Spring 2022

Undergraduate researchers: Jordan Grant, Jeremy Krill, Samuel Perales

Mentor: Teddy Weisman

Faculty advisor: Jeff Danciger

This semester, the Ping Pong Group finished its work from the previous two semesters of TXGL. We finalized an algorithm which worked with a generalized version of the Ping Pong Lemma to find intervals of \(\mathbb{R} \mathbb{P} ^{1}\) meeting certain containment conditions which guarantee the faithfulness of a particular group representation in \(SL(2, \mathbb{R})\). To showcase our work, we create a new visualization tool in the GitHub repository along with a web-based demo of a few valid intervals we found for a cyclic free product, triangle group, and surface group.