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.

• Michigan Postdoc Algebraic Geometry Seminar, co-organized with Matt Satriano.
• Michigan Commutative Algebra Seminar, co-organized with Mel Hochster and Wenliang Zhang.
• Michigan Derived Algebraic Geometry Learning Workshop, co-organized with Bhargav Bhatt.
• Michigan Computation Algebraic Geometry Day, organized by Tony Shaska.

An equivariant pure resolution, from here.

Research

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.

Odds and Ends

• Open Questions in Algebraic Geometry
  These are unofficial notes from a session on open questions at the Spring 2009 MSRI semester on algebraic geometry.
  
  
• Open Questions Related to Boij-Söderberg Theory
  These are unofficial notes from the 2008 conference on Minimal Free Resolutions at Cornell University. Frank Moore and Joanna Nilsson helped me edit this document. (NOTE: Progress has been made on some of these questions since 2008. If you're curious about the state of the art of any particular question, feel free to email me.)
  
  
• The CME Project
  I was one of many authors for this NSF-funded high school curriculum. The lead developer of the project was Al Cuoco.

More Activities

• MSRI Summer School on Commutative Algebra
  Together with Irena Swanson and Amelia Taylor, I co-organized a summer school on commutative algebra at MSRI for 2011. The wiki from that workshop can be found here .
• MathOverflow.net
  I am a fan of MathOverflow, a site for asking and answering questions about research mathematics.
• K-12 Education Consulting
  I do small amount of consulting on K-12 education projects, often through the Instructional Research Group.
• Detroit Tigers
  Go Tigers!