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)

A degeneration of a hyperelliptic curve, from here.

• Michigan Postdoc Algebraic Geometry Seminar, co-organized with Matt Satriano.
• Michigan Commutative Algebra Seminar, co-organized with Mel Hochster.

An equivariant pure resolution, from here.

Research Papers

1. Semiample Bertini Theorems over finite fields
   (w/ Melanie Matchett Wood.)
   Submitted.
   
2. Asymptotics of random Betti tables
   (w/ Lawrence Ein and Rob Lazarsfeld.)
   Submitted.
   
3. Categorified duality in Boij--Söderberg Theory and invariants of free complexes
   (w/ David Eisenbud.)
   Submitted.
   
4. Three flavors of extremal Betti tables
   (w/ Christine Berkesch and Manoj Kummini.)
   Submitted.
   
5. Gauss Composition for P^1, and the universal Jacobian of the Hurwitz space of double covers
   (w/ Melanie Matchett Wood.)
   Submitted.
   


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

• 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

• Michigan Derived Algebraic Geometry Learning Workshop, co-organized with Bhargav Bhatt.
• Michigan Computation Algebraic Geometry Day, organized by Tony Shaska.
• 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!

The semigroup of Betti diagrams.