Research

Last updated: March 20, 2008

Publications and Preprints

The reviews of my published papers can be found on MathSciNet. Copies of manuscripts are on the arXiv.

       I.      Preprints

1.      Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals (with Chris A. Francisco and Adam Van Tuyl)
Preprint. (PDF)

2.      Splittings of monomial ideals (with Chris A. Francisco and Adam Van Tuyl)
Accepted to Proceedings of American Mathematical Society. (PDF)

3.      Algebraic methods for detecting odd holes in a graph (with Chris A. Francisco and Adam Van Tuyl)
Preprint. (PDF)

4.      Embedded associated primes of powers of square-free monomial ideals (with Susan Morey)
Accepted to Journal of Pure and Applied Algebra. (PDF)

5.      Cohen-Macaulay admissible clutters (with Susan Morey and Rafael H. Villarreal)
Accepted in Journal of Commutative Algebra. (PDF)

6.      Cohen-Macaulay multigraded modules (with C-Y. Jean Chan and Christine Cumming)
Accepted in Illinois Journal of Mathematics. (PDF)

    II.      Published in 2006 - 2010

1.      Monomial ideals, edge ideals of hypergraphs, and their minimal graded Betti numbers (with Adam Van Tuyl)
Journal of Algebraic Combinatorics. 27 (2008), no. 2, 215-245. (PDF).

2.      Whiskers and sequentially Cohen-Macaulay graphs (with Chris A. Francisco)
Journal of Combinatorial Theory, Series A. 115 (2008), no. 2, 304-316. (PDF).

3.      Resolution of square-free monomial ideals via facet ideals: a survey (with Adam Van Tuyl)
Contemporary Mathematics. 448 (2007), 91-117. (PDF).

4.      Adjoint line bundles and syzygies of projective varieties
Vietnam Journal of Mathematics. 35 (2007), no. 2, 135-151. (PDF)

5.      Minimal free resolutions and asymptotic behaviour of multigraded regularity (with Brent Strunk)
Journal of Algebra. 311 (2007), no. 2, 492-510. (PDF)

6.      Multigraded regularity, a*-invariants and the minimal free resolution
Journal of Algebra. 310 (2007), no. 1, 156-179. (PDF)

7.      Splittable ideals and the resolutions of monomial ideals (with Adam Van Tuyl)
Journal of Algebra. 309 (2007), no. 1, 405-425. (PDF)

8.      Homology multipliers and the relation type of parameter ideals (with I.M. Aberbach and L. Ghezzi)
Pacific Journal of Mathematics. 226 (2006), no. 1, 1-40. (PDF, PS)

9.      Toroidalization of generating sequences in dimension two function fields (with Olga Kashcheyeva and Laura Ghezzi)
Journal of Algebra. 301 (2006), no. 2, 838-866. (PDF)

 III.      Published in 2001 - 2005

1.      Asymptotic behaviour of the length of local cohomology (with S.D. Cutkosky, H. Srinivasan and E. Theodorescu).
Canadian Journal of Mathematics. 57 (2005), no. 6, 1178-1192. (PDF, PS)

2.      Asymptotic behaviour of arithmetically Cohen-Macaulay blow-ups (with N.V. Trung).
Transactions of American Mathematical Society. 357 (2005), no. 9, 3655-3672. (PDF, PS)

3.      Arithmetic Macaulayfication of projective schemes (with S.D. Cutkosky).
Journal of Pure and Applied Algebra. 201 (2005), no. 1-3, 49-61. (in the special volume for Vasconcelos). (PDF, PS)

4.      The depth of the associated graded ring of ideals with any reduction number (with I.M. Aberbach and L. Ghezzi).
Journal of Algebra. 276 (2004), 168-179. (PDF, PS, MathSciNet)

5.      Projective embeddings of projective schemes blown up at subschemes
Mathematische Zeitschrift. 246 (2004), no 1-2, 111-124. (PDF, PS,, MathSciNet)

6.      The regularity of points in multiprojective spaces (with A. VanTuyl)
Journal of Pure and Applied Algebra. 187 (2004), no 1-3, 153-167. (PDF, PS, MathSciNet)

7.      On the Rees algebra of certain codimension two perfect ideals
Manuscripta Mathematica. 107 (2002), 479-501. (PDF, PS, MathSciNet)

8.      Box-shaped matrices and the defining ideal of certain blown up surfaces
Journal of Pure and Applied Algebra. 167 (2002), no 2-3, 203-224. (PDF, PS, MathSciNet)

9.      Computing the Spreading and Covering numbers (with E. Carlini and A. Van Tuyl).
Communications in Algebra. 29 (2001), no 12, 5687-5699. (PDF, PS, MathSciNet)

 

Publications in non-refereed journals

  1. The graph and the image of a rational map from Pn to Pm. The Curves Seminar at Queen's. Vol. XII. 141-162, Queen's Papers in Pure and Appl. Math. 114, Queen's Univ., Kingston, ON, 1998. (with A. Van Tuyl).
  2. Tutorial 2: A Chess Puzzle. Proceedings of COCOA VI International School, Queen's Papers in Pure and Appl. Math. 120 (2001), 215-221. (with E. Carlini and A. Van Tuyl).
  3. Tutorial 3: Hilbert Function of Points. Proceedings of COCOA VI International School, Queen's Papers in Pure and Appl. Math. 120 (2001), 227-237. (with E. Carlini and A. Van Tuyl).
  4. Tutorial 5: The Ideal Generation Conjecture. Proceedings of COCOA VI International School, Queen's Papers in Pure and Appl Math. 120 (2001), 245-262. (with E. Carlini and A. Van Tuyl).
  5. Tutorial 6: The Minimal Resolution Conjecture. Proceedings of COCOA VI International School, Queen's Papers in Pure and Appl. Math. 120 (2001), 263-273. (with E. Carlini and A. Van Tuyl).

 

Thesis and Dissertation

  1. PhD Thesis. Rational surfaces from an algebraic perspective. (PDF, PS).
    Queen's University, Kingston, Canada.
  2. Honours Dissertation. Cycles in graphs.
    Curtin University of Technology, Perth, Australia.