Ezra Miller's Publications and Preprints

Books and expository articles

8. 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.
7. What is ... a toric variety? Notices of the American Mathematical Society 55, no. 5 (May, 2008), 586-587. official online version.   Unofficial version of 16 February 2008:   PDF
6. 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
5. 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 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.
4. 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.   arXiv:math.AG/0601202     Unofficial version of 23 December 2005:   PDF   (15 figures)
3. 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.
2. 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.   PDF   (7 pages, one figure)
1. 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
   96 pages, 41 figures (55 .eps detections when LaTeX is run);   Click here for download options

Submitted journal articles

2. Lattice point methods for combinatorial games (with Alan Guo), 18 pages.   arXiv:math.CO/0908.3473   version of 24 August 2009:   PDF   DVI   LaTeX
1. Positivity and Kleiman transversality in equivariant K-theory of homogeneous spaces (with Dave Anderson and Stephen Griffeth), 23 pages.   arXiv:math.AG/0808.2785   version of 5 November 2009:   PDF   LaTeX (you'll need diagrams.sty for this)  

Peer-reviewed articles

30. Binomial D-modules (with Alicia Dickenstein and Laura Matusevich), Duke Mathematical Journal, to appear, 33 pages. arXiv:math.AG/0610353   version of 9 May 2009:   PDF  
29. Topological Cohen-Macaulay criteria for monomial ideals, in #8 listed above under Books and expository items, pp. 137-156.   arXiv:math.AC/0809.1458   Unofficial (but final, officially-formatted) version:   PDF   DVI   LaTeX (you'll need the Contemporary Math .cls file for this)
28. 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.   arXiv:math.AG/0502144   Unofficial version of 15 March 2005:   PDF   DVI   LaTeX   abstract/contents
27. 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  
26. Tableau complexes (with Allen Knutson and Alex Yong), to appear in Israel Journal of Mathematics 163 (2008), 317-343.   arXiv:math.CO/0510487   Unofficial version of 17 March 2006:   PDF   gzipped tarball   abstract/contents
25. Multiplier ideals of sums via cellular resolutions (with Shin-Yao Jow), Mathematical Research Letters 15 (2008), no. 2, 359-373.   arXiv:math.AG/0703299   slides for AMS Toric Varieties session   Unofficial version of 4 September 2007:   PDF   DVI   LaTeX   abstract and references  
24. 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  
23. Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings (with Igor Pak), Discrete and Computational Geometry 39 (2008), no. 1-3, 339-388.   arXiv:math.AC/0312253   Unofficial version of 22 February 2006:   PDF   abstract/table of contents
22. A Kleiman-Bertini theorem for sheaf tensor products (with David E Speyer), Journal of Algebraic Geometry 17 (2008), no. 2, 335-340.   arXiv:math.AG/0601202   Unofficial version of 8 February 2007:   PDF   DVI  
21. Four positive formulae for type A quiver polynomials (with Allen Knutson and Mark Shimozono), Inventiones Mathematicae 166 (2006), no. 2, 229-325.   arXiv:math.AC/0308142   version of 16 January 2006:   PDF   DVI   (78 pages)   abstract/contents/references
20. Combinatorics of rank jumps in simplicial hypergeometric systems. (with Laura Matusevich), Proceedings of the AMS 134 (2006), 1375-1381.   arXiv:math.AC/0402071     unofficial version of 20 November 2004   PDF   DVI   LaTeX   abstract/references
19. 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:   PDF   DVI   LaTeX
18. Homological methods for hypergeometric families. (with Laura Matusevich and Uli Walther), Journal of the American Mathematical Society 18 (2005), no. 4, 919-941.   arXiv:math.AG/0406383
17. Alternating formulas for K-theoretic quiver polynomials, Duke Mathematical Journal 128 (2005), 1-17.   arXiv:math.CO/0312250   abstract   Unofficial version of 13 June 2004:   PDF   DVI   LaTeX
16. Gröbner geometry of Schubert polynomials (with Allen Knutson), Annals of Mathematics 161 (2005), 1245-1318.   arXiv:math.AG/0110058   abstract/contents   Unofficial version of 9 September 2003:   PDF   DVI   LaTeX (53 pages)
    Note: the old (very long) version is still available
15. Algorithms for graded injective resolutions and local cohomology over semigroup rings (with David Helm), Journal of Symbolic Computation 39 (2005), 373-395.   arXiv:math.AC/0309256   abstract/contents/references   Unofficial (but final journal-formatted) version:   PDF   DVI   LaTeX
14. Toric degeneration of Schubert varieties and Gelfand-Tsetlin polytopes (with Misha Kogan), Advances in Mathematics 193 (2005), no. 1, 1-17.   arXiv:math.AG/0303208   abstract/references   Unofficial version of 16 January 2004:   PDF   DVI   LaTeX
13. Reciprocal domains and Cohen-Macaulay d-complexes 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 journal-formatted) version:   PDF   DVI   LaTeX
12. Subword complexes in Coxeter groups (with Allen Knutson), Advances in Mathematics 184 (2004), no. 1, 161-176.   arXiv:math.CO/0309259   abstract/references   Unofficial version of 11 March 2003:   PDF   DVI   LaTeX
11. Bass numbers of semigroup-graded local cohomology (with David Helm), Pacific Journal of Math 209, no. 1 (2003), 41-66.   electronically published   arXiv:math.AG/0010003   Unofficial version of 8 November 2001: PDF   gzipped tarfile (LaTeX and .eps figure)   (19 pages, 1 figure)
10. Mitosis recursion for coefficients of Schubert polynomials, Journal of Combinatorial Theory, Series A 103 (2003), 223-235.   arXiv:math.CO/0212131   abstract   Unofficial version of 2 December 2002:   PDF   DVI   LaTeX
9. Cohen-Macaulay quotients of normal affine semigroup rings via irreducible resolutions   Math. Research Letters   9 (2002) 117-128.   arXiv:math.AC/0110096   PDF   DVI   LaTeX   (9 pages, LaTeX drawings)
8. 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.   PDF   DVI   LaTeX   abstract
7. Planar graphs as minimal resolutions of trivariate monomial ideals   Documenta Mathematica 7 (2002) 43-90. (electronically published: all links are to the official published version)   PDF   other download options   abstract
6. 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)  
5. The Alexander duality functors and local duality with monomial support, Journal of Algebra 231 (2000), 180-234.   electronically published   abstract   Unofficial version:   PDF   gzipped tarfile (LaTeX and .eps figures)
4. Generic and cogeneric monomial ideals (with Bernd Sturmfels and Kohji Yanagawa), Journal of Symbolic Computation 29 (2000), 691-708.   electronically published   arXiv:math.AC/9812126  
3. Icosahedra constructed from congruent triangles.   Discrete and Computational Geometry 24 (2000), 437-451.   PDF   gzipped tarfile (LaTeX and .eps figures)   abstract (my undergraduate honors thesis).
2. 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.   PDF   gzipped tarfile (LaTeX and .eps figures)   abstract
1. Multiplicities of ideals in Noetherian rings, Beiträge zur Algebra und Geometrie 39 (1998), no. 1, 47-51.  electronically published   abstract

Conference publications (peer-reviewed and/or invited)

6. 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.
   PDF   DVI   LaTeX   (3 pages)
5. Extended abstract: Binomial D-modules (with Alicia Dickenstein and Laura Matusevich), Proceedings MEGA (Effective Methods in Algebraic Geometry) 2007, Strobl, Austria.
   official version   slightly updated version:   PDF   DVI   LaTeX   (13 pages)
4. 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.
   PDF   (3 pages)
3. 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.
   PDF   (3 pages)
2. 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.
   PDF   (5 pages)
1. Extended abstract: Gröbner geometry of Schubert polynomials (with Allen Knutson), Proceedings FPSAC 2002, Melbourne, Australia.   10 December 2001
   PDF   DVI   LaTeX   (12 pages, 3 LaTeX figures)

Other publications

1. Alexander duality for monomial ideals and their resolutions, Rejecta Mathematica 1 (2009), no. 1, 18-57.   arXiv:math.AC/9812095.   abstract
   official Rejecta version   (37 pages, 8 figures)

Some unpublished items

4. Binomial Exercises   Three pages of exercises for my course on Primary Decomposition of Binomial Ideals at the International School on Combinatorics "Pilar Pis\'on-Casares", 25-30 January 2010.
PDF   (3 pages, no figures)
3. 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, 21-25 May 2007.
PDF   (5 pages, no figures)
2. Long version of Gröbner Geometry of Schubert Polynomials   29 December 2001
PDF   DVI   LaTeX   (98 pages)
Extended notes for MIT combinatorics seminar on 16 February 2001, 19 PostScript pages
1. 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.
   PDF   DVI   LaTeX   (2 pages, no figures)