Kari Matthews is a BA student at La Trobe University majoring in mathematics and philosophy. Although philosophy still fascinates her, she gains most satisfaction from mathematical proofs and logic and intends to commence honours study in mathematics midway through 2015. Kari spends her free time reading, bike riding, playing board games and walking an adorable beagle-cavalier cross.
Free groups generated by a pair of parabolic matrices
It is a long standing open problem to determine which pair of parabolic 2×2 complex matrices generates a free group. This project will first survey this topic, and the candidate will acquire standard techniques such as the ping-pong lemma. The candidate will then investigate specific pairs of generators for which it is currently unknown where or not they generate a free group. The project will enable the candidate to acquire a broader knowledge of aspects of contemporary geometry group theory, and to learn certain computational methods using Maple. Furthermore, it will provide the candidate with the opportunity to engage in open research problems in this area.