Ezra Miller's Publications and Preprints
Not current; last updated 16 December 2012
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 29-31, 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), 586-587.
online version.   Unofficial version of 16 February 2008:
Twenty-four 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
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 11-31, 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. 1-17.
Unofficial version of 23 December 2005:
PDF   (15 figures)
- Combinatorial Commutative Algebra
(with Bernd Sturmfels), Graduate Texts in Math Vol. 227,
Springer-Verlag, New York, 2004. xiv+417 pp.
Title page, Preface, and Contents
429 pages, many figure-like 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. 153-180.
(7 pages, one figure)
- Eight lectures on monomial ideals (with David
Perkinson).   COCOA VI: Proceedings of the International School,
Villa Gualino -- May-June, 1999, (Anthony V. Geramita, ed.), Queens
Papers in Pure and Applied Mathematics, no. 120, Queen's Univ.,
Kingston, ON, 2001, pp. 3-105. [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
- 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.
- A projection argument for differential inclusions,
with applications to persistence of mass-action kinetics
(with Manoj Gopalkrishnan and Anne Shiu), SIGMA (Symmetry,
Integrability, and Geometry: Methods and Applications),
accepted per revision, 32 pages.
- Decompositions of commutative monoid congruences and
binomial ideals (with Thomas Kahle), Algebra \& Number
Theory, accepted per revision, 62 pages.
- 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.
stratifications from finite misère quotients, Journal
of Algebraic Combinatorics (2013), to appear, 9 pages.
for lattice games (with Alan Guo), International
Journal of Game Theory (2012), to appear, 12 pages.
- Face rings
of simplicial complexes with singularities (with Isabella
Novik and Ed Swartz), Mathematische Annalen 351
Lattice point methods for combinatorial games
(with Alan Guo), Advances in Applied Mathematics 46
Corrigendum: ibid. 48 (2012), 269–271.
and Kleiman transversality in equivariant K-theory of
homogeneous spaces (with Dave Anderson and Stephen Griffeth),
J. European Math Society 13 (2011), 57–84.
- Binomial D-modules
(with Alicia Dickenstein and Laura Matusevich), Duke
Mathematical Journal 151, no.~3 (2010), 385–429.
- Topological Cohen-Macaulay criteria for monomial ideals,
in #8 listed above under Books and expository items, pp. 137-156.
Unofficial (but final, officially-formatted) version:
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), 1-31.
Unofficial version of 15 March 2005:
- Combinatorics of binomial primary decomposition
(with Alicia Dickenstein and Laura Matusevich),
Mathematische Zeitschrift, to appear, 19 pages.
version of 25 March 2008:
- Tableau complexes (with Allen Knutson and Alex Yong), to
appear in Israel Journal of Mathematics 163 (2008), 317-343.
Unofficial version of 17 March 2006:
- Multiplier ideals of sums via cellular resolutions
(with Shin-Yao Jow), Mathematical Research Letters
15 (2008), no. 2, 359-373.
slides for AMS Toric Varieties session
Unofficial version of 4 September 2007:
abstract and references
- Duality of antidiagonals and pipe dreams (with Ning Jia),
Lotharingien de Combinatoire, B58e [the fifth paper in Issue
58] (2008), 6 pp.
- Metric combinatorics of convex polyhedra: cut loci and
nonoverlapping unfoldings (with Igor Pak), Discrete and
Computational Geometry 39 (2008), no. 1-3, 339-388.
Unofficial version of 22 February 2006:
abstract/table of contents
- A Kleiman-Bertini theorem for sheaf tensor products
(with David E Speyer), Journal of Algebraic Geometry
17 (2008), no. 2, 335-340.
Unofficial version of 8 February 2007:
- Four positive formulae for type A quiver polynomials
(with Allen Knutson and Mark Shimozono),
Inventiones Mathematicae 166 (2006), no. 2, 229-325.
version of 16 January 2006:
Combinatorics of rank jumps in simplicial hypergeometric systems.
(with Laura Matusevich),
Proceedings of the AMS 134 (2006), 1375-1381.
unofficial version of 20 November 2004
Stanley's simplicial poset conjecture, after M. Masuda
(with Vic Reiner),
Communications in Algebra 34 (2006), no. 3, 1049-1053.
unofficial version of 21 December 2004:
- Homological methods for hypergeometric families.
(with Laura Matusevich and Uli Walther),
Journal of the American Mathematical Society 18 (2005), no. 4,
- Alternating formulas for K-theoretic quiver polynomials,
Mathematical Journal 128 (2005), 1-17.
Unofficial version of 13 June 2004:
- Gröbner geometry of Schubert polynomials
(with Allen Knutson),
Annals of Mathematics 161 (2005), 1245-1318.
Unofficial version of 9 September 2003:
- Algorithms for graded injective resolutions and local
cohomology over semigroup rings (with David Helm), Journal of Symbolic Computation
39 (2005), 373-395.
Unofficial (but final journal-formatted) version:
Toric degeneration of Schubert varieties and Gelfand-Tsetlin polytopes
(with Misha Kogan), Advances in Mathematics
193 (2005), no. 1, 1-17.
Unofficial version of 16 January 2004:
Reciprocal domains and Cohen-Macaulay d-complexes in R^d
(with Vic Reiner),
The Electronic Journal of Combinatorics 11(2) (2005)
#N1 (9 pages).
Unofficial (but final journal-formatted) version:
- Subword complexes in Coxeter groups
(with Allen Knutson), Advances in Mathematics
184 (2004), no. 1, 161-176.
Unofficial version of 11 March 2003:
- Bass numbers of semigroup-graded local cohomology (with David
Journal of Math 209, no. 1 (2003), 41-66.
Unofficial version of 8 November 2001:
gzipped tarfile (LaTeX and .eps figure)
(19 pages, 1 figure)
- Mitosis recursion for coefficients of Schubert polynomials,
of Combinatorial Theory, Series A 103 (2003), 223-235.
Unofficial version of 2 December 2002:
- Cohen-Macaulay quotients of normal affine semigroup rings via
irreducible resolutions   Math. Research Letters
9 (2002) 117-128.
LaTeX   (9 pages, LaTeX drawings)
- Graded Greenlees-May 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. 233-253.
- Planar graphs as minimal resolutions of trivariate monomial ideals
Mathematica 7 (2002) 43-90. (electronically
published: all links are to the official published version)
- Resolutions and duality for monomial ideals,
Ph.D. thesis, University of California, Berkeley, 2000, 107 pages.
gzipped .tar file (200K)
- The Alexander duality functors and local duality with monomial
support, Journal of Algebra 231 (2000), 180-234.
gzipped tarfile (LaTeX and
- Generic and cogeneric monomial ideals (with Bernd Sturmfels
and Kohji Yanagawa), Journal of Symbolic Computation 29 (2000),
- Icosahedra constructed from congruent triangles.
Discrete and Computational Geometry 24 (2000), 437-451.
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
Error-Correcting Codes, [M. Fossorier, H. Imai, S. Lin and
A. Poli, eds.], Proceedings of AAECC-13 (Honolulu, Nov. 1999),
Springer Lecture Notes in Computer Science 1719 19-28.
(LaTeX and .eps figures)
- Multiplicities of ideals in Noetherian rings,
Beiträge zur Algebra und Geometrie 39 (1998), no. 1, 47-51.
Conference publications (peer-reviewed 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
19-25 April 2009, organized by W. Bruns, H. Flenner, and C. Huneke,
Oberwolfach reports 22 (2009), 23-26.
- Extended abstract: Binomial D-modules
(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 Shin-Yao 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, 195-271.
- 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, 253-316.
- 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
(12 pages, 3 LaTeX figures)
- Alexander duality for monomial ideals and their resolutions,
1 (2009), no. 1,
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 Pisón-Casares", 25-30 January 2010.
(3 pages, no figures)
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, 21-25 May 2007.
(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 Stanley-Reisner 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 DMS-0071549,
Grant DMS-0304789, or CAREER Grant DMS-0449102, or supported by a
University of Minnesota McKnight Land-Grant Professorship.