Research Papers

Publications and Preprint:

• The Alpha Problem & Line Count Configurations (with S. G. Hartke). Expected submission Jan. 2011.
  
• The Eisenbud-Green-Harris Conjecture for Ideals of Points. Expected submission Jan. 2011.
  
• Multiplicities and Enumeration of Semidualizing Modules (with S. Sather-Wagstaff). Submitted to the Illinois Journal of Mathematics (2010).
  
• Combinatorial Bounds on Hilbert Functions of Fat Points in Projective Space (with B. Harbourne and Z. Teitler), Journal of Pure and Applied Algebra, accepted (2010).
  
• Algebraic Interpretation of a Theorem of Clements & Lindstrom (with L. Roberts), Journal of Commutative Algebra, 1 (2009), no. 3, pp. 361 - 380.
  
• The Gale Transform and Multi-Graded Determinantal Schemes (with S. Diaz), Journal of Algebra, 319 (2008), issue 8, pp. 3120 - 3127.
  
• Growth Conditions for a Family of Ideals Containing Regular Sequences, Journal of Pure and Applied Algebra, 212 (2007), no. 1, pp. 122 - 131.
  
• Notes on Integral Closure (with L. Roberts), The Curves Seminar at Queen's, Queen's Papers in Pure and Applied Mathematics, 13 (1999).
  

Geometry and Algebra Projects in Progress:

• Invariants of Fat Points Supported on Complete Intersections.
  
• Hilbert Functions of Fat Points in Multi-Projective Spaces (with A. Van Tuyl & B. Harbourne).
  
• Generalizations of the Gale Transformation (with S. Diaz).