Papers

  1. 1. A Generalization of Stillman's Conjecture via Twisted Commutative Algebra
    (w/ Steven V Sam and Andrew Snowden).
  2. 2. A Distributed Numerical Approach to Syzygies on P2
    (w/ Juliette Bruce, Steve Goldstein, and Jay Yang).
  3. 3. Random Flag Complexes and Asymptotic Syzygies
    (w/ Jay Yang).
  4. 4. Virtual Resolutions for a Product of Projective Spaces
    (w/ Christine Berkesch Zamaere and Gregory G. Smith).
  5. 5. A probabilistic approach to systems of parameters and Noether normalization
    (w/ Juliette Bruce)

  6. 6. Divergent series and Serre's intersection formula for graded rings
    Advances in Mathematics, to appear.
  7. 7. Categorified duality in Boij--Söderberg Theory and invariants of free complexes
    (w/ David Eisenbud.)
    J. Eur. Math. Soc. (JEMS), to appear.
  8. 8. Questions about Boij-Söderberg Theory
    (w/ Steven V Sam)
    Surveys on recent developments in algebraic geometry, eds Coskun, de Fernex, Gibney, (2017).
  9. 9. Gauss Composition for P^1, and the universal Jacobian of the Hurwitz space of double covers
    (w/ Melanie Matchett Wood.)
    Journal of Algebra, 470, 320-352 (2017).
  10. 10. Supernatural analogues of Beilinson Monads
    (w/ Steven V Sam.)
    Compositio, 152 , 2545-2562 (2016).
  11. 11. Furstenberg sets and Furstenberg schemes over finite fields
    (w/ Jordan S. Ellenberg.)
    Algebra and Number Theory, 10, 1415-1436 (2016).
  12. 12. A quick proof of nonvanishing for asymptotic syzygies
    (w/ Lawrence Ein and Rob Lazarsfeld.)
    Algebraic Geometry, 3, 211-22 (2016).
  13. 13. Semiample Bertini Theorems over finite fields
    (w/ Melanie Matchett Wood.)
    Duke Math. J. 164, 1-38 (2015).
  14. 14. A heuristic for the distribution of point counts for random curves over a finite field
    (w/ Jeffrey D. Achter, Kiran S. Kedlaya, Melanie Matchett Wood, and David Zureick-Brown.)
    Philosophical Transactions A, 373 (2015).
  15. 15. Tate resolutions for products of projective spaces
    (w/ David Eisenbud and Frank-Olaf Schreyer.)
    Acta Math. Vietnam. 40, 5-36 (2015).
  16. 16. The Betti table of a high degree curve is asymptotically pure.
    Recent advances in algebraic geometry: A volume in honor of Rob Lazarsfeld's 60th birthday (ed. Christopher Hacon, Mircea Mustata, and Mihnea Popa)
    pp. 200-206, London Mathematical Society Lecture Notes (No. 417), Cambridge University Press, Cambridge, 2015.
  17. 17. Asymptotics of random Betti tables
    (w/ Lawrence Ein and Rob Lazarsfeld.)
    Journal für die reine und angewandte Mathematik (Crelle's Journal), to appear.
  18. 18. Tensor complexes: Multilinear free resolutions constructed from higher tensors
    (w/ Christine Berkesch, Manoj Kummini, and Steven V Sam.)
    J. Eur. Math. Soc. (JEMS) 15, 2257-2295 (2013).
  19. 19. Three flavors of extremal Betti tables
    (w/ Christine Berkesch and Manoj Kummini.)
    Commutative algebra: expository papers dedicated to David Eisenbud on the occasion of his 65th birthday (ed. Irena Peeva), 99-121, Springer, New York, 2013.
  20. 20. Filtering free resolutions (formerly titled Beyond numerics: The existence of pure filtrations)
    (w/ David Eisenbud and Frank-Olaf Schreyer.)
    Compositio Mathematica, 149, 754-772 (2013).
  21. 21. Murphy's Law for Hilbert function strata in the Hilbert scheme of points
    Mathematical Research Letters, 19, 1277-1281 (2012).
  22. 22. Shapes of free resolutions over a local ring
    (w/ Christine Berkesch, Manoj Kummini, and Steven V Sam.)
    Mathematische Annalen, 354, 939-9545 (2012).
  23. 23. Poset structures in Boij-Söderberg theory
    (w/ Christine Berkesch, Manoj Kummini, and Steven V Sam.)
    International Mathematics Research Notices, 2012, 5132-5160 (2012).
  24. 24. The cone of Betti diagrams over a hypersurface ring of low embedding dimension
    (w/ Christine Berkesch, Jesse Burke and Courtney Gibbons.)
    Journal of Pure and Applied Algebra, 216 (2012), 2256-2268.
  25. 25. Secant varieties of P^2 x P^n embedded by O(1,2)
    (w/ Dustin A. Cartwright and Luke Oeding.)
    Journal of the London Mathematical Society, 85 (2012), 121-141.
  26. 26. Laurent polynomials and Eulerian numbers
    (w/ Gregory G. Smith and Anthony Várilly-Alvarado.)
    Journal of Combinatorial Theory, Series A, 118 (2011), 396-402.
  27. 27. A syzygetic approach to the smoothability of zero dimensional schemes
    (w/ Mauricio Velasco.)
    Advances in Mathematics, 224 (2010), 1143-1166.
  28. 28. A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture
    Mathematical Research Letters, 17 (2010), 1079-1089.
  29. 29. The Semigroup of Betti Diagrams
    Algebra and Number Theory, 3 (2009), 341-365.
  30. 30. Hilbert schemes of 8 points
    (w/ Dustin A. Cartwright, Mauricio Velasco and Bianca Viray.)
    Algebra and Number Theory, 3 (2009), 763-795.