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Papers
- "Lifting Splittings and the Strong Direct Summand Conjecture." in preparation.
- "A Polynomial Bound on the Regularity of an Ideal in
Terms of Half of the Syzygies." preprint. [arXiv]
- Joint with Jesse Beder, Luis Nunez, Alexandra Seceleanu, Bart Snapp and Branden Stone. "Ideals
with Larger Projective Dimension and Regularity." [arXiv]
[link]
- "A Family of Ideals with Few Generators in Low Degree and
Large Projective Dimension." Proceedings of the AMS. Volume 139,
No. 6. pp. 2017-2023. [arXiv] [link]
- "On the Strong Direct Summand Conjecture." PhD Thesis. University of Illinois. 2009.
- "A Note on the Strong Direct Summand Conjecture." Proceedings of
the AMS. Volume 127, No. 9. 2009. pp. 2857-2864. [pdf]
[link]
- joint with Eric Torng.
"SRPT optimally uses faster machines to minimize flow time." ACM
Transactions on Algorithms. Volume 5, No. 1. November 2008. pp. 1-25. [pdf]
- joint with Benjamin
Lundell.
"A Generalized Floor Bound on the Minimum Distance of Geometric Goppa
Codes." Journal of Pure and Applied Algebra. Volume 207, Issue 1.
September 2006. pp. 155-164. [link]
[pdf]
Selected Conference/Invited Talks
- "Ideals with Large(r) Projective Dimension and Stillman's
Question." AMS Sectional Meeting, Special on Commutative Algebra.
University of Utah. Salt Lake City, UT. 2011 [Slides]
- "Ideals with Large(r) Projective Dimension and
Regularity." Computational and Commutative Algebra Seminar. Cornell
Univeristy. Ithaca, NY. 2011. [Slides] [M2 File]
- "Graded Ideals and Homological Dimension or What is a Syzygy?."
Reed College Colloquium. Portland, OR. 2011.
- "Lifting Splittings and the Strong Direct Summand
Conjecture." Joint Math Meetings, Special Session on Local
Commutative Algebra. New Orleans, LA, 2011. [Slides]
- "Bounding Projective Dimension and Regularity." Mathematical Research Community in Commutative Algebra, Snowbird, UT, 2010.
- "On the Strong Direct Summand Conjecture." AMS Spring Central Sectional Meeting, Special Session on Local and Homological Methods in Commutative Algebra, Urbana, IL, 2009. [Slides]
- (with
Ben Lundell) "A Generalized Floor Bound on the
Minimum Distance of Geometric Goppa Codes." Joint
Mathematics Meetings.
Special Session on Algebraic-Geometry
Codes. Atlanta, GA, 2005.
Macaulay 2 Packages
- BigIdeal.m2 - This
package generates the ideals defined in "Ideals with Larger
Projective Dimension and Regularity" by Beder, McCullough, Nunez,
Seceleanu, Snapp and Stone. These ideals have very large projective
dimension and regularity relative to the degree and number of
generators.
- PowerSeries.m2 - This package allows for computation of and manipulation of power series in which more series terms may always be computed later on. Support for rational functions and generating functions is built in.
- FrobeniusMultiplicities.m2 - This package computes approximations of Hilbert-Kunz multiplicities and their higher derived counterparts. See the file demoFrobeniusMultiplicities.m2 for some sample computations. (I recommend downloading both files to one directory and opening demoFrobeniusMultiplicities.m2 in Emacs. Follow the directions from there.)
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