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. The representation theory of Brauer categories I: triangular categories
    (with Andrew Snowden)
    arXiv (last updated 6/7/2020)
  2. VIC-modules over noncommutative rings
    (with Andrew Putman)
    arXiv (last updated 5/14/2020)
  3. Schubert varieties and finite free resolutions of length three
    (with Jerzy Weyman)
    arXiv (last updated 5/4/2020)
  4. Sp-equivariant modules over polynomial rings in infinitely many variables
    (with Andrew Snowden)
    arXiv (last updated 2/8/2020)
  5. Periodicity in the cohomology of finite general linear groups via q-divided powers
    (with Rohit Nagpal and Andrew Snowden)
    arXiv (last updated 10/12/2019)
  6. Bi-graded Koszul modules, K3 carpets, and Green's conjecture
    (with Claudiu Raicu)
    arXiv (last updated 9/19/2019)
  7. Linear independence of powers
    (with Andrew Snowden)
    arXiv (last updated 7/5/2019)
  8. Small projective spaces and Stillman uniformity for cohomology of sheaves
    (with Daniel Erman and Andrew Snowden)
    arXiv (last updated 2/10/2020)
  9. Big polynomial rings with imperfect coefficient fields
    (with Daniel Erman and Andrew Snowden)
    arXiv (last updated 6/11/2018)
  10. Generalizations of Stillman's conjecture via twisted commutative algebras
    (with Daniel Erman and Andrew Snowden)
    Int. Math. Res. Not. IMRN, to appear
    arXiv (last updated 4/25/2018)
  11. Strength and Hartshorne's conjecture in high degree
    (with Daniel Erman and Andrew Snowden)
    Math. Z., to appear
    arXiv (last updated 4/25/2018) | Journal
  12. Big polynomial rings and Stillman's conjecture
    (with Daniel Erman and Andrew Snowden)
    Invent. Math. 218 (2019), no. 2, 413–439.
    arXiv (last updated 6/18/2018) | Journal
  13. An equivariant Hilbert basis theorem
    (with Daniel Erman and Andrew Snowden)
    Math. Res. Lett. 27 (2020), no. 1, 67–77.
    arXiv (last updated 4/8/2020) | Journal
  14. Stability in the homology of unipotent groups
    (with Andrew Putman and Andrew Snowden)
    Algebra Number Theory 14 (2020), no. 1, 119–154.
    arXiv (last updated 8/19/2019) | Journal
  15. Some generalizations of Schur functors
    (with Andrew Snowden)
    Proc. Amer. Math. Soc. 147 (2019), no. 1, 77–90.
    arXiv (last updated 8/21/2017) | Journal
  16. On the (non-)vanishing of syzygies of Segre embeddings
    (with Luke Oeding and Claudiu Raicu)
    Algebr. Geom. 6 (2019), no. 5, 571–591.
    arXiv (last updated 8/12/2017) | Journal
  17. Hilbert series for twisted commutative algebras
    (with Andrew Snowden)
    Algebraic Combinatorics 1 (2018), no. 1, 147–172.
    arXiv (last updated 1/31/2018) | Journal
  18. Homological vanishing for the Steinberg representation
    (with Avner Ash and Andrew Putman)
    Compos. Math. 154 (2018), no. 6, 1111–1130.
    arXiv (last updated 11/27/2017) | Journal
  19. Regularity bounds for twisted commutative algebras
    (with Andrew Snowden)
    Bull. Lond. Math. Soc. 52 (2020), no. 2, 299–315.
    arXiv (last updated 4/5/2017) | Journal
  20. Regularity of FI-modules and local cohomology
    (with Rohit Nagpal and Andrew Snowden)
    Proc. Amer. Math. Soc. 146 (2018), no. 10, 4117–4126.
    arXiv (last updated 10/13/2019) | Journal
  21. GL-equivariant modules over polynomial rings in infinitely many variables. II
    (with Andrew Snowden)
    Forum Math. Sigma 7 (2019), e5, 71pp.
    arXiv (last updated 11/15/2018) | Journal
  22. Invariant theory of 3(9) and genus 2 curves
    (with Eric M. Rains)
    Algebra Number Theory 12 (2018), no. 4, 935–957.
    arXiv (last updated 1/22/2018) | Journal
  23. Noetherianity of some degree two twisted skew-commutative algebras
    (with Rohit Nagpal and Andrew Snowden)
    Selecta Math. (N.S.) 25 (2019), no. 1, Art. 4, 26pp.
    arXiv (last updated 10/4/2016) | Journal
  24. 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) | Journal
  25. 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
  26. 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)
  27. Vector bundles on genus 2 curves and trivectors
    (with Eric M. Rains)
    Algebr. Geom. 6 (2019), no. 3, 328–345.
    arXiv (last updated 1/22/2018) | Journal
  28. 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
  29. Combinatorial constructions of derived equivalences
    (with Daniel Halpern-Leistner)
    J. Amer. Math. Soc. 33 (2020), 735–773.
    arXiv (last updated 2/25/2016) | Journal
  30. 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
  31. Supernatural analogues of Beilinson monads
    (with Daniel Erman)
    Compos. Math. 152 (2016), no. 12, 2545–2562.
    arXiv (last updated 11/14/2016) | Journal
  32. 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
  33. 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
  34. 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
  35. 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
  36. Representations of categories of G-maps
    (with Andrew Snowden)
    J. Reine Angew. Math. 750 (2019), 197–226.
    arXiv (last updated 9/6/2016) | Journal
  37. 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
  38. 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
  39. 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
  40. 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)
  41. Jacobi-Trudi determinants and characters of minimal affinizations
    Pacific J. Math. 272 (2014), no. 1, 237–244.
    arXiv (last updated 9/3/2014) | Journal
  42. Homology of analogues of Heisenberg Lie algebras
    Math. Res. Lett. 22 (2015), no. 4, 1223–1241.
    arXiv (last updated 7/10/2015) | Journal
  43. 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
  44. 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
  45. 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
  46. 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
  47. Stability patterns in representation theory
    (with Andrew Snowden)
    Forum Math. Sigma 3 (2015), e11, 108 pp.
    arXiv (last updated 5/12/2015) | Journal
  48. 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
  49. 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
  50. 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
  51. 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
  52. Derived supersymmetries of determinantal varieties
    J. Commut. Algebra 6 (2014), no. 2, 261–286.
    arXiv (last updated 7/13/2012) | Journal
  53. 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
  54. 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
  55. 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
  56. 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
  57. Equations and syzygies of some Kalman varieties
    Proc. Amer. Math. Soc. 140 (2012), 4153–4166.
    arXiv (last updated 9/7/2011) | Journal
  58. 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
  59. 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
  60. 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
  61. 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
  62. 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
  63. Schubert complexes and degeneracy loci
    J. Algebra 337 (2011), 103–125.
    arXiv (last updated 4/28/2011) | Extended abstract | Journal
  64. 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
  65. 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
  66. 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
  67. 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
  68. A bijective proof for a theorem of Ehrhart
    Amer. Math. Monthly 116 (2009), no. 8, 688–701.
    arXiv (last updated 6/27/2008) | Journal
  69. 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
  70. 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. Structures in representation stability
    Notices Amer. Math. Soc. 67 (2020), no. 1, 38–43.
    arXiv (last updated 12/23/2019) | Journal
  2. Cubics in 10 variables vs. cubics in 1000 variables: Uniformity phenomena for bounded degree polynomials
    (with Daniel Erman and Andrew Snowden)
    Bull. Amer. Math. Soc. (N.S.) 56 (2019), no. 1, 87–114.
    arXiv (last updated 9/25/2018) | Journal
  3. 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
  4. Introduction to twisted commutative algebras
    (with Andrew Snowden)
    arXiv (last updated 9/21/2012)

Appendices

Software

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