Publications Resulting from Research Funded by the VIGRE Grant

University of Georgia VIGRE Algebra Group, "Varieties of Nilpotent Matrices for Simple Lie Algebras I: Good Primes," Journal of Algebra, p. 719-737, vol. 280 (2004). Published.

University of Georgia VIGRE Algebra Group, "Varieties of Nilpotent Matrices for Simple Lie Algebras II: Bad Primes," Journal of Algebra, p. 65-99, vol. 292 (2005). Published.

University of Georgia VIGRE Algebra Group, "Support Varieties for Weyl Modules Over Bad Primes," Journal of Algebra, p.602-633, vol.312 (2007). Published.

University of Georgia VIGRE Algebra Group, "On Kostant's Theorem for Lie Algebra Cohomology," Contemp. Math, p. 39-60, vol. 478 (2009). Published.

University of Georgia VIGRE Algebra Group, "Cohomology of Quantum Groups: An Analog of Kostant's Theorem". Submitted.

University of Georgia VIGRE Mathematical Biology Group on Defining Ecosystem Health, "Throughflow Analysis: a Stochastic Approach," Ecological Modeling. Submitted.

Alexander Brown, Eleanor Dannenberg, Jennifer Fox, Joshua Hanna, Katherine Keck, Alexander Moore, Zachary Robbins, Brandon Samples and James Stankewicz, "On a Generalization of the Frobenius Number." Preprint: http://www.math.uga.edu/~lorenz/OnAGeneralizationFrobenius.pdf

Jason Cantarella, X.W. Faber, Chad Mullikin, "Upper Bounds for Ropelength as a Function of Crossing Number," Topology and Its Applications, p.253, vol. 135 (2003). Published.

Jason Cantarella, Joseph Fu, Rob Kusner, John Sullivan, Nancy Wrinkle, "Criticality for the Gehring Link Problem," Geometry and Topology, p. 2055, vol. 10 (2006). Published.

Jason Cantarella, Jason Parsley, "A New Cohomological Formula for Helicity in R^{2k+1} Reveals the Effect of a Diffeomorphism on Helicity, arXiv: 0903.1465 (March 2009). Submitted.

Ted Ashton and Jason Cantarella, "A Fast Octree-Based Algorithm for Computing Ropelength," Physical and Numerical Models in Knot Theory and Their Applications to the Life Sciences, p.323 (2005). Published.

Jason Cantarella and Michael Piatek, "TSNNLS: A Solver for Large Sparse Least Squares Problems with Non-Negative Variables." Submitted.

Jason Cantarella, Michael Piatek, and Eric Rawdon, "Visualizing the Tightening of Knots," Proceedings of IEEE Visualization, p. 575 (2005). Published.

Ted Ashton, Jason Cantarella, Michael Piatek, Eric Rawdon, "Self-Contact Sets for 50 Tightly Knotted and Linked Tubes." Preprint.

Pete L. Clark, Patrick Corn, Steve Lane, Alex Rice, Jim Stankewicz, Nathan Walters, Steve Winburn, Ben Wyser, "Computing Torsion Subgroups of CM Elliptic Curves," soon to be submitted to Mathematics of Computation.

Pete L. Clark, Brian Cook and Jim Stankewicz, "Torsion Points on Elliptic Curves with Complex Multiplication," in revision, International Journal of Number Theory.

X. W. C. Faber, "On the Finite Field Kakeya Probleim in Two Dimensions," Journal of Number Theory, p. 248-257, vol. 124 (2007). Published.

L. Matamba, C. Kazanci, J.R. Schramski, M. Blessing, P. Alexander, and B.C. Patten, "Throughflow Analysis: A Stochastic Approach," in press and available online: (doi:10.1016/j.ecolmodel.2009.07.001) http://dx.doi.org/10.1016/j.ecolmodel.2009.07.001.

Other Specific Products Resulting from Research Funded by the VIGRE Grant

Product Type: Software (or netware)
Product Description: Jason Cantarella and Ted Ashton, octrope 1.3, A fast octree-based algorithm for computing ropelength
Sharing Information: The software can be downloaded from http://www.jasoncantarella.com/webpage/index.php?title=Octrope.

Product Type: Software (or netware)
Product Description: Jason Cantarella and Michael Piatek, tsnnls 2.2.3, A solver for large sparse least squares problems with non-negative variables.Tsnnls is used in a variety of commercial applications, including CAD (TSplines, Inc), fish-finding sonar (Atlantic Consulting), and gene sequencing (Illumina, Inc).Sharing Information: It can be downloaded from http://www.jasoncantarella.com/webpage/index.php?title=Tsnnls.

Product Type: Software (or netware)
Product Description: Jason Cantarella, plCurve 2.0.2, a library for efficiently handling space polygons.
Sharing Information: The software can be downloaded from http://www.jasoncantarella.com/webpage/index.php?title=PlCurve.

Product Type: Software (or netware)
Product Description: University of Georgia VIGRE Algebra Group, UGA3, GAP program that computes support varieties of induced modules for exceptional groups over bad primes.
Sharing Information: A description of the software can be found at http://www.math.uga.edu/nakano/vigre/vigre.html. The software can be downloaded from http://www.math.uga.edu/brian/UGA3.tar.gz.