Ezra Miller's Publications and Preprints
Books and expository articles

Theory and applications of lattice point methods for binomial ideals,
in Combinatorial Aspects of Commutative Algebra and Algebraic
Geometry, Proceedings of Abel Symposium held at Voss, Norway,
1–4 June 2009, Abel Symposia, vol. 6, Springer Berlin
Heidelberg, 2011, pp. 99–154.

Combinatorial aspects of commutative algebra
(book edited with Viviana Ene), Proceedings of an Exploratory Workshop
on Combinatorial Commutative Algebra and Computer Algebra held in
Mangalia, Romania, May 2931, 2008. Contemporary Mathematics, vol. 502,
American Mathematical Society, Providence, RI, 2009. vii+184pp.
 What is ... a toric variety?
Notices of the American Mathematical Society 55,
no. 5 (May, 2008), 586587.
official
online version. Unofficial version of 16 February 2008:
PDF

Twentyfour hours of local cohomology
(book with Srikanth Iyengar, Graham Leuschke, Anton Leykin,
Claudia Miller, Anurag Singh, and Uli Walther), Graduate
Studies in Mathematics, vol. 87, American Mathematical Society,
Providence, RI. xvi+282 pages
 Geometric
Combinatorics (book edited with Vic Reiner and Bernd
Sturmfels), Lectures from the Graduate Summer School of the
Institute for Advanced Study/Park City Mathematics Institute held
in Park City, UT, July 1131, 2004. IAS/Park City Mathematics
Series, vol. 13, American Mathematical Society, Providence, RI;
Institute for Advanced Study (IAS), Princeton, NJ, 2007. xii+691pp.
 What is geometric combinatorics?An overview of the graduate
summer school (with Vic Reiner), in Geometric combinatorics,
IAS/Park City Mathematics Series, vol. 13, American Mathematical
Society, Providence, RI, 2007, pp. 117.
arXiv:math.AG/0601202
Unofficial version of 23 December 2005:
PDF (15 figures)
 Combinatorial Commutative Algebra
(with Bernd Sturmfels), Graduate Texts in Math Vol. 227,
SpringerVerlag, New York, 2004. xiv+417 pp.
Title page, Preface, and Contents
429 pages, many figurelike objects (between 100 and 200,
depending on how you count).
No longer is the whole book available online; but there are
download options for certain parts.
 Hilbert schemes of points in the plane, appendix to
Commutative algebra of N points in the plane, by Mark
Haiman, in Luchezar Avramov et al., (eds.), Trends in
Commutative Algebra, MSRI Publications Vol. 51, Cambridge
University Press, New York, pp. 153180.
PDF
(7 pages, one figure)
 Eight lectures on monomial ideals (with David
Perkinson). COCOA VI: Proceedings of the International School,
Villa Gualino  MayJune, 1999, (Anthony V. Geramita, ed.), Queens
Papers in Pure and Applied Mathematics, no. 120, Queen's Univ.,
Kingston, ON, 2001, pp. 3105. [This item is not on MathSciNet, and I
don't know why; I've tried to fix it, to no avail.]
Contents and Preface
Submitted journal articles
Peerreviewed articles
 Systems of parameters and holonomicity of
hypergeometric systems (with Christine Berkesch and Stephen
Griffeth), preprint, 5 pages.
 Averaging metric phylogenetic trees (with Megan
Owen and Scott Provan), preprint, 43 pages.
arXiv:math.MG/1211.7046
 A projection argument for differential inclusions,
with applications to persistence of massaction kinetics
(with Manoj Gopalkrishnan and Anne Shiu), SIGMA (Symmetry,
Integrability, and Geometry: Methods and Applications),
accepted per revision, 32 pages.
arXiv:math.DS/1208.0874
 Decompositions of commutative monoid congruences and
binomial ideals (with Thomas Kahle), Algebra \& Number
Theory, accepted per revision, 62 pages.
arXiv:mathAC/1107.4699
 Sticky central limit theorems on open books
(with Thomas Hotz, Stephan Huckemann, Huiling Le, J. S. Marron,
Jonathan C. Mattingly, James Nolen, Megan Owen, Vic Patrangenaru, and
Sean Skwerer), Annals of Applied Probability (2013), to appear, 20 pages.
arXiv:math.PR/1202.4267
 Affine
stratifications from finite misère quotients, Journal
of Algebraic Combinatorics (2013), to appear, 9 pages.
arXiv:math.CO/1009.2199
 Algorithms
for lattice games (with Alan Guo), International
Journal of Game Theory (2012), to appear, 12 pages.
arXiv:math.CO/1105.5413
 Face rings
of simplicial complexes with singularities (with Isabella
Novik and Ed Swartz), Mathematische Annalen 351
(2011), 857–875.
arXiv:math.AC/1001.2812

Lattice point methods for combinatorial games
(with Alan Guo), Advances in Applied Mathematics 46
(2011), 363–378.
arXiv:math.CO/0908.3473;
Corrigendum: ibid. 48 (2012), 269–271.
arXiv:math.CO/1105.5420
 Positivity
and Kleiman transversality in equivariant Ktheory of
homogeneous spaces (with Dave Anderson and Stephen Griffeth),
J. European Math Society 13 (2011), 57–84.
arXiv:math.AG/0808.2785
 Binomial Dmodules
(with Alicia Dickenstein and Laura Matusevich), Duke
Mathematical Journal 151, no.~3 (2010), 385–429.
arXiv:math.AG/0610353
 Topological CohenMacaulay criteria for monomial ideals,
in #8 listed above under Books and expository items, pp. 137156.
arXiv:math.AC/0809.1458
Unofficial (but final, officiallyformatted) version:
PDF
DVI
LaTeX (you'll need the Contemporary Math
.cls file for this)
 Gröbner geometry of vertex decompositions and of flagged
tableaux (with Allen Knutson and Alex Yong), Journal
für die reine und angewandte Mathematik (Crelle's Journal)
630 (2009), 131.
arXiv:math.AG/0502144
Unofficial version of 15 March 2005:
PDF
DVI
LaTeX
abstract/contents
 Combinatorics of binomial primary decomposition
(with Alicia Dickenstein and Laura Matusevich),
Mathematische Zeitschrift, to appear, 19 pages.
arXiv:math.AC/0803.3846
version of 25 March 2008:
PDF
 Tableau complexes (with Allen Knutson and Alex Yong), to
appear in Israel Journal of Mathematics 163 (2008), 317343.
arXiv:math.CO/0510487
Unofficial version of 17 March 2006:
PDF
gzipped tarball
abstract/contents
 Multiplier ideals of sums via cellular resolutions
(with ShinYao Jow), Mathematical Research Letters
15 (2008), no. 2, 359373.
arXiv:math.AG/0703299
slides for AMS Toric Varieties session
Unofficial version of 4 September 2007:
PDF
DVI
LaTeX
abstract and references
 Duality of antidiagonals and pipe dreams (with Ning Jia),
Séminaire
Lotharingien de Combinatoire, B58e [the fifth paper in Issue
58] (2008), 6 pp.
arXiv:0706.3031
 Metric combinatorics of convex polyhedra: cut loci and
nonoverlapping unfoldings (with Igor Pak), Discrete and
Computational Geometry 39 (2008), no. 13, 339388.
arXiv:math.AC/0312253
Unofficial version of 22 February 2006:
PDF
abstract/table of contents
 A KleimanBertini theorem for sheaf tensor products
(with David E Speyer), Journal of Algebraic Geometry
17 (2008), no. 2, 335340.
arXiv:math.AG/0601202
Unofficial version of 8 February 2007:
PDF
DVI
 Four positive formulae for type A quiver polynomials
(with Allen Knutson and Mark Shimozono),
Inventiones Mathematicae 166 (2006), no. 2, 229325.
arXiv:math.AC/0308142
version of 16 January 2006:
PDF
DVI
(78 pages)
abstract/contents/references

Combinatorics of rank jumps in simplicial hypergeometric systems.
(with Laura Matusevich),
Proceedings of the AMS 134 (2006), 13751381.
arXiv:math.AC/0402071
unofficial version of 20 November 2004
PDF
DVI
LaTeX
abstract/references

Stanley's simplicial poset conjecture, after M. Masuda
(with Vic Reiner),
Communications in Algebra 34 (2006), no. 3, 10491053.
unofficial version of 21 December 2004:
PDF
DVI
LaTeX
 Homological methods for hypergeometric families.
(with Laura Matusevich and Uli Walther),
Journal of the American Mathematical Society 18 (2005), no. 4,
919941.
arXiv:math.AG/0406383
 Alternating formulas for Ktheoretic quiver polynomials,
Duke
Mathematical Journal 128 (2005), 117.
arXiv:math.CO/0312250
abstract
Unofficial version of 13 June 2004:
PDF
DVI
LaTeX
 Gröbner geometry of Schubert polynomials
(with Allen Knutson),
Annals of Mathematics 161 (2005), 12451318.
arXiv:math.AG/0110058
abstract/contents
Unofficial version of 9 September 2003:
PDF
DVI
LaTeX
(53 pages)
 Algorithms for graded injective resolutions and local
cohomology over semigroup rings (with David Helm), Journal of Symbolic Computation
39 (2005), 373395.
arXiv:math.AC/0309256
abstract/contents/references
Unofficial (but final journalformatted) version:
PDF
DVI
LaTeX

Toric degeneration of Schubert varieties and GelfandTsetlin polytopes
(with Misha Kogan), Advances in Mathematics
193 (2005), no. 1, 117.
arXiv:math.AG/0303208
abstract/references
Unofficial version of 16 January 2004:
PDF
DVI
LaTeX

Reciprocal domains and CohenMacaulay dcomplexes in R^d
(with Vic Reiner),
The Electronic Journal of Combinatorics 11(2) (2005)
#N1 (9 pages).
arXiv:math.CO/0408169
abstract/references
Unofficial (but final journalformatted) version:
PDF
DVI
LaTeX
 Subword complexes in Coxeter groups
(with Allen Knutson), Advances in Mathematics
184 (2004), no. 1, 161176.
arXiv:math.CO/0309259
abstract/references
Unofficial version of 11 March 2003:
PDF
DVI
LaTeX
 Bass numbers of semigroupgraded local cohomology (with David
Helm), Pacific
Journal of Math 209, no. 1 (2003), 4166.
electronically published
arXiv:math.AG/0010003
Unofficial version of 8 November 2001:
PDF
gzipped tarfile (LaTeX and .eps figure)
(19 pages, 1 figure)
 Mitosis recursion for coefficients of Schubert polynomials,
Journal
of Combinatorial Theory, Series A 103 (2003), 223235.
arXiv:math.CO/0212131
abstract
Unofficial version of 2 December 2002:
PDF
DVI
LaTeX
 CohenMacaulay quotients of normal affine semigroup rings via
irreducible resolutions Math. Research Letters
9 (2002) 117128.
arXiv:math.AC/0110096
PDF
DVI
LaTeX (9 pages, LaTeX drawings)
 Graded GreenleesMay Duality and the Cech Hull.
Local cohomology and its applications (Guanajuato, Mexico),
Lect. Notes in Pure and Appl. Math., no. 226, Dekker,
New York, 2001, pp. 233253.
PDF
DVI
LaTeX
abstract
 Planar graphs as minimal resolutions of trivariate monomial ideals
Documenta
Mathematica 7 (2002) 4390. (electronically
published: all links are to the official published version)
PDF
other
download options
abstract
 Resolutions and duality for monomial ideals,
Ph.D. thesis, University of California, Berkeley, 2000, 107 pages.
PDF (947K)
gzipped .tar file (200K)
Preface (32K)
Contents (20K)
 The Alexander duality functors and local duality with monomial
support, Journal of Algebra 231 (2000), 180234.
electronically published
abstract
Unofficial version:
PDF
gzipped tarfile (LaTeX and
.eps figures)
 Generic and cogeneric monomial ideals (with Bernd Sturmfels
and Kohji Yanagawa), Journal of Symbolic Computation 29 (2000),
691708.
electronically published
arXiv:math.AC/9812126
 Icosahedra constructed from congruent triangles.
Discrete and Computational Geometry 24 (2000), 437451.
PDF
gzipped tarfile (LaTeX and .eps figures)
abstract (my undergraduate honors thesis).
 Monomial ideals and planar graphs (with Bernd
Sturmfels). In Applied Algebra, Algebraic Algorithms and
ErrorCorrecting Codes, [M. Fossorier, H. Imai, S. Lin and
A. Poli, eds.], Proceedings of AAECC13 (Honolulu, Nov. 1999),
Springer Lecture Notes in Computer Science 1719 1928.
PDF
gzipped tarfile
(LaTeX and .eps figures)
abstract
 Multiplicities of ideals in Noetherian rings,
Beiträge zur Algebra und Geometrie 39 (1998), no. 1, 4751.
electronically
published abstract
Conference publications (peerreviewed and/or invited)
 Extended abstract: Potential applications of commutative algebra
to combinatorial game theory (with Alan Guo and Mike Weimerskirch),
in Kommutative Algebra, abstracts from the workshop held
1925 April 2009, organized by W. Bruns, H. Flenner, and C. Huneke,
Oberwolfach reports 22 (2009), 2326.
 Extended abstract: Binomial Dmodules
(with Alicia Dickenstein and Laura Matusevich), Proceedings MEGA
(Effective Methods in Algebraic Geometry) 2007, Strobl, Austria.
 Extended abstract: Cellular resolutions of multiplier ideals of sums
(with ShinYao Jow), in Topological and geometric combinatorics,
abstracts from the workshop held 28 January  3 February, 2007, organized by
A. Björner, G. Kalai, and G. Ziegler, Oberwolfach reports 4 (2007),
no. 1, 195271.
 Extended abstract: Homological methods for hypergeometric families
(with Laura Matusevich and Uli Walther), in
Convex and algebraic geometry, abstracts from the
workshop held 29 January  4 February, 2006, organized by
K. Altmann, V. Batyrev, and B. Teissier, Oberwolfach reports
3 (2006), no. 1, 253316.
 Extended abstract: Algorithms for graded injective
resolutions and local cohomology over semigroup rings
(with David Helm), Proceedings MEGA (Effective Methods in
Algebraic Geometry) Kaiserslautern, Germany, 2003.
 Extended abstract: Gröbner geometry of Schubert polynomials
(with Allen Knutson), Proceedings FPSAC 2002, Melbourne, Australia.
10 December 2001
Other publications
 Alexander duality for monomial ideals and their resolutions,
Rejecta Mathematica
1 (2009), no. 1,
1857.
arXiv:math.AC/9812095.
abstract
Some unpublished items
 Binomial Exercises
Three pages of exercises for my course on Primary
Decomposition of Binomial Ideals at the
International School on
Combinatorics "Pilar PisónCasares", 2530 January 2010.
PDF
(3 pages, no figures)
 Binomial Exercises
Five pages of exercises for my course on Multivariate
Hypergeometric Series and Binomial Ideals at the CRM
School on Interactions between Algebraic Combinatorics and
Algebraic Geometry, 2125 May 2007.
PDF
(5 pages, no figures)
 Long version of Gröbner Geometry of Schubert Polynomials
29 December 2001
Extended notes for MIT
combinatorics seminar on 16 February 2001, 19 PostScript pages
 Local cohomology has finite Bass numbers over StanleyReisner rings
(with David Helm). In this note, we use a change of rings
formula for the Cech hull to prove finiteness of Bass numbers of
local cohomology over quotients by monomial ideals.
Date last modified: Sun Dec 16 06:58:13 EST 2012
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Some of the items listed here are based upon work supported by the
National Science Foundation under Postdoctoral Grant DMS0071549,
Grant DMS0304789, or CAREER Grant DMS0449102, or supported by a
University of Minnesota McKnight LandGrant Professorship.