Spring 2022
Ping Pong Patches
Students: Jordan Grant, Jeremy Krill, Samuel Perales
Mentor: Teddy Weisman
Faculty advisor: Jeff Danciger
This project finalized the work of the two previous semesters to create an algorithm which can computational generate proofs of a representations faithfulness in SL(2,R)SL(2,R). The work includes a demo in the form of a web application of proofs for a cyclic free product, triangle group, and surface group.
Fall 2021
Stable commutator length
Students: Simon Xiang, Jimmy Xin, Ruiqi Zou
Faculty advisor: Lvzhou (Joe) Chen
Billiards in the projective plane
Students: Andrew Bacon, Henry Castillo, Vincent Solon
Mentor: Charlie Reid
Faculty advisor: Jeff Danciger
Automatic ping-pong
Students: Jordan Grant, Jeremy Krill, Samuel Perales
Mentor: Teddy Weisman
Faculty advisor: Jeff Danciger
This project studied representations of strongly geodesically automatic groups in SL(2,R)SL(2,R) using a generalized form of the ping-pong lemma. It extended work from the previous ping-pong project to develop an algorithm that searches for an upper-bound on the kernel of a representation.
Spring 2021
Convex domains in projective geometry
Students: Sarah Bruce, Maxwell Nakos, John Teague, Anabel T. To
Mentors: Florian Stecker, Neža Žager Korenjak
Faculty advisor: Jeff Danciger
This project explored fundamentals of projective geometry and properties of convex subsets of RP2RP2. It produced some interactive demos illustrating the Benzecri cocompactness theorem, an important result in convex projective geometry. View them here!
Ping-pong and beyond
Students: Jordan Grant, Abhay Katyal, Samuel Perales
Mentors: Max Riestenberg, Teddy Weisman
Faculty advisor: Jeff Danciger
This project studied free groups in SL(2,R)SL(2,R) using the ping-pong lemma. It involved using the lemma to design and implement an algorithm that decides if a given set of matrices generate a free group. See a demonstration here!