UW-Madison REU 2022
The Carpenter's Rule Problem asks if a polygon or polygonal arc can be moved to a convex polygon or line segment without distorting edge lengths. My students very successfully implemented a linear programming solution to this problem due to Connelly, Demaine, and Rote. We are currently studying other approaches and implementations of this problem in the Madison Expermiental Math Lab.
In the Summer of 2022, I mentored a group at the Michigan Research Experience for Graduates where we studied the Generalizations of the Analyst's Traveling Salesman Theorem (ATST)
As part of our work, we did explicit computations using the curve to the left and together found evidence of a "critical exponent" phenomena. We started to study the proof of the ATST in hope of generalizing what we found.