Brett Barwick
Assistant Professor, Mathematics
USC Upstate
Division of Mathematics and Computer Science
Hodge Center 239

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Curriculum Vitae (10/3/12)
Research Statement (10/30/11)

Papers

Computing Buchsbaum-Eisenbud Matrices, in preparation.

Generic Hilbert Burch Matrices for Certain Families of Homogeneous Ideals in k[x,y], in preparation.

Computing Free Bases for Projective Modules (Joint with Branden Stone), published in Journal of Software for Algebra and Geometry, Vol. 5, pg. 26-32, 2013. [PDF / M2]

A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices. Ph.D. Dissertation at University of South Carolina, 2012.

Macaulay2 Packages

QuillenSuslin.m2 - (Joint with Branden Stone, last updated September 2013)
A package containing methods for computing free bases for projective modules over polynomial rings and solving related problems concerning completion of unimodular rows to square invertible matrices in Macaulay2. This package implements the algorithms given by Logar-Sturmfels in their 1992 paper ``Algorithms for the Quillen-Suslin Theorem'' with some modifications as described in a Ph.D. thesis ``Algorithmic Analysis of Presentations of Groups and Modules'' by Anna Fabianska. Algorithms for computing completions of unimodular rows over Laurent polynomial rings, due to Park, are also provided. Some explanation of the general algorithm is given in this paper.

Student Projects

Students interested in pursuing undergraduate projects related to algebra or number theory (or related areas of mathematics) may contact me at bbarwick@uscupstate.edu or visit my office in Hodge 239 to discuss possible project ideas. Information regarding undergraduate research at USC Upstate may be found on the Center for Undergraduate Research and Scholarship webpage. Possible competitive funding opportunities offered by the university may be found here.

Other Writing

Boij-Söderberg Theory in the nonstandard graded case - (with J. Biermann, D. Cook II, W. F. Moore, C. Raicu, and D. Stamate)
Report from work at the 2010 Mathematical Research Community on Commutative Algebra held in Snowbird, Utah.