Preprints and Publications
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Items in each section appear in reverse chronological order. Links to each document are in roughly decreasing order of utility: "DOI", "book text", or "journal text" is a published text (contact me for access if needed); "arXiv" is a stable preprint (superseded by a published version when the latter exists) posted on arxiv.org; "pdf" is a PDF file here or elsewhere (possibly unstable when indicated). Other links are explained in place.
Opinions expressed in my writings need not reflect the views of my institutional affiliates or funding agencies (for more on whom see here).
This file last modified Wednesday, 16-May-2012 19:22:09 EDT.
Contents
On separate pages:- Overflow (includes dissertation)
- Talks and presentations
- Advised projects
Books
| Formats | Title and Citation |
|---|---|
| CUP page, pdf, AMS review, errata |
p-adic Differential Equations,
Cambridge Studies in Advanced Mathematics 125, Cambridge Univ. Press, 2010.
In accordance with my publishing agreement with Cambridge University Press, I have posted a PDF version of this book. Please do not redistribute this file! Thank you. |
| AMS 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, 2008.
The original AWS notes are also available at the AWS home page. |
| 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. |
| website | Geometry Unbound, open-source e-book (see website). |
Preprints
This section includes work in progress (contact me before reading!), stable preprints, and papers accepted for publication. Anything marked "in preparation" is not circulating publicly, but if you ask nicely I might send you a draft.| Formats | Title (work in progress; unstable) |
|---|---|
| Untitled project (computation of p-adic cohomology of nondegenerate toric hypersurfaces, with David Harvey), in preparation. | |
| Good formal structures for flat meromorphic connections, III: Towards functorial modifications, in preparation. | |
| The Laurent-Robbins phenomenon (with Joe Buhler), in preparation. | |
| On the Witt vector Frobenius (with Chris Davis), draft of 3 Nov 2011. | |
| New methods for (phi, Gamma)-modules, draft of 23 Jan 2012. | |
|
Relative p-adic Hodge theory, II: (phi, Gamma)-modules (with
Ruochuan Liu), draft of 31 Jul 2011. We have not yet updated this paper to reflect the current version of "Relative p-adic Hodge theory, I". The previous version of that paper (from 20 Jul 2011) is here. |
| Formats | Title (stable preprint) |
|---|---|
| arXiv | Cohomology of arithmetic families of (phi, Gamma)-modules (with Jay Pottharst and Liang Xiao), arXiv:1203.5718 (2012). |
| Relative p-adic Hodge theory, I: Foundations (with Ruochuan Liu), submitted (version of 26 Jan 2012). | |
| arXiv | An algebraic Sato-Tate group and Sato-Tate conjecture (with Grzegorz Banaszak), arXiv:1109.4449v1 (2011), submitted. |
| Witt vectors with p-adic coefficients and Fontaine's rings (with Chris Davis), in revision (version of 21 Feb 2011). | |
|
Slope filtrations and (phi, Gamma)-modules in families
(version of 25 Feb 10).
These are the notes (edited afterwards) for a three-lecture minicourse given at the Institut Henri Poincaré (Paris) in January 2010, as part of the Galois Trimester. See also my ICM 2010 lecture notes. |
| Formats | Title (accepted for publication) |
|---|---|
| arXiv | Nonarchimedean geometry of Witt vectors, arXiv:1004.0466v5 (2012), to appear in Nagoya Mathematical Journal. |
| arXiv |
Sato-Tate distributions and Galois endomorphism modules in genus 2
(with Francesc Fité, Víctor Rotger, and Andrew Sutherland),
arXiv:1110.6638v2 (2012); to appear in Compositio Mathematica.
We have submitted final page proofs for this article. |
| arXiv |
Effective bounds for Frobenius structures (with Jan Tuitman),
arXiv:1111.0136v2 (2012);
to appear in Rendiconti del Seminario Matematico della
Università di Padova.
We have submitted final page proofs for this article. |
| pdf, sage |
Effective p-adic cohomology for cyclic cubic threefolds,
to appear in Computational Algebraic and Analytic Geometry of Low-dimensional Varieties, Contemporary Mathematics, American Mathematical
Society (version of 26 Dec 11).
I have submitted final page proofs for this article. These are the notes from a six-lecture series I gave at a summer school on p-adic cohomology, held in Mainz in September-October 2008. The "sage" link is to a Sage worksheet which I used for demonstrations during the lectures. |
| arXiv | The probability that a complete intersection is smooth (with Alina Bucur), arXiv:1003.5222v2 (2011); to appear in Journal de Théorie des Nombres de Bordeaux. |
Research (mostly) publications
Note that arXiv versions are preprints, and in some cases differ quite significantly from the published versions. To be safe, download (or ask me for) official electronic published versions.
General caution: the older papers in this list (particularly those predating my PhD in 2000) are not very representative of my current mathematical interests, or of topics in which I am willing to review papers.
| Formats | Title and Citation (published) |
|---|---|
| 2012 | |
| arxiv, journal | A construction of polynomials with squarefree discriminants, arXiv:1103.5728v1 (2011); to appear in Proceedings of the American Mathematical Society (published online 2012). |
| 2011 | |
| journal |
Fast polynomial factorization and modular composition
(with Christopher Umans), SIAM Journal of Computing
40 (2011), 1767-1802 (STOC 2008 special issue).
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". |
| DOI, arXiv |
Semistable reduction for overconvergent F-isocrystals, IV:
Local semistable reduction at nonmonomial valuations,
Compositio Mathematica 147 (2011), 467-523.
For context, see my page on the semistable reduction project. |
| DOI, arXiv | Swan conductors for p-adic differential modules, II: Global variation, Journal de l'Institut de Mathematiques de Jussieu 10 (2011), 191-224. |
| DOI | Appendix and erratum to Minhyong Kim, "Massey products for elliptic curves of rank 1" (with Jennifer Balakrishnan and Minhyong Kim), Journal of the American Mathematical Society 24 (2011), 281-291. |
| DOI, arXiv | Good formal structures for flat meromorphic connections, II: Excellent schemes, Journal of the American Mathematical Society 24 (2011), 183-229. |
| 2010 | |
| DOI, arXiv | On families of (phi, Gamma)-modules (with Ruochuan Liu), Algebra and Number Theory 4 (2010), 943-967. |
| DOI, arXiv, erratum | Good formal structures for flat meromorphic connections, I: Surfaces, Duke Mathematical Journal 154 (2010), 343-418. |
| arXiv | Relative p-adic Hodge theory and Rapoport-Zink period domains, in Proceedings of the International Congress of Mathematicians (Hyderabad, 2010), Volume II, Hindustan Book Agency/World Scientific, 2010, 258-279. |
| DOI, arXiv | Explicit Coleman integration for hyperelliptic curves (with Jennifer Balakrishnan and Robert Bradshaw), Algorithmic Number Theory (ANTS-IX), Lecture Notes in Computer Science 6197, Springer-Verlag, 2010, 16-31. |
| DOI, arXiv, erratum: DOI | Differential modules on p-adic polyannuli (with Liang Xiao), Journal de l'Institut de Mathematiques de Jussieu 9 (2010), 155-201; erratum, ibid. 9 (2010), 669-671. |
| 2009 | |
| book text, arXiv, magma |
Bounding Picard numbers of surfaces using p-adic
cohomology (with Timothy G. Abbott and David Roe), in
Arithmetic, Geometry and Coding
Theory (AGCT 2005), Séminaires et Congrès 21,
Societé
Mathématique de France, 2009, 125-159 (text available online).
The "magma" link is to (a tar file of) the Magma implementation described in the final part of the paper. See also Johan de Jong's project. |
| journal text, arXiv |
Some new directions in p-adic Hodge theory,
Journal de Théorie des Nombres de Bordeaux
21 (2009), 285-300.
These are the edited notes from my talk at the conference Journées Arithmétiques in 2007. |
| arXiv, volume | Hyperelliptic curves, L-polynomials, and random matrices (with Andrew Sutherland), in Arithmetic, Geometry, Cryptography, and Coding Theory (AGC^2T 2007), Contemporary. Math. 487, Amer. Math. Soc., 2009. |
| DOI, arXiv | Detecting integral polyhedral functions (with Philip Tynan), Confluentes Mathematici 1 (2009), 87-109. |
| arXiv, volume | p-adic cohomology, in D. Abramovich et al. (eds.), Algebraic Geometry: Seattle 2005, Proceedings of Symposia in Pure Math. 80, Amer. Math. Soc., 2009, 667-684. |
| DOI, arXiv | Semistable reduction for overconvergent F-isocrystals, III: local semistable reduction at monomial valuations, Compositio Mathematica 145 (2009), 143-172. |
| arXiv, volume |
Generalizations of product-free subsets (with Xuancheng Shao),
in T. Chow and D. Isaksen (eds.),
Communicating Mathematics,
Contemporary Math. 479, Amer. Math. Soc., 2009, 179-188.
This paper is related to "Product-free subsets of groups, then and now" (see below). |
| arXiv, volume |
Product-free subsets of groups, then and now,
in T. Chow and D. Isaksen (eds.),
Communicating Mathematics,
Contemporary Math. 479, Amer. Math. Soc., 2009, 169-178.
The volume is the proceedings from the conference of the same name in honor of Joe Gallian. |
| DOI, arXiv |
Locally decodable codes from nice subsets of finite fields and
prime factors of Mersenne numbers (with Sergey Yekhanin),
journal version: SICOMP 38 (2009), 1952-1969.
For the conference version, see 2008 publications. |
| 2008 | |
| arXiv, journal, erratum | Slope filtrations for relative Frobenius, Astérisque 319 (2008), 259-301. |
| pdf, conference |
Fast modular composition in any characteristic (with Christopher Umans),
in 49th Annual IEEE Symposium on
Foundations of Computer Science 2008 (FOCS '08), 2008, 146-155.
Invited to the FOCS 2008 special issue of SICOMP. However, it will not appear there because it is being combined with an earlier paper by Umans; see "Fast polynomial factorization and modular composition" above. |
| From quadratic reciprocity to class field theory, in
W.T. Gowers (ed.),
The
Princeton Companion to Mathematics,
Princeton Univ. Press, 2008. This is a short expository article on the cited topic. |
|
| arXiv, AMS bookstore, 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" link is to the associated source code. The "sage" link is some older source code, written jointly with Andre Wibisono. |
| DOI, 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.
For the journal version, see 2009 publications. |
| DOI, arXiv | Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach, Compositio Mathematica 144 (2008), 657-672. |
| arXiv, volume |
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. |
| DOI, arXiv | On the geometry of p-typical covers in characteristic p, Canadian Journal of Mathematics 60 (2008), 140-163. |
| 2007 | |
| journal, arXiv | The p-adic local monodromy theorem for fake annuli, Rendiconti del Seminario Mathematico della Università di Padova 118 (2007), 101-146. |
| DOI, arXiv |
Swan conductors for p-adic differential modules, I: A local construction, Algebra and Number Theory
1 (2007), 269-300.
Errata (Liang Xiao): in Hypothesis 2.1.3(b), l must be separable over k. |
|
DOI,
arXiv
erratum: pdf |
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. |
| DOI, arXiv, tar |
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 | |
| journal text, arXiv | Finite automata and algebraic extensions of function fields, Journal de Théorie des Nombres de Bordeaux 18 (2006), 379-420. |
| DOI, arXiv |
Fourier transforms and p-adic "Weil II",
Compositio Mathematica 142 (2006), 1426-1450.
The published version is somewhat abbreviated from the arXiv version. |
| DOI, arXiv, errata | Finiteness of rigid cohomology with coefficients, Duke Mathematical Journal 134 (2006), 15-97, MR 2239343. |
| DOI, arXiv | Quantum computation of zeta functions of curves, Computational Complexity 15 (2006), 1-19, MR 2226067. |
| 2005 | |
|
journal text,
arXiv
errata: journal text |
Slope filtrations revisited, Documenta Mathematica 10 (2005), 447-525, MR 2184462; errata, ibid. 12 (2007), 361-362. |
| DOI, arXiv, errata, corrected pdf | Orbits of automorphism groups of fields (with Bjorn Poonen), Journal of Algebra 293 (2005), 167-184, MR 2173971 (2006h:12006). |
| DOI, arXiv, errata | Local monodromy of p-adic differential equations: an overview, International Journal of Number Theory 1 (2005) 109-154, MR 2172335 (2006g:12013). |
| journal text, arXiv | Frobenius modules and de Jong's theorem, Mathematical Research Letters 12 (2005), 303-320, MR 2150886. |
| DOI, arXiv | In search of Robbins stability (with Jim Propp), Advances in Applied Mathematics 34 (2005), 659-668, MR 2128991. |
| journal text, arXiv | More étale covers of affine spaces in positive characteristic, Journal of Algebraic Geometry 14 (2005), 187-192, MR 2092132 (2005h:14035). |
| 2004 | |
| journal text, arXiv |
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, DOI |
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)). |
| DOI, arXiv |
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 | |
| journal text, arXiv | Semistable reduction for overconvergent F-isocrystals on a curve, Mathematical Research Letters 10 (2003), 151-159, MR 1981892 (2005e:12010). |
| 2002 | |
| DOI, arXiv |
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
errata: pdf |
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). |
| DOI | 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). |
| DOI |
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 | |
| DOI | Another combinatorial determinant, Journal of Combinatorial Theory, Series A 90 (2000), 221-223. |
| 1999 | |
| journal text | Continuous functions on compact subsets of local fields (with Manjul Bhargava), Acta Arithmetica 91 (1999), 191-198, MR1735672 (2001d:11117). |
| journal |
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). |
| 1998 | |
| journal | 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). |
| DOI, tar |
Solving constrained Pell equations, Mathematics of
Computation 67 (1998), 833-842, MR 1443123
(98g:11147). The tar file contains the Mathematica code described in the paper. |
| journal, erratum |
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). |
| 1997 | |
| DOI |
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. |
| DOI |
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 | |
| DOI |
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 | Proof of a mixed arithmetic-mean, geometric-mean inequality, American Mathematical Monthly 101 (1994), 355-357, MR 1270962 (95b:26022). |