Daniel Erman
Simons Postdoctoral Fellow
Department of Mathematics
University of Michigan
East Hall, Ann Arbor, MI

Office: 4839 East Hall
Phone: (734)-764-0317
Email: erman at umich dot edu.

A degeneration of a hyperelliptic
curve, from here.

Webpage for Math 615.
I am currently co-organizing or helping out with some seminars and workshops:

An equivariant pure resolution, from here.

Research Papers

I am interested in the study of syzygies and in the use of free complexes in algebraic geometry and commutative algebra. Recently, I have become particularly interested in the study of syzygies under various asymptotic constructions, and in the study of algebraic geometry over finite fields.
  1. Semiample Bertini Theorems over finite fields
    (w/ Melanie Matchett Wood.)
  2. Asymptotics of random Betti tables
    (w/ Lawrence Ein and Rob Lazarsfeld.)
  3. Categorified duality in Boij--Söderberg Theory and invariants of free complexes
    (w/ David Eisenbud.)
  4. Three flavors of extremal Betti tables
    (w/ Christine Berkesch and Manoj Kummini.)
  5. Gauss Composition for P^1, and the universal Jacobian of the Hurwitz space of double covers
    (w/ Melanie Matchett Wood.)

  6. Filtering free resolutions (formerly titled Beyond numerics: The existence of pure filtrations)
    (w/ David Eisenbud and Frank-Olaf Schreyer.)
    Compositio Mathematica, to appear.
  7. Tensor complexes: Multilinear free resolutions constructed from higher tensors
    (w/ Christine Berkesch, Manoj Kummini, and Steven V Sam.)
    Journal of the European Mathematical Society, to appear.
  8. Murphy's Law for Hilbert function strata in the Hilbert scheme of points
    Mathematical Research Letters, to appear.
  9. Shapes of free resolutions over a local ring
    (w/ Christine Berkesch, Manoj Kummini, and Steven V Sam.)
    Mathematische Annalen, to appear.
  10. Poset structures in Boij-Söderberg theory
    (w/ Christine Berkesch, Manoj Kummini, and Steven V Sam.)
    International Mathematics Research Notices, to appear.
  11. 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.
  12. 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.
  13. Laurent polynomials and Eulerian numbers
    (w/ Gregory G. Smith and Anthony Várilly-Alvarado.)
    Journal of Combintorial Theory, Series A, 118 (2011), 396-402.
  14. A syzygetic approach to the smoothability of zero dimensional schemes
    (w/ Mauricio Velasco.)
    Advances in Mathematics, 224 (2010), 1143-1166.
  15. A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture
    Mathematical Research Letters, 17 (2010), 1079-1089.
  16. The Semigroup of Betti Diagrams
    Algebra and Number Theory, 3 (2009), 341-365.
  17. Hilbert schemes of 8 points
    (w/ Dustin A. Cartwright, Mauricio Velasco and Bianca Viray.)
    Algebra and Number Theory, 3 (2009), 763-795.

The syzygies of random Betti tables converge towards a normal distribution.

Odds and Ends

More Activities

The semigroup of Betti diagrams.