Writings

The articles whose arXiv date is in red contain changes made after journal publication. A list of changes can be found here.
For forward references to my papers, see my Google Scholar profile.
A listing of these papers on arXiv can be found at this link: http://arxiv.org/a/sam_s_1

Research

  1. Big polynomial rings with imperfect coefficient fields
    (with Daniel Erman and Andrew Snowden)
    arXiv (last updated 6/11/2018)
  2. Generalizations of Stillman's conjecture via twisted commutative algebras
    (with Daniel Erman and Andrew Snowden)
    arXiv (last updated 4/25/2018)
  3. Strength and Hartshorne's conjecture in high degree
    (with Daniel Erman and Andrew Snowden)
    arXiv (last updated 4/25/2018)
  4. Big polynomial rings and Stillman's conjecture
    (with Daniel Erman and Andrew Snowden)
    arXiv (last updated 1/30/2018)
  5. An equivariant Hilbert basis theorem
    (with Daniel Erman and Andrew Snowden)
    arXiv (last updated 12/20/2017)
  6. Stability in the homology of unipotent groups
    (with Andrew Putman and Andrew Snowden)
    arXiv (last updated 11/29/2017)
  7. Some generalizations of Schur functors
    (with Andrew Snowden)
    Proc. Amer. Math. Soc., to appear
    arXiv (last updated 8/21/2017) | Journal
  8. On the (non-)vanishing of syzygies of Segre embeddings
    (with Luke Oeding and Claudiu Raicu)
    arXiv (last updated 8/12/2017)
  9. Hilbert series for twisted commutative algebras
    (with Andrew Snowden)
    Algebraic Combinatorics 1 (2018), no. 1, 147–172.
    arXiv (last updated 1/31/2018) | Journal
  10. Homological vanishing for the Steinberg representation
    (with Avner Ash and Andrew Putman)
    Compos. Math. 154 (2018), no. 6, 1111–1130.
    arXiv (last updated 4/26/2017) | Journal
  11. Regularity bounds for twisted commutative algebras
    (with Andrew Snowden)
    arXiv (last updated 4/5/2017)
  12. Regularity of FI-modules and local cohomology
    (with Rohit Nagpal and Andrew Snowden)
    Proc. Amer. Math. Soc., to appear
    arXiv (last updated 3/20/2017) | Journal
  13. GL-equivariant modules over polynomial rings in infinitely many variables. II
    (with Andrew Snowden)
    arXiv (last updated 3/13/2017)
  14. Invariant theory of 3(9) and genus 2 curves
    (with Eric M. Rains)
    Algebra Number Theory, to appear
    arXiv (last updated 2/15/2017)
  15. Noetherianity of some degree two twisted skew-commutative algebras
    (with Rohit Nagpal and Andrew Snowden)
    arXiv (last updated 10/4/2016)
  16. Towards Boij-Söderberg theory for Grassmannians: the case of square matrices
    (with Nicolas Ford and Jake Levinson)
    Algebra Number Theory 12 (2018), no. 2, 285–303.
    arXiv (last updated 1/8/2018)
  17. Syzygies of bounded rank symmetric tensors are generated in bounded degree
    Math. Ann. 368 (2017), no. 3, 1095–1108.
    arXiv (last updated 1/6/2017) | Journal
  18. Questions about Boij–Söderberg theory
    (with Daniel Erman)
    Surveys on recent developments in algebraic geometry, 285–304,
    Proc. Sympos. Pure Math. 95, Amer. Math. Soc., Providence, RI, 2017.
    arXiv (last updated 6/6/2016)
  19. Vector bundles on genus 2 curves and trivectors
    (with Eric M. Rains)
    Algebr. Geom., to appear
    arXiv (last updated 5/14/2016)
  20. Infinite rank spinor and oscillator representations
    (with Andrew Snowden)
    J. Comb. Algebra 1 (2017), no. 2, 145–183.
    arXiv (last updated 3/26/2017) | Journal
  21. Combinatorial constructions of derived equivalences
    (with Daniel Halpern-Leistner)
    arXiv (last updated 2/25/2016)
  22. Ideals of bounded rank symmetric tensors are generated in bounded degree
    Invent. Math. 207 (2017), no. 1, 1–21.
    arXiv (last updated 4/21/2016) | Journal
  23. Supernatural analogues of Beilinson monads
    (with Daniel Erman)
    Compos. Math. 152 (2016), no. 12, 2545–2562.
    arXiv (last updated 11/14/2016) | Journal
  24. Equations for the fifth secant variety of Segre products of projective spaces
    (with Luke Oeding)
    Exp. Math. 25 (2016), no. 1, 94–99.
    arXiv (last updated 4/1/2015) | Journal
  25. Noetherianity of some degree two twisted commutative algebras
    (with Rohit Nagpal and Andrew Snowden)
    Selecta Math. (N.S.) 22 (2016), no. 2, 913–937.
    arXiv (last updated 9/29/2015) | Journal
  26. Proof of Stembridge's conjecture on stability of Kronecker coefficients
    (with Andrew Snowden)
    J. Algebraic Combin. 43 (2016), no. 1, 1–10.
    arXiv (last updated 7/11/2015) | Journal
  27. The cone of Betti tables over three non-collinear points in the plane
    (with Iulia Gheorghita)
    J. Commut. Algebra 8 (2016), no. 4, 537–548.
    arXiv (last updated 12/22/2014) | Journal
  28. Representations of categories of G-maps
    (with Andrew Snowden)
    J. Reine Angew. Math., to appear
    arXiv (last updated 9/6/2016) | Journal
  29. On Cohen-Macaulayness of Sn-invariant subspace arrangements
    (with Aaron Brookner, David Corwin, and Pavel Etingof)
    Int. Math. Res. Not. IMRN (2016), no. 7, 2104–2126.
    arXiv (last updated 6/14/2015) | Journal
  30. Gröbner methods for representations of combinatorial categories
    (with Andrew Snowden)
    J. Amer. Math. Soc. 30 (2017), 159–203.
    arXiv (last updated 2/8/2016) | Journal | Related documents
  31. Representation stability and finite linear groups
    (with Andrew Putman)
    Duke Math. J. 166 (2017), no. 13, 2521–2598.
    arXiv (last updated 2/15/2017) | Journal | Related documents
  32. Orthosymplectic Lie superalgebras, Koszul duality, and a complete intersection analogue of the Eagon-Northcott complex
    J. Eur. Math. Soc. (JEMS) 18 (2016), no. 12, 2691–2732.
    arXiv (last updated 9/7/2016) | Journal | Supplementary article (last updated 9/7/2016)
  33. Jacobi-Trudi determinants and characters of minimal affinizations
    Pacific J. Math. 272 (2014), no. 1, 237–244.
    arXiv (last updated 9/3/2014) | Journal
  34. Homology of analogues of Heisenberg Lie algebras
    Math. Res. Lett. 22 (2015), no. 4, 1223–1241.
    arXiv (last updated 7/10/2015) | Journal
  35. Representations of rational Cherednik algebras of G(m,r,n) in positive characteristic
    (with Sheela Devadas)
    J. Commut. Algebra 6 (2014), no. 4, 525–559.
    arXiv (last updated 10/13/2013) | Journal
  36. Jack polynomials as fractional quantum Hall states and the Betti numbers of the (k+1)-equals ideal
    (with Christine Berkesch and Stephen Griffeth)
    Comm. Math. Phys. 330 (2014), no. 1, 415–434.
    arXiv (last updated 4/23/2014) | Journal
  37. Tropicalization of classical moduli spaces
    (with Qingchun Ren and Bernd Sturmfels)
    Math. Comput. Sci. 8 (2014), no. 2, Special issue on computational algebraic geometry, 119–145.
    arXiv (last updated 11/16/2013) | Journal
  38. Littlewood complexes and analogues of determinantal varieties
    (with Jerzy Weyman)
    Int. Math. Res. Not. IMRN (2015), no. 13, 4663–4707.
    arXiv (last updated 5/22/2014) | Journal
  39. Stability patterns in representation theory
    (with Andrew Snowden)
    Forum Math. Sigma 3 (2015), e11, 108 pp.
    arXiv (last updated 5/12/2015) | Journal
  40. The cone of Betti tables over a rational normal curve
    (with Manoj Kummini)
    Commutative Algebra and Noncommutative Algebraic Geometry, 251–264,
    Math. Sci. Res. Inst. Publ., 68, Cambridge Univ. Press, Cambridge, 2015.
    arXiv (last updated 10/29/2013) | Book version
  41. Alternating trilinear forms on a 9-dimensional space and degenerations of (3,3)-polarized Abelian surfaces
    (with Laurent Gruson)
    Proc. Lond. Math. Soc. (3) 110 (2015), no. 3, 755–785.
    arXiv (last updated 9/15/2014) | Journal
  42. Homology of Littlewood complexes
    (with Andrew Snowden and Jerzy Weyman)
    Selecta Math. (N.S.) 19 (2013), no. 3, 655–698.
    arXiv (last updated 2/8/2013) | Journal
  43. The universal Kummer threefold
    (with Qingchun Ren, Gus Schrader, and Bernd Sturmfels)
    Exp. Math. 22 (2013), no. 3, 327–362.
    arXiv (last updated 6/12/2013) | Journal | Supplementary materials
  44. Derived supersymmetries of determinantal varieties
    J. Commut. Algebra 6 (2014), no. 2, 261–286.
    arXiv (last updated 7/13/2012) | Journal
  45. GL-equivariant modules over polynomial rings in infinitely many variables
    (with Andrew Snowden)
    Trans. Amer. Math. Soc. 368 (2016), 1097–1158.
    arXiv (last updated 6/29/2015) | Journal
  46. Combinatorial realizations of crystals via torus actions on quiver varieties
    (with Peter Tingley)
    J. Algebraic Combin. 39 (2014), no. 2, 271–300.
    arXiv (last updated 5/1/2013) | Journal
  47. Koszul homology of codimension 3 Gorenstein ideals
    (with Jerzy Weyman)
    Proc. Amer. Math. Soc. 142 (2014), 401–408.
    arXiv (last updated 3/14/2012) | Journal
  48. Moduli of Abelian varieties, Vinberg θ-groups, and free resolutions
    (with Laurent Gruson and Jerzy Weyman)
    Commutative Algebra (edited by Irena Peeva), 419–469, Springer, 2013.
    arXiv (last updated 1/21/2013) | Book version
  49. Equations and syzygies of some Kalman varieties
    Proc. Amer. Math. Soc. 140 (2012), 4153–4166.
    arXiv (last updated 9/7/2011) | Journal
  50. Shapes of free resolutions over a local ring
    (with Christine Berkesch, Daniel Erman, and Manoj Kummini)
    Math. Ann. 354 (2012), no. 3, 939–954.
    arXiv (last updated 11/8/2011) | Journal
  51. Tensor complexes: Multilinear free resolutions constructed from higher tensors
    (with Christine Berkesch, Daniel Erman, and Manoj Kummini)
    J. Eur. Math. Soc. (JEMS) 15 (2013), no. 6, 2257–2295.
    arXiv (last updated 10/13/2013) | Journal
  52. Matrices with restricted entries and q-analogues of permutations
    (with Joel Brewster Lewis, Ricky Ini Liu, Alejandro H. Morales, Greta Panova, and Yan Zhang)
    J. Comb. 2 (2011), no. 3, 355–396.
    arXiv (last updated 2/10/2012) | Extended abstract | Journal
  53. Poset structures in Boij–Söderberg theory
    (with Christine Berkesch, Daniel Erman, and Manoj Kummini)
    Int. Math. Res. Not. IMRN (2012), no. 22, 5132–5160.
    arXiv (last updated 11/2/2011) | Journal
  54. Symmetric quivers, invariant theory, and saturation theorems for the classical groups
    Adv. Math. 229 (2012), no. 2, 1104–1135.
    arXiv (last updated 10/20/2011) | Journal
  55. Schubert complexes and degeneracy loci
    J. Algebra 337 (2011), 103–125.
    arXiv (last updated 4/28/2011) | Extended abstract | Journal
  56. Generalized Ehrhart polynomials
    (with Sheng Chen and Nan Li)
    Trans. Amer. Math. Soc. 364 (2012), 551–569.
    arXiv (last updated 10/30/2010) | Extended abstract | Journal
  57. Pieri resolutions for classical groups
    (with Jerzy Weyman)
    J. Algebra 329 (2011), Special issue celebrating the 60th birthday of Corrado De Concini, 222–259.
    arXiv (last updated 5/26/2012) | Journal
  58. Positivity theorems for solid-angle polynomials
    (with Matthias Beck and Sinai Robins)
    Beiträge Algebra Geom. 51 (2010), no. 2, 493–507.
    arXiv (last updated 6/26/2015) | Journal | Corrigendum
  59. A finite calculus approach to Ehrhart polynomials
    (with Kevin M. Woods)
    Electron. J. Combin. 17 (2010), no. 1, Research Paper 68, 13pp.
    arXiv (last updated 5/2/2010) | Journal
  60. A bijective proof for a theorem of Ehrhart
    Amer. Math. Monthly 116 (2009), no. 8, 688–701.
    arXiv (last updated 6/27/2008) | Journal
  61. Grid graphs, Gorenstein polytopes, and domino stackings
    (with Matthias Beck and Christian Haase)
    Graphs Combin. 25 (2009), 409–426.
    arXiv (last updated 4/28/2009) | Journal
  62. Maximal periods of (Ehrhart) quasi-polynomials
    (with Matthias Beck and Kevin M. Woods)
    J. Combin. Theory Ser. A 115 (2008), 517–525.
    arXiv (last updated 8/17/2007) | Journal

Expository

  1. Noetherian properties in representation theory
    Representations of algebras, 215–224, Contemp. Math., 705, Amer. Math. Soc., 2018.
    arXiv (last updated 7/3/2017) | Book version
  2. Introduction to twisted commutative algebras
    (with Andrew Snowden)
    arXiv (last updated 9/21/2012)

Appendices

Software

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