Daniel Erman

Simons Postdoctoral Fellow
Department of Mathematics
University of Michigan
East Hall, Ann Arbor, MI
48109-1043

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



The semigroup of Betti diagrams.

I am currently co-organizing or helping out with some seminars and workshops:

An equivariant pure resolution, from here.

Research

I am interested in the study of syzygies and in the use of free resolutions 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. Categorified duality in Boij--Söderberg Theory and invariants of free complexes
    (w/ David Eisenbud.)
    Submitted.
  2. Murphy's Law for Hilbert function strata in the Hilbert scheme of points
    Submitted.
  3. Gauss Composition for P^1, and the universal Jacobian of the Hurwitz space of double covers
    (w/ Melanie Matchett Wood.)
    Submitted.
  4. Filtering Free Resolutions (formerly titled Beyond Numerics: The Existence of Pure Filtrations)
    (w/ David Eisenbud and Frank-Olaf Schreyer.)
    Submitted.
  5. 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.
  6. 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, to appear.
  7. Shapes of free resolutions over a local ring
    (w/ Christine Berkesch, Manoj Kummini, and Steven V Sam.)
    Mathematische Annalen, to appear.
  8. Poset structures in Boij-Söderberg theory
    (w/ Christine Berkesch, Manoj Kummini, and Steven V Sam.)
    International Mathematics Research Notices, to appear.
  9. 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, to appear.
  10. Laurent polynomials and Eulerian numbers
    (w/ Gregory G. Smith and Anthony Várilly-Alvarado.)
    Journal of Combintorial Theory, Series A, 118 (2011), 396-402.
  11. A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture
    Mathematical Research Letters, 17 (2010), 1079-1089.
  12. A syzygetic approach to the smoothability of zero dimensional schemes
    (w/ Mauricio Velasco.)
    Advances in Mathematics,, 224 (2010), 1143-1166.
  13. The Semigroup of Betti Diagrams
    Algebra and Number Theory, 3 (2009), 341-365.
  14. Hilbert schemes of 8 points
    (w/ Dustin A. Cartwright, Mauricio Velasco and Bianca Viray.)
    Algebra and Number Theory, 3 (2009), 763-795.


A degeneration of a hyperelliptic curve, from here.

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