Fall 2021

Undergraduate researchers: Jordan Grant, Jeremy Krill, Samuel Perales

Mentor: Teddy Weisman

Faculty advisor: Jeff Danciger

In this project, we focus on extending the work done last semester by designing an algorithm around a generalized version of the Ping Pong Lemma to work for a larger set of groups. The previous project allowed us to find intervals of \(\mathbb{R} \mathbb{P} ^{1}\) which met certain containment conditions, guaranteeing the faithfulness of particular representations of free groups in \(SL(2, \mathbb{R})\). Here, we attempt to generalize these conditions to work for any group with an automatic structure. This will allow us to find valid intervals under a different set of conditions to work for non-free groups such as cyclic free products and triangle groups.