Ezra Miller's Publications and Preprints

  1. What is ... a toric variety? Notices of the American Mathematical Society 55, no. 5 (May, 2008), 586-587. official online version.   version of 16 February 2008:  
  2. 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.
  3. Geometric Combinatorics (book edited with Vic Reiner and Bernd Sturmfels). Lecture 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. Multiplier ideals of sums via cellular resolutions (with Shin-Yao Jow), Mathematical Research Letters 15 (2008), no. 2, 359-373.   version of 4 September 2007   Abstract and References,   slides for AMS Toric Varieties session
  5. Duality of antidiagonals and pipe dreams (with Ning Jia), Séminaire Lotharingien de Combinatoire, B58e [the fifth paper in Issue 58] (2008), 6 pp.   final published version of 18 May 2008:
  6. Combinatorics of binomial primary decomposition (with Alicia Dickenstein and Laura Matusevich).
    version of 25 March 2008   Abstract
  7. Binomial D-modules (with Alicia Dickenstein and Laura Matusevich).   version of 26 March 2008   Abstract and contents
  8. What is geometric combinatorics?---An overview of the graduate summer school (with Vic Reiner), in Geometric combinatorics, pages 1-17, IAS/Park City Mathematics Series, vol. 13, American Mathematical Society, Providence, RI, 2007.   version of 23 December 2005  
  9. A Kleiman-Bertini theorem for sheaf tensor products (with David E Speyer), Journal of Algebraic Geometry 17 (2008), no. 2, 335-340.   version of 8 February 2007   Abstract
  10. Combinatorial Commutative Algebra (with Bernd Sturmfels), Graduate Texts in Math Vol. 227, Springer-Verlag, New York, 2004. xiv+417 pp.
  11. Tableau complexes (with Allen Knutson and Alex Yong), to appear in Israel Journal of Mathematics.   version of 17 March 2006   Abstract/Contents
  12. Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings (with Igor Pak),Discrete and Computational Geometry 39 (2008), no. 1-3, 339-388.   version of 22 February 2006   Abstract/Table of contents
  13. Gröbner geometry of vertex decompositions and of flagged tableaux (with Allen Knutson and Alex Yong), to appear in Journal für die reine und angewandte Mathematik (Crelle's Journal).   version of 15 March 2005   Abstract/Contents
  14. Homological methods for hypergeometric families. (with Laura Matusevich and Uli Walther), Journal of the American Mathematical Society 18 (2005), no. 4, 919-941.   Abstract/Contents/References   Unofficial but nonetheless journal-formatted version:
  15. 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   Abstract/Contents/References
  16. 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   Abstract: see the title
  17. 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   Abstract/References
  18. Alternating formulas for K-theoretic quiver polynomials, Duke Mathematical Journal 128 (2005), 1-17.   Abstract   Unofficial version of 13 June 2004:
  19. Gröbner geometry of Schubert polynomials (with Allen Knutson), Annals of Mathematics 161 (2005), 1245-1318.   Abstract/Contents   Unofficial version of 9 September 2003:
  20. Algorithms for graded injective resolutions and local cohomology over semigroup rings (with David Helm), Journal of Symbolic Computation 39 (2005), 373-395.   Abstract/Contents/References   Unofficial but nonetheless final journal-formatted version:
  21. Reciprocal domains and Cohen-Macaulay d-complexes in R^d (with Vic Reiner), The Electronic Journal of Combinatorics 11(2) (2005) #N1 (9 pages).   Abstract/References   Unofficial but nonetheless final journal-formatted version:
  22. 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.
  23. Toric degeneration of Schubert varieties and Gelfand-Tsetlin polytopes (with Misha Kogan), Advances in Mathematics 193 (2005), no. 1, 1-17.   Abstract/References   Unofficial version of 16 January 2004:
  24. Subword complexes in Coxeter groups (with Allen Knutson), Advances in Mathematics 184 (2004), no. 1, 161-176.   Abstract/References   Unofficial version of 11 March 2003:
  25. Bass Numbers of Semigroup-Graded Local Cohomology (with David Helm), Pacific Journal of Math 209, no. 1 (2003), 41-66.   Abstract   Unofficial version of 8 November 2001:
  26. Mitosis recursion for coefficients of Schubert polynomials, Journal of Combinatorial Theory, Series A 103 (2003), 223-235.   Abstract   Unofficial version of 2 December 2002:
  27. 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.   Abstract
  28. Extended abstract: `Gröbner Geometry of Schubert Polynomials' (with Allen Knutson), Proceedings FPSAC 2002.   10 December 2001
  29. Cohen-Macaulay quotients of normal affine semigroup rings via irreducible resolutions   10 January 2002.   Math. Research Letters  9, 117-128 (2002). Abstract
  30. Planar Graphs as Minimal Resolutions of Trivariate Monomial Ideals   Documenta Mathematica  7, 43-90 (2002). (electronically published: all links are to the official published version) Abstract
  31. 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.   Contents and Preface
  32. Resolutions and Duality for Monomial Ideals.   Ph.D. thesis, version of 9 May 2000.   Preface (32K) Contents (20K)
  33. The Alexander Duality Functors and Local Duality with Monomial Support.   Journal of Algebra 231 (2000), 180-234.   Abstract   Unofficial version:
  34. Generic and Cogeneric Monomial Ideals (with Bernd Sturmfels and Kohji Yanagawa).   Journal of Symbolic Computation 29 (2000), 691-708.   Abstract   Unofficial version:
  35. Icosahedra Constructed from Congruent Triangles.   Discrete and Computational Geometry 24 (2000), 437-451.   Abstract (my undergraduate honors thesis).
  36. 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.   Abstract
  37. Multiplicities of Ideals in Noetherian Rings.   Beitrage zur Algebra und Geometrie. Volume 39 (1998), No. 1, 47-51 (electronically published) Abstract

Some unpublished items

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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.