equations, draft (version of 29 Jul 08). This is a book in progress, based on notes from the course 18.787 (Topics in Number Theory, MIT, fall 2007). This version corrects a few typos from, and adds a few remarks to, the 8 Feb 08 version. For the original course web page, see here.

Formats Title (stable preprint)

pdf Fast polynomial factorization and modular composition (with Christopher Umans), submitted.
This is a combined journal version of Umans's STOC 2008 paper "Fast modular composition in small characteristic" and our joint FOCS 2008 paper "Fast modular composition in any characteristic".

arXiv
Swan conductors for p-adic differential modules, II: Global variation, arXiv:0705.0031v2 (2008).
This is a complete rewrite of the previous arXiv version, using theorems from my course on p-adic differential equations (see above) and from "Differential modules on p-adic polyannuli" (see below).

arXiv Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations, arXiv:0712.3400v2 (version of 8 Feb 08).
This replaces "Semistable reduction for overconvergent F-isocrystals, IV: Refining the local approach", and concludes the series. Note that there is a logical dependence on my course on p-adic differential equations (see above). Also note that the arXiv version is not quite current.
For context, see my semistable reduction page.

arXiv Some new directions in p-adic Hodge theory, arXiv:0709.1970v1 (2007).
These are the notes from my talk at the conference Journées Arithmétiques, slightly edited.

Formats	Title (stable preprint)
pdf	Fast polynomial factorization and modular composition (with Christopher Umans), submitted. This is a combined journal version of Umans's STOC 2008 paper "Fast modular composition in small characteristic" and our joint FOCS 2008 paper "Fast modular composition in any characteristic".
arXiv	Swan conductors for p-adic differential modules, II: Global variation, arXiv:0705.0031v2 (2008). This is a complete rewrite of the previous arXiv version, using theorems from my course on p-adic differential equations (see above) and from "Differential modules on p-adic polyannuli" (see below).
arXiv	Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations, arXiv:0712.3400v2 (version of 8 Feb 08). This replaces "Semistable reduction for overconvergent F-isocrystals, IV: Refining the local approach", and concludes the series. Note that there is a logical dependence on my course on p-adic differential equations (see above). Also note that the arXiv version is not quite current. For context, see my semistable reduction page.
arXiv	Some new directions in p-adic Hodge theory, arXiv:0709.1970v1 (2007). These are the notes from my talk at the conference Journées Arithmétiques, slightly edited.

Research (mostly) publications

This section now includes articles accepted for publication but not yet published; they appear in the separate table at the beginning.

Format notes: "rep" and "ep" denote physical and electronic reprints, respectively; these are available upon request. Note that arXiv versions are preprints, and in some cases differ quite significantly from the published versions; to be safe, ask for an electronic reprint instead.

General caution (particularly addressed to journal editors looking for referees): the oldest papers in this list are from quite early in my mathematical life, and so are not representative of what I am thinking about nowadays.

Formats Title (accepted for publication)

arXiv Hyperelliptic curves, L-polynomials, and random matrices (with Andrew Sutherland), arXiv:0803.4462v2 (2008); to appear in Arithmetic, Geometry, Cryptography, and Coding Theory , Amer. Math. Soc. (series Contemporary Mathematics).

arXiv Differential modules on p-adic polyannuli (with Liang Xiao), arXiv:0804.1495v2 (2008); to appear in Journal de l'Institut de Mathematiques de Jussieu.
The arXiv version is now current.
This extends to higher-dimensional (generalized) polyannuli some results on variation of generic and subsidiary generic radii of convergence, from my course on p-adic differential equations (see above).

pdf Fast modular composition in any characteristic (with Christopher Umans), preprint (2008, updated August 4); accepted to FOCS 2008.
There will also be a somewhat longer journal version; see "Fast polynomial factorization and modular composition" above.

pdf From quadratic reciprocity to class field theory, to appear in W.T. Gowers (ed.), The Princeton Companion to Mathematics, Princeton Univ. Press.
This is a short expository article on the cited topic.

arXiv
Semistable reduction for overconvergent F-isocrystals, III: local semistable reduction at monomial valuations, arXiv:math/0609645v3 (2008); to appear in Compositio Mathematica.
The arXiv version is now current.

arXiv

p-adic cohomology, arXiv:math/0601507v2 (2008); to appear in the proceedings of the 2005 AMS Summer Research Institute in Algebraic Geometry.

arXiv Generalizations of product-free subsets (with Xuancheng Shao), arXiv:0804.0687v1 (2008); to appear in T. Chow and D. Isaksen (eds.), Communicating Mathematics, Amer. Math. Soc.
This paper is related to "Product-free subsets of groups, then and now" (see below).

arXiv Product-free subsets of groups, then and now, arXiv:0708.2295v2 (2007); to appear in T. Chow and D. Isaksen (eds.), Communicating Mathematics, Amer. Math. Soc.
The volume is the proceedings from the conference of the same name in honor of Joe Gallian.

arXiv Slope filtrations for relative Frobenius, arXiv:math/0609272v2 (version of 6 Sep 2007); to appear in Astérisque.
I have submitted the final version of this article.

arXiv, mgm.tar

Bounding Picard numbers of surfaces using p-adic cohomology (with Timothy G. Abbott and David Roe), arXiv:math/0601508 (version of 18 Jan 2007); to appear in Arithmetic, Geometry and Coding Theory (AGCT 2005), Societé Mathématique de France.
The arXiv version is now current. The tar file contains the Magma implementation described in the final part of the paper. See also Johan de Jong's project.

Formats	Title (accepted for publication)
arXiv	Hyperelliptic curves, L-polynomials, and random matrices (with Andrew Sutherland), arXiv:0803.4462v2 (2008); to appear in Arithmetic, Geometry, Cryptography, and Coding Theory , Amer. Math. Soc. (series Contemporary Mathematics).
arXiv	Differential modules on p-adic polyannuli (with Liang Xiao), arXiv:0804.1495v2 (2008); to appear in Journal de l'Institut de Mathematiques de Jussieu. The arXiv version is now current. This extends to higher-dimensional (generalized) polyannuli some results on variation of generic and subsidiary generic radii of convergence, from my course on p-adic differential equations (see above).
pdf	Fast modular composition in any characteristic (with Christopher Umans), preprint (2008, updated August 4); accepted to FOCS 2008. There will also be a somewhat longer journal version; see "Fast polynomial factorization and modular composition" above.
pdf	From quadratic reciprocity to class field theory, to appear in W.T. Gowers (ed.), The Princeton Companion to Mathematics, Princeton Univ. Press. This is a short expository article on the cited topic.
arXiv	Semistable reduction for overconvergent F-isocrystals, III: local semistable reduction at monomial valuations, arXiv:math/0609645v3 (2008); to appear in Compositio Mathematica. The arXiv version is now current.
arXiv	p-adic cohomology, arXiv:math/0601507v2 (2008); to appear in the proceedings of the 2005 AMS Summer Research Institute in Algebraic Geometry.
arXiv	Generalizations of product-free subsets (with Xuancheng Shao), arXiv:0804.0687v1 (2008); to appear in T. Chow and D. Isaksen (eds.), Communicating Mathematics, Amer. Math. Soc. This paper is related to "Product-free subsets of groups, then and now" (see below).
arXiv	Product-free subsets of groups, then and now, arXiv:0708.2295v2 (2007); to appear in T. Chow and D. Isaksen (eds.), Communicating Mathematics, Amer. Math. Soc. The volume is the proceedings from the conference of the same name in honor of Joe Gallian.
arXiv	Slope filtrations for relative Frobenius, arXiv:math/0609272v2 (version of 6 Sep 2007); to appear in Astérisque. I have submitted the final version of this article.
arXiv, mgm.tar	Bounding Picard numbers of surfaces using p-adic cohomology (with Timothy G. Abbott and David Roe), arXiv:math/0601508 (version of 18 Jan 2007); to appear in Arithmetic, Geometry and Coding Theory (AGCT 2005), Societé Mathématique de France. The arXiv version is now current. The tar file contains the Magma implementation described in the final part of the paper. See also Johan de Jong's project.

Formats Title and Citation (published)

2008

arXiv, AMS bookstore, rep, sage.tar (current code), sage (old code) Search techniques for root-unitary polynomials, in K.E.Lauter and K.A. Ribet (eds.), Computational Arithmetic Geometry, Contemporary Math. 463, Amer. Math. Soc., 2008, 71--82.
The tar file is the associated new source code; the lone sage file is the old source code, written jointly with Andre Wibisono.

arXiv Locally decodable codes from nice subsets of finite fields and prime factors of Mersenne numbers (with Sergey Yekhanin), conference version: Proc. of the 23th IEEE Computational Complexity Conference (CCC), 2008, 175-186; journal version, SICOMP, to appear.

arXiv, journal, rep, ep

Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach, Compositio Mathematica 144 (2008), 657-672.

arXiv, volume, ep Computing L-series of hyperelliptic curves (with Andrew V. Sutherland), in Algorithmic Number Theory, Springer Lecture Notes in Computer Science 5011, 2008, 312-326.
The volume is the proceedings of the ANTS VIII conference.

arXiv, journal, ep

On the geometry of p-typical covers in characteristic p, Canadian Journal of Mathematics 60 (2008), 140-163.

2007

arXiv, journal, rep

The p-adic local monodromy theorem for fake annuli, Rendiconti del Seminario Mathematico della Università di Padova 118 (2007), 101-146.

arXiv, journal, ep
Swan conductors for p-adic differential modules, I: A local construction, Algebra and Number Theory 1 (2007), 269-300.
Erratum (Liang Xiao): in Hypothesis 2.1.3(b), l must be separable over k.

arXiv, journal, rep, ep
erratum: tex, dvi, pdf, ps

Semistable reduction for overconvergent F-isocrystals, I: Unipotence and logarithmic extensions, Compositio Mathematica 143 (2007), 1164-1212.
The erratum was pointed out by Atsushi Shiho.

arXiv, journal, tar, ep

Mass formulas for local Galois representations (with an appendix by Daniel Gulotta), International Mathematics Research Notices 2007 (2007), article ID rnm021 (25 pages).
The tar file contains the programs referenced in the paper.

2006

arXiv, journal, ep

Finite automata and algebraic extensions of function fields, Journal de Théorie des Nombres de Bordeaux 18 (2006), 379-420.

arXiv, journal, ep

Fourier transforms and p-adic "Weil II", Compositio Mathematica 142 (2006), 1426-1450.
The published version is somewhat abbreviated from the arXiv version.

arXiv, journal, rep, ep

Finiteness of rigid cohomology with coefficients, Duke Mathematical Journal 134 (2006), 15-97, MR 2239343.

arXiv, journal, rep, ep

Quantum computation of zeta functions of curves, Computational Complexity 15 (2006), 1-19, MR 2226067.

2005

arXiv, journal, ep
errata: journal

Slope filtrations revisited, Documenta Mathematica 10 (2005), 447-525, MR 2184462; errata, ibid. 12 (2007), 361-362.

arXiv, journal, errata, rep, ep

Orbits of automorphism groups of fields (with Bjorn Poonen), Journal of Algebra 293 (2005), 167-184, MR 2173971 (2006h:12006).

arXiv, journal, errata, rep, ep

Local monodromy of p-adic differential equations: an overview, International Journal of Number Theory 1 (2005) 109-154, MR 2172335 (2006g:12013).

arXiv, journal, rep, ep

Frobenius modules and de Jong's theorem, Mathematical Research Letters 12 (2005), 303-320, MR 2150886.

arXiv, journal, rep, ep

In search of Robbins stability (with Jim Propp), Advances in Applied Mathematics 34 (2005), 659-668, MR 2128991.

arXiv, journal, rep, ep

More étale covers of affine spaces in positive characteristic, Journal of Algebraic Geometry 14 (2005), 187-192, MR 2092132 (2005h:14035).

2004

arXiv, journal, rep, ep

A p-adic local monodromy theorem, Annals of Mathematics 160 (2004), 93-184, MR 2119719.
The journal version differs significantly from the arXiv version due to a number of late corrections.

arXiv, rep

Full faithfulness for overconvergent F-isocrystals, in (refereed proceedings) Adolphson et al (eds.), Geometric Aspects of Dwork Theory (Volume II), de Gruyter (Berlin), 2004, 819-835, MR 2099088 (2005g:14040).
Erratum (Chris Davis): page 821, line 10: k should be k((t)).

arXiv, volume, ep

Computing zeta functions via p-adic cohomology, in Algorithmic Number Theory, Springer Lecture Notes in Computer Science 3076, 2004, 1-17, MR 2137340.
The volume is the proceedings of the ANTS VI conference.

2003

arXiv, journal, rep, ep

Semistable reduction for overconvergent F-isocrystals on a curve, Mathematical Research Letters 10 (2003), 151-159, MR 1981892 (2005e:12010).

2002

arXiv, journal, rep, ep

Étale covers of affine spaces in positive characteristic, Comptes Rendus de l'Academie des Sciences de Paris Series I 335 (2002), 921-926, MR 1952550 (2004a:14015).
With abbreviated French version. (C'est vrai!)

2001

arXiv, rep
errata: tex, dvi, pdf, ps, rep

Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, Journal of the Ramanujan Mathematical Society 16 (2001), 323-338, MR 1877805 (2002m:14019); errata, ibid. 18 (2003), 417-418, MR 2043934 (2005c:14027).

journal, rep, ep

The algebraic closure of the power series field in positive characteristic, Proceedings of the American Mathematical Society 129 (2001), 3461-3470, MR 1860477 (2003a:13025).

journal, rep, ep

Power series and p-adic algebraic closures, Journal of Number Theory 89 (2001), 324-339, MR 1845241 (2002i:11116).
Errata (Chris Davis): p. 336, line -2: missing 1 in "c_n = f(1 - b_1 p^{-1} - ...)"; p. 337, point 2 above Theorem 11: missing a in "f(i) = x_{(j+i)/a}".

2000

journal, rep, ep Another combinatorial determinant, Journal of Combinatorial Theory, Series A 90 (2000), 221-223.

1999

journal, ep

Continuous functions on compact subsets of local fields (with Manjul Bhargava), Acta Arithmetica 91 (1999), 191-198, MR1735672 (2001d:11117).

journal, ep

A weighted mixed-mean inequality, American Mathematical Monthly 106 (1999), 355-358.
A sequel to "Proof of a mixed arithmetic-mean, geometric-mean inequality" (see below).

text D. Wallner, E. Harder, and R. Agee, Key management for multicast: Issues and architectures, Internet RFC 2627, June 1999.
I am not an author on this paper; it is listed here because it is based on work I did with Noam Shazeer and Salil Vadhan at the 1995 NSA Director's Summer Program.

1998

journal, ep

The rook on the half-chessboard, or how not to diagonalize a matrix (with Lenny Ng), American Mathematical Monthly 105 (1998), 900-906, MR 1650874 (99i:15014).

tar, journal, rep, ep

Solving constrained Pell equations, Mathematics of Computation 67 (1998), 833-842, MR 1443123 (98g:11147).
From an internship at Supercomputing Research Center (now Center for Computing Sciences). The tar file contains the Mathematica code described in the paper.

journal, ep
Product-free subsets of groups, American Mathematical Monthly 105 (1998), 819-824.
This mostly expository article expands upon "Large product-free subsets of finite groups" (see below). Erratum (pointed out in this paper): the proof of Theorem 3 is not correct as stated, as it does not allow for the possibility that g^2 is in S. Otherwise put, Theorem 3 as stated only applies to the modified notion of product-free subsets, where you consider products of distinct pairs of elements of the subset.

1997

journal, ep

Urn sampling and a majorization inequality, Journal of Combinatorial Theory Series A 79 (1997), 173-179, MR 1449756 (97m:05002).
From the 1996 Duluth REU.

original article, comment, backstory

Comments on: G.S. Bhat and C.D. Savage, Balanced Gray codes, Electronic Journal of Combinatorics 3(1) (1996) R25 (comment posted 9 Apr 1997), MR 1715389 (2000g:05009).
The backstory explains why I bothered mentioning this one-paragraph comment.

journal, rep, ep

Large product-free subsets of finite groups, Journal of Combinatorial Theory Series A 77 (1997), 339-343, MR 1429085 (97m:20033).
From the 1994 Duluth REU. It seems that a bit of interest in this paper has been generated by a recent paper of Gowers; see also this preprint.

1996

journal, rep, ep

Outerplanar partitions of planar graphs, Journal of Combinatorial Theory Series B 67 (1996), 238-248, MR 1399677 (98a:05057).
From the 1994 Duluth REU.

1994

journal, ep

Proof of a mixed arithmetic-mean, geometric-mean inequality, American Mathematical Monthly 101 (1994), 355-357, MR 1270962 (95b:26022).

Formats	Title and Citation (published)
2008
arXiv, AMS bookstore, rep, sage.tar (current code), sage (old code)	Search techniques for root-unitary polynomials, in K.E.Lauter and K.A. Ribet (eds.), Computational Arithmetic Geometry, Contemporary Math. 463, Amer. Math. Soc., 2008, 71--82. The tar file is the associated new source code; the lone sage file is the old source code, written jointly with Andre Wibisono.
arXiv	Locally decodable codes from nice subsets of finite fields and prime factors of Mersenne numbers (with Sergey Yekhanin), conference version: Proc. of the 23th IEEE Computational Complexity Conference (CCC), 2008, 175-186; journal version, SICOMP, to appear.
arXiv, journal, rep, ep	Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach, Compositio Mathematica 144 (2008), 657-672.
arXiv, volume, ep	Computing L-series of hyperelliptic curves (with Andrew V. Sutherland), in Algorithmic Number Theory, Springer Lecture Notes in Computer Science 5011, 2008, 312-326. The volume is the proceedings of the ANTS VIII conference.
arXiv, journal, ep	On the geometry of p-typical covers in characteristic p, Canadian Journal of Mathematics 60 (2008), 140-163.
2007
arXiv, journal, rep	The p-adic local monodromy theorem for fake annuli, Rendiconti del Seminario Mathematico della Università di Padova 118 (2007), 101-146.
arXiv, journal, ep	Swan conductors for p-adic differential modules, I: A local construction, Algebra and Number Theory 1 (2007), 269-300. Erratum (Liang Xiao): in Hypothesis 2.1.3(b), l must be separable over k.
arXiv, journal, rep, ep erratum: tex, dvi, pdf, ps	Semistable reduction for overconvergent F-isocrystals, I: Unipotence and logarithmic extensions, Compositio Mathematica 143 (2007), 1164-1212. The erratum was pointed out by Atsushi Shiho.
arXiv, journal, tar, ep	Mass formulas for local Galois representations (with an appendix by Daniel Gulotta), International Mathematics Research Notices 2007 (2007), article ID rnm021 (25 pages). The tar file contains the programs referenced in the paper.
2006
arXiv, journal, ep	Finite automata and algebraic extensions of function fields, Journal de Théorie des Nombres de Bordeaux 18 (2006), 379-420.
arXiv, journal, ep	Fourier transforms and p-adic "Weil II", Compositio Mathematica 142 (2006), 1426-1450. The published version is somewhat abbreviated from the arXiv version.
arXiv, journal, rep, ep	Finiteness of rigid cohomology with coefficients, Duke Mathematical Journal 134 (2006), 15-97, MR 2239343.
arXiv, journal, rep, ep	Quantum computation of zeta functions of curves, Computational Complexity 15 (2006), 1-19, MR 2226067.
2005
arXiv, journal, ep errata: journal	Slope filtrations revisited, Documenta Mathematica 10 (2005), 447-525, MR 2184462; errata, ibid. 12 (2007), 361-362.
arXiv, journal, errata, rep, ep	Orbits of automorphism groups of fields (with Bjorn Poonen), Journal of Algebra 293 (2005), 167-184, MR 2173971 (2006h:12006).
arXiv, journal, errata, rep, ep	Local monodromy of p-adic differential equations: an overview, International Journal of Number Theory 1 (2005) 109-154, MR 2172335 (2006g:12013).
arXiv, journal, rep, ep	Frobenius modules and de Jong's theorem, Mathematical Research Letters 12 (2005), 303-320, MR 2150886.
arXiv, journal, rep, ep	In search of Robbins stability (with Jim Propp), Advances in Applied Mathematics 34 (2005), 659-668, MR 2128991.
arXiv, journal, rep, ep	More étale covers of affine spaces in positive characteristic, Journal of Algebraic Geometry 14 (2005), 187-192, MR 2092132 (2005h:14035).
2004
arXiv, journal, rep, ep	A p-adic local monodromy theorem, Annals of Mathematics 160 (2004), 93-184, MR 2119719. The journal version differs significantly from the arXiv version due to a number of late corrections.
arXiv, rep	Full faithfulness for overconvergent F-isocrystals, in (refereed proceedings) Adolphson et al (eds.), Geometric Aspects of Dwork Theory (Volume II), de Gruyter (Berlin), 2004, 819-835, MR 2099088 (2005g:14040). Erratum (Chris Davis): page 821, line 10: k should be k((t)).
arXiv, volume, ep	Computing zeta functions via p-adic cohomology, in Algorithmic Number Theory, Springer Lecture Notes in Computer Science 3076, 2004, 1-17, MR 2137340. The volume is the proceedings of the ANTS VI conference.
2003
arXiv, journal, rep, ep	Semistable reduction for overconvergent F-isocrystals on a curve, Mathematical Research Letters 10 (2003), 151-159, MR 1981892 (2005e:12010).
2002
arXiv, journal, rep, ep	Étale covers of affine spaces in positive characteristic, Comptes Rendus de l'Academie des Sciences de Paris Series I 335 (2002), 921-926, MR 1952550 (2004a:14015). With abbreviated French version. (C'est vrai!)
2001
arXiv, rep errata: tex, dvi, pdf, ps, rep	Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, Journal of the Ramanujan Mathematical Society 16 (2001), 323-338, MR 1877805 (2002m:14019); errata, ibid. 18 (2003), 417-418, MR 2043934 (2005c:14027).
journal, rep, ep	The algebraic closure of the power series field in positive characteristic, Proceedings of the American Mathematical Society 129 (2001), 3461-3470, MR 1860477 (2003a:13025).
journal, rep, ep	Power series and p-adic algebraic closures, Journal of Number Theory 89 (2001), 324-339, MR 1845241 (2002i:11116). Errata (Chris Davis): p. 336, line -2: missing 1 in "c_n = f(1 - b_1 p^{-1} - ...)"; p. 337, point 2 above Theorem 11: missing a in "f(i) = x_{(j+i)/a}".
2000
journal, rep, ep	Another combinatorial determinant, Journal of Combinatorial Theory, Series A 90 (2000), 221-223.
1999
journal, ep	Continuous functions on compact subsets of local fields (with Manjul Bhargava), Acta Arithmetica 91 (1999), 191-198, MR1735672 (2001d:11117).
journal, ep	A weighted mixed-mean inequality, American Mathematical Monthly 106 (1999), 355-358. A sequel to "Proof of a mixed arithmetic-mean, geometric-mean inequality" (see below).
text	D. Wallner, E. Harder, and R. Agee, Key management for multicast: Issues and architectures, Internet RFC 2627, June 1999. I am not an author on this paper; it is listed here because it is based on work I did with Noam Shazeer and Salil Vadhan at the 1995 NSA Director's Summer Program.
1998
journal, ep	The rook on the half-chessboard, or how not to diagonalize a matrix (with Lenny Ng), American Mathematical Monthly 105 (1998), 900-906, MR 1650874 (99i:15014).
tar, journal, rep, ep	Solving constrained Pell equations, Mathematics of Computation 67 (1998), 833-842, MR 1443123 (98g:11147). From an internship at Supercomputing Research Center (now Center for Computing Sciences). The tar file contains the Mathematica code described in the paper.
journal, ep	Product-free subsets of groups, American Mathematical Monthly 105 (1998), 819-824. This mostly expository article expands upon "Large product-free subsets of finite groups" (see below). Erratum (pointed out in this paper): the proof of Theorem 3 is not correct as stated, as it does not allow for the possibility that g^2 is in S. Otherwise put, Theorem 3 as stated only applies to the modified notion of product-free subsets, where you consider products of distinct pairs of elements of the subset.
1997
journal, ep	Urn sampling and a majorization inequality, Journal of Combinatorial Theory Series A 79 (1997), 173-179, MR 1449756 (97m:05002). From the 1996 Duluth REU.
original article, comment, backstory	Comments on: G.S. Bhat and C.D. Savage, Balanced Gray codes, Electronic Journal of Combinatorics 3(1) (1996) R25 (comment posted 9 Apr 1997), MR 1715389 (2000g:05009). The backstory explains why I bothered mentioning this one-paragraph comment.
journal, rep, ep	Large product-free subsets of finite groups, Journal of Combinatorial Theory Series A 77 (1997), 339-343, MR 1429085 (97m:20033). From the 1994 Duluth REU. It seems that a bit of interest in this paper has been generated by a recent paper of Gowers; see also this preprint.
1996
journal, rep, ep	Outerplanar partitions of planar graphs, Journal of Combinatorial Theory Series B 67 (1996), 238-248, MR 1399677 (98a:05057). From the 1994 Duluth REU.
1994
journal, ep	Proof of a mixed arithmetic-mean, geometric-mean inequality, American Mathematical Monthly 101 (1994), 355-357, MR 1270962 (95b:26022).

Key to format types

tex: TeX file (plain text)
dvi: DVI file (view with xdvi)
pdf: PDF file (view with Acrobat Reader, ggv, etc.)
ps.gz: compressed Postscript file (uncompress with gunzip, then view with GhostScript; note that your browser may uncompress automatically)
rep: physical reprint (published version) available upon request
ep: electronic eprint (published version) available upon request
mgm.tar: tar file whose entries are Magma source files
sage: SAGE source file
sage.tar: tar file whose entries are SAGE source files
arXiv: link to arXiv e-print server (follow link, then download in your favorite format); typically not a published version
journal: link to article at journal's web site (follow link if permitted at your institution, otherwise request an eprint from me)

Preprints and Publications

Contents

Books

Preprints

Research (mostly) publications

Key to format types