Spring 2017

During Spring 2017 MEGL ran a program with 16 participants. There were three research groups (Orbits, Special Words, Polytopes), two visualization groups (Geometric Surfaces, Virtual Reality), and one public outreach group (Outreach). The research and visualization groups engaged in experimental exploration involving faculty, graduate students, and undergraduates. Teams met weekly to conduct experiments generating data, to make conjectures from data, and to work on theory resulting from conjectures. The outreach group involved faculty, graduate students, and undergraduates to develop and implement activities for elementary middle and high school students that were presented at local schools and public libraries. We concluded with final reports from all teams and an end of term symposium.

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This project continues the study of the dynamics of the outer automorphism group of a free group of rank r, denoted $Out(F_{r})$, on the finite field points of the relative $SL_2(\mathbb{C})$ character varieties of $F_r$. We are interested in two main problems (1) understanding the length of the largest orbit and which classes achieve it, and also (2) defining and proving the action is "ergodic" in this arithmetic setting. Additionally we are working on creating, in 3D print, visualizations of this family of dynamical systems.

There has been some recent interest in this problem from other researchers and we have also been investing time in reading the work and methods of these other researchers.

View our symposium presentation here: Presentation

View our symposium Mathematica Notebook here: Mathematica

Symposium Pictures

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