Jessica Appel, Gina Grosso, Madison Howard, Angela Vichitbandha, Kate Ponto

University of Kentucky Math Lab
University of Kentucky
Lexington, KY, USA

The University of Kentucky Math Lab aims to encourage undergraduate math interest across a range of projects. These include research projects and outreach as well visualization projects. We interpret visualization broadly making room for both 3d printing of polyhedra, simplicial complexes, and string diagrams and more traditional textile crafts such has quilting and crochet.

Brill-Noether theory via partitions
63 x 63 x 1 cm
Textiles - Quilting

Brill-Noether theory is the study of line bundles on algebraic curves. A central problem is to determine how many curves possess line bundles with given invariants. Pflueger showed that this problem can be reduced to the study tableaux.

This quilt represents a tableau in which the numbers are replaced with colors, in rainbow order. It demonstrates that the space of genus g curves possessing a line bundle of rank 7 and degree g-1 has the expected dimension, for g at least 34.

This tableau was found using code developed by Kristopher Andrew, Jessica Appel, Madison Howard, Elijah Jackson, Jackson Morris, and Dave Jensen. Photo courtesy of Katie Davenport.