Stick numbers and polygonal knot theory (25rit038)

The Banff International Research Station will host the "Stick numbers and polygonal knot theory" workshop in Banff from July 20 - 27, 2026.

A new collaboration between mathematicians Jason Cantarella, Andrew Rechnitzer, and Clayton Shonkwiler at the Banff International Research Station in Banff, Canada will look for new insights into rigid knots. Imagine building a knot out of pieces of uncooked spaghetti joined at their ends. More complicated knots require more pasta. Mathematicians abstract this problem and try to find out how many straight line segments are required to tie each knot. The least number of segments required is called the ``stick number''. Despite decades of interest in the problem, the stick number of most knots is still unknown. The team will use advanced computational algorithms to find new stick numbers, shedding light on the type of knot complexity measured by sticks. The results will improve our ability to understand the behavior of complex semiflexible structures like proteins and composite materials.