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Publications of Ezra Miller

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Peer-reviewed journal articles published

  1. Miller, E. "Stratifications of real vector spaces from constructible sheaves with conical microsupport." Journal of Applied and Computational Topology (2021).
  2. Katthän, L; Michałek, M; Miller, E. "When is a Polynomial Ideal Binomial After an Ambient Automorphism?." Foundations of Computational Mathematics 19.6 (December, 2019): 1363-1385. [doi]  [abs]
  3. Ene, V; Miller, E. "Preface." Springer Proceedings in Mathematics and Statistics 238 (January, 2018): v-viii.
  4. Berenstein, A; Braverman, M; Miller, E; Retakh, V; Weitsman, J. "Andrei Zelevinsky, 1953–2013." Advances in Mathematics 300 (September, 2016): 1-4. [doi]
  5. Kahle, T; Miller, E; O'Neill, C. "Irreducible decomposition of binomial ideals." Compositio Mathematica 152.6 (June, 2016): 1319-1332. [arXiv:1503.02607], [1503.02607], [doi]  [abs]
  6. Bendich, P; Marron, JS; Miller, E; Pieloch, A; Skwerer, S. "Persistent homology analysis of brain artery trees." Annals of Applied Statistics 10.1 (2016): 198-218. [arXiv:1411.6652], [1411.6652v1], [doi]  [abs]
  7. Miller, E. "Fruit flies and moduli: Interactions between biology and mathematics." Notices of the American Mathematical Society 62.10 (November, 2015): 1178-1184. [doi]
  8. Miller, E; Owen, M; Provan, JS. "Polyhedral computational geometry for averaging metric phylogenetic trees." Advances in Applied Mathematics 68 (July, 2015): 51-91. [doi]  [abs]
  9. Zamaere, CB; Griffeth, S; Miller, E. "Systems of parameters and holonomicity of A-hypergeometric systems." Pacific Journal of Mathematics 276.2 (January, 2015): 281-286. [doi]  [abs]
  10. with Gopalkrishnan, M; Miller, E; Shiu, A. "A geometric approach to the global attractor conjecture." Siam Journal on Applied Dynamical Systems 13.2 (January, 2014): 758-797. (49 pages) [math.DS/1305.5303], [doi]  [abs]
  11. Skwerer, S; Bullitt, E; Huckemann, S; Miller, E; Oguz, I; Owen, M; Patrangenaru, V; Provan, S; Marron, JS. "Tree-oriented analysis of brain artery structure." Journal of Mathematical Imaging and Vision 50.1 (January, 2014): 126-143. (25 pages) [doi]  [abs]
  12. Huckemann, S; Mattingly, JC; Miller, E; Nolen, J. "Sticky central limit theorems at isolated hyperbolic planar singularities." Arxiv Preprint Arxiv:1410.6879 20 (2014). [repository], [doi]  [abs]
  13. Miller, E. "Affine stratifications from finite misère quotients." Journal of Algebraic Combinatorics 37.1 (February, 2013): 1-9. [math.CO/1009.2199], [DOI:10.1007/s10801-012-0355-3], [doi]  [abs]
  14. with Hotz, T; Huckemann, S; Le, H; Marron, JS; Mattingly, JC; Miller, E; Nolen, J; Owen, M; Patrangenaru, V; Skwerer, S. "Sticky central limit theorems on open books." The Annals of Applied Probability 23.6 (2013): 2238-2258. [math.PR/1202.4267], [12-AAP899], [doi]  [abs]
  15. Guo, A; Miller, E. "Erratum: Lattice point methods for combinatorial games (Advances in Applied Mathematics (2011) 46:1 (363-378))." Advances in Applied Mathematics 48.1 (January, 2012): 269-271. [doi]
  16. with Gopalkrishnan, M; Shiu, A. "A projection argument for differential inclusions, with applications to persistence of mass-action kinetics." Sigma (Symmetry, Integrability, and Geometry: Methods and Applications) 9 (2012). (paper 025, 25 pages) [math.DS/1208.0874], [DOI:10.3842/SIGMA.2013.025], [doi]  [abs]
  17. with Thomas Kahle,. "Decompositions of commutative monoid congruences and binomial ideals." Algebra & Number Theory 8.6 (2012): 1297-1364. (62 pages) [math.AC/1107.4699], [doi]  [abs]
  18. Miller, E. "Theory and applications of lattice point methods for binomial ideals." Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: the Abel Symposium 2009Combinatorial aspects of commutative algebra and algebraic geometry, Proceedings of Abel Symposium held at Voss, Norway, 1--4 June 2009 Abel Symposia 6 (December, 2011): 99-154. [math.AC/1009.2823], [Gateway.cgi], [doi]  [abs]
  19. with Miller, E; Novik, I; Swartz, E. "Face rings of simplicial complexes with singularities." Mathematische Annalen 351.4 (December, 2011): 857-875. [math.AC/1001.2812], [DOI:10.1007/s00208-010-0620-5], [doi]  [abs]
  20. with Anderson, D; Griffeth, S; Miller, E. "Positivity and Kleiman transversality in equivariant K-theory of homogeneous spaces." Journal of the European Mathematical Society 13.1 (January, 2011): 57-84. [math.AG/0808.2785], [DOI:10.4171/JEMS/244], [doi]  [abs]
  21. with Guo, A; Miller, E. "Lattice point methods for combinatorial games." Advances in Applied Mathematics 46.1-4 (January, 2011): 363-378. ([math.CO/0908.3473] [math.CO/1105.5420]) [repository], [doi]  [abs]
  22. with Dickenstein, A; Matusevich, LF; Miller, E. "Combinatorics of binomial primary decomposition." Mathematische Zeitschrift 264.4 (April, 2010): 745-763. [math.AC/0803.3846], [DOI:10.1007/s00209-009-0487-x], [doi]  [abs]
  23. with Ezra Miller,. "Binomial D-modules." Duke Mathematical Journal 151.3 (2010): 385-429. [math.AG/0610353], [DOI:10.1215/00127094-2010-002], [doi]  [abs]
  24. Knutson, A; Miller, E; Yong, A. "Gröbner geometry of vertex decompositions and of flagged tableaux." Journal Fur Die Reine Und Angewandte Mathematik 2009.630 (May, 2009): 1-31. [doi]  [abs]
  25. Miller, E. "Topological Cohen-Macaulay criteria for monomial ideals." Surveys on Discrete and Computational Geometry: Twenty Years LaterCombinatorial aspects of commutative algebra Contemporary Mathematics 502 (January, 2009): 137-155. [math.AC/0809.1458], [Gateway.cgi]
  26. Miller, E. "What is... a toric variety?." Notices of the American Mathematical Society 55.5 (May, 2008): 586-587. [MR2404030]
  27. with Ezra, M; Speyer, DE. "A kleiman-bertini theorem for sheaf tensor products." Journal of Algebraic Geometry 17.2 (January, 2008): 335-340. [MR2008k:14044], [math.AG/0601202], [doi]  [abs]
  28. with Miller, E; Pak, I. "Metric combinatorics of convex polyhedra: Cut loci and nonoverlapping unfoldings." Discrete & Computational Geometry 39.1-3 (January, 2008): 339-388. [MR2008m:52027], [math.MG/0312253], [doi]  [abs]
  29. with Knutson, A; Miller, E; Yong, A. "Tableau complexes." Israel Journal of Mathematics 163.1 (January, 2008): 317-343. [MR2009b:05264], [math.CO/0510487], [doi]  [abs]
  30. with Shin Yao Jow,. "Multiplier ideals of sums via cellular resolutions." Mathematical Research Letters 15.2 (2008): 359-373. [MR2009b:14004], [math.AG/0703299], [doi]  [abs]
  31. Jow, SY; Miller, E. "Multiplier ideals of sums via cellular resolutions." Mathematical Research Letters 15.2-3 (2008): 359-373.  [abs]
  32. with Victor Reiner. "What is geometric combinatorics?---An overview of the graduate summer school." Geometric combinatorics IAS/Park City Math. Ser. 13 (2007): 1-17. [MR2383124]
  33. with Ning Jia,. "Duality of antidiagonals and pipe dreams." SÉMinaire Lotharingien De Combinatoire 58 (2007). [MR2009m:05196], [math.CO/0706.3031]
  34. with Knutson, A; Miller, E; Shimozono, M. "Four positive formulae for type A quiver polynomials." Inventiones Mathematicae 166.2 (November, 2006): 229-325. [MR2007k:14098], [math.AG/0308142], [doi]  [abs]
  35. with Matusevich, LF; Miller, E. "Combinatorics of rank jumps in simplicial hypergeometric systems." Proceedings of the American Mathematical Society 134.5 (May, 2006): 1375-1381. [MR2006j:33016], [math.AC/0402071], [doi]  [abs]
  36. with Miller, E; Reiner, V. "Stanley's simplicial poset conjecture, after M. Masuda." Communications in Algebra 34.3 (February, 2006): 1049-1053. [MR2006m:13023], [doi]  [abs]
  37. with Matusevich, LF; Miller, E; Walther, U. "Homological methods for hypergeometric families." Journal of the American Mathematical Society 18.4 (October, 2005): 919-941. [MR2007d:13027], [math.AG/0406383], [doi]
  38. with Miller, E. "Alternating formulas for K-theoretic quiver polynomials." Duke Mathematical Journal 128.1 (May, 2005): 1-17. [MR2006e:05181], [math.CO/0312250], [doi]  [abs]
  39. with Kogan, M; Miller, E. "Toric degeneration of Schubert varieties and Gelfand-Tsetlin polytopes." Advances in Mathematics 193.1 (May, 2005): 1-17. [MR2006d:14054], [math.AG/0303208], [doi]  [abs]
  40. Helm, D; Miller, E. "Algorithms for graded injective resolutions and local cohomology over semigroup rings." Journal of Symbolic Computation 39.3-4 SPEC. ISS. (March, 2005): 373-395. [doi]  [abs]
  41. Miller, E; Reiner, V. "Reciprocal domains and Cohen-Macaulay d-complexes in ℝd." Electronic Journal of Combinatorics 11.2 N (January, 2005): 1-9.  [abs]
  42. Knutson, A; Miller, E. "Gröbner geometry of Schubert polynomials." Annals of Mathematics 161.3 (January, 2005): 1245-1318. [doi]  [abs]
  43. with Knutson, A; Miller, E. "Subword complexes in Coxeter groups." Advances in Mathematics 184.1 (May, 2004): 161-176. [MR2005c:20066], [math.CO/0309259], [doi]  [abs]
  44. Appendix to: Mark Haiman. "Commutative algebra of n points in the plane." Trends in commutative algebra Math. Sci. Res. Inst. Publ. 51 (2004): 153-180. [MR2006c:14005]
  45. with Victor Reiner,. "Reciprocal domains and Cohen-Macaulay d-complexes in R^d." Electronic Journal of Combinatorics 11.2 (2004): Note 1, 9 pp.. [MR2005k:52024], [math.CO/0408169]
  46. with Helm, D; Miller, E. "Bass numbers of semigroup-graded local cohomology." Pacific Journal of Mathematics 209.1 (January, 2003): 41-66. [MR2004c:13028], [math.AG/0010003], [doi]  [abs]
  47. Miller, E. "Mitosis recursion for coefficients of Schubert polynomials." Journal of Combinatorial Theory, Series A 103.2 (January, 2003): 223-235. [MR2004i:05157], [math.CO/0212131], [doi]  [abs]
  48. Miller, E. "Planar graphs as minimal resolutions of trivariate monomial ideals." Documenta Mathematica 7.1 (December, 2002): 43-90. [MR2003d:05055], [download]  [abs]
  49. Miller, E. "Cohen-Macaulay quotients of normal semioroup rings via irreducible resolutions." Mathematical Research Letters 9.1 (January, 2002): 117-128. [MR2003a:13015], [math.AC/0110096], [doi]  [abs]
  50. "Graded Greenlees-May duality and the Čech hull." Local cohomology and its applications (Guanajuato, 1999) Lecture Notes in Pure and Appl. Math. 226 (2002): 233-253. [MR2004b:13019]
  51. Miller, E. "Graded greenlees-may duality and the cech hull." Local Cohomology and its Applications (January, 2001): 233-253.  [abs]
  52. with David Perkinson,. "Eight lectures on monomial ideals." Queen'S Papers in Pure and Applied Mathematics 120 (2001): 3-105.
  53. Miller, E. "The Alexander duality functors and local duality with monomial support." Journal of Algebra 231.1 (September, 2000): 180-234. [MR2001k:13028], [pdf], [doi]  [abs]
  54. Miller, EN. "Icosahedra constructed from congruent triangles." Discrete & Computational Geometry 24.2-3 (January, 2000): 437-451. (The Branko Grünbaum birthday issue) [MR2001d:52021], [doi]  [abs]
  55. with Miller, E; Sturmfels, B; Yanagawa, K. "Generic and cogeneric monomial ideals." Journal of Symbolic Computation 29.4-5 (January, 2000): 691-708. (Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998)) [MR2001m:13051], [doi]  [abs]
  56. Ezra Miller,. "Multiplicities of ideals in Noetherian rings." BeitrÄGe Zur Algebra Und Geometrie 39.1 (1998): 47-51. [MR99c:13044]
  57. with Miller, E; Sturmfels, B. "Monomial ideals and planar graphs." Applied Algebra, Algebraic Algorithms and Error Correcting CodesApplied algebra, algebraic algorithms and error-correcting codes (Honolulu, HI, 1999) Lecture Notes in Computer Science 1719 (1998): 19-28. [MR2002h:13041], [doi]  [abs]


  1. edited with Viviana Ene. Combinatorial aspects of commutative algebra. Contemporary Mathematics502 AMS, 2009.
  2. edited with Victor Reiner and Bernd Sturmfels. Geometric combinatorics (Lectures from the Graduate Summer School held in Park City, UT, 2004). IAS/Park City Mathematics Series13 American Mathematical Society, 2007. xii+691 pp. [MR2009i:05001]
  3. with Srikanth Iyengar, Graham Leuschke, Anton Leykin, Claudia Miller, Anurag Singh, and Uli Walther. Twenty-four hours of local cohomology. Graduate Studies in Mathematics87 American Mathematical Society, 2007. xviii+282 pp. [MR2009a:13025]
  4. with Bernd Sturmfels. Combinatorial commutative algebra. Graduate Texts in Mathematics227 Springer-Verlag, 2005. xiv+417 pp. [MR2006d:13001]

Peer-reviewed journal articles under review

  1. with Megan Owen and Scott Provan. "Polyhedral computational geometry for averaging metric phylogenetic trees." (2012). (43 pages) [math.MG/1211.7046]  [abs]
  2. with Christine Berkesch and Stephen Griffeth. "Systems of parameters and holonomicity of hypergeometric systems." (2012). (5 pages)  [abs]


  1. with Alan Guo and Mike Weimerskirch. "Potential applications of commutative algebra to combinatorial game theory." Kommutative Algebra Oberwolfach Reports, 22 (2009): 23-26.
  2. "Alexander duality for monomial ideals and their resolutions." Rejecta Mathematica 1 (2009): 18-57. [math.AC/9812095], [download]  [author's comments]
  3. with Alicia Dickenstein and Laura Matusevich. "Extended abstract: Binomial D-modules." Proceedings MEGA (Effective Methods in Algebraic Geometry), Strobl, Austria 13 pages. (2007). [pdf]
  4. with Shin-Yao Jow. "Extended abstract: Cellular resolutions of multiplier ideals of sums." Topological and geometric combinatorics, abstracts from the Jan. 28-Feb. 3, 2007 workshop Oberwolfach Reports, 4.1 3 pages. (2007).
  5. with Laura Matusevich and Uli Walther. "Extended abstract: Homological methods for hypergeometric families." Convex and algebraic geometry, abstracts from the workshop held Jan. 29-Feb. 4, 2006 Oberwolfach Reports, 3.1 3 pages. (2006).
  6. with David Helm. "Extended abstract: Algorithms for graded injective resolutions and local cohomology over semigroup rings." Proceedings MEGA (Effective Methods in Algebraic Geometry), Kaiserslautern, Germany 5 pages. (2003).
  7. with Allen Knutson. "Extended abstract: Gröbner geometry of Schubert polynomials." Proceedings FPSAC (Formal Power Series and Algebraic Combinatorics), Melbourne 10 pages. (2002).