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 RP1RP1 which met certain containment conditions, guaranteeing the faithfulness of particular representations of free groups in SL(2,R)SL(2,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.