Brett Barwick
USC Department of Mathematics
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Mathematics
Papers:
- The QuillenSuslin Package for Macaulay2 [arXiv] - (Joint with Branden Stone, University of Kansas), submitted to the Journal of Software for Algebra and Geometry.
Macaulay2 Packages:
- QuillenSuslin.m2 - (Joint with Branden Stone, University of Kansas)
A package 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 a modification of the algorithm given by Logar-Sturmfels in their 1992 paper ``Algorithms for the Quillen-Suslin Theorem.'' Some explanation of the general algorithm is given in the above paper.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.Mathematical Activities at the University of South Carolina:
- Spring 2004 - Fall 2005: Mathematics Tutor for ACE/Leconte Math Labs
- Spring 2004 - Present: Private Mathematics Tutor
- Fall 2005 - Fall 2006: Grader for Undergraduate Math Courses
- Spring 2006: Supplemental Instruction Leader for Math 111 (Cui)
- Fall 2006: Supplemental Instruction Leader for Math 111 (Jordan)
- Spring 2007: Supplemental Instruction Leader for Math 142 (Diestel)
- Spring 2006 - Spring 2007: Member of Pi Mu Epsilon
- December 2005/2006/2008/2010: Volunteer Proctor for Annual USC High
School Math Contest- Spring 2006/2009/2010/2011: Volunteer Proctor for Practice AP Calculus
Exam at USC- Spring 2007: Winner of the USC Problem of the Month Competition
- Fall 2007: Graduate Teaching Assistant for Math 142 (Ivanov)
- Spring 2008: Graduate Teaching Assistant for Math 142 (Narayan)
- Summer II 2008: Taught Math 115 - Precalculus
- Fall 2008: Taught Math 111 - College Algebra
- Spring 2009: Taught Math 115 - Precalculus
- Summer II 2009: Taught Math 115 - Precalculus
- Fall 2009: Taught Math 111 - College Algebra
- Spring 2010: Taught Math 122 - Business Calculus
- Fall 2010: Taught Math 115 - Precalculus
- Fall 2010: Taught Math 122 - Business Calculus
- Spring 2011: Taught Math 141 - Calculus I
- Fall 2011: Taught Math E142 - Calculus II
Academic/Teaching Awards:
- Fall 2006 - Spring 2007: Thomas L. Markham Mathematics Scholarship
- Spring 2007: Jeong S. Yang Award for Excellence in Mathematics
- Spring 2010: USC Department of Mathematics Outstanding Graduate Teaching Assistant
- Spring 2011: USC Department of Mathematics Outstanding Graduate Teaching Assistant - Honorable Mention
Conferences and Workshops Attended:
- AMS Southeastern Sectional Meeting - Wake Forest University, Winston-Salem, NC - September 24-25, 2011. Talk presented: Generic Hilbert-Burch Matrices for Ideals Generated by Triples of Homogeneous Forms in k[x,y].
- Macaulay2 Workshop - IMA, Minneapolis - July 24-30, 2011.
- AMS Southeastern Sectional Meeting - Georgia Southern University, Statesboro, GA - March 12-13, 2011. Talk presented: An Algorithmic Approach to the Quillen-Suslin Theorem over ZZ[x_1,...,x_n].
- Joint Mathematics Meetings - New Orleans - January 6-9, 2011.
- Macaulay2 Workshop - Colorado College - August 7-13, 2010.
- Mathematics Research Community on Commutative Algebra - Snowbird, Utah - June 26-July 2, 2010. (Pictures)
- Commutative Algebra Meetings in the Southeast - Regional Meeting - Atlanta, Georgia - March 20-21, 2010.
- Commutative Algebra Meetings in the Southeast - National Meeting - Orlando, Florida - January 23-24, 2010.
- 2009 Fall Southeastern AMS Meeting - Boca Raton, Florida - October 30-November 1, 2009.
- Commutative Algebra Meetings in the Southeast - Regional Meeting - Columbia, South Carolina - September 12-13, 2009.
- GSU-USC Commutative Algebra Seminar - Columbia, South Carolina - April 4-5, 2009.
- GSU-USC Commutative Algebra Seminar - Columbia, South Carolina - November 14-16, 2008.