Guin Bixler

I subscribe to the four axioms of Federico Ardila-Mantilla:

1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

4. Every student deserves to be treated with dignity and respect.

Research

I am broadly interested in dynamical systems, particularly those with a differential-geometric flair. So far, I have focused on rigidity phenomena in dynamical systems arising from hyperbolic geometry.

My current project is on local rigidity of group actions. A group action is locally rigid if you can't wiggle it: every nearby group action is equivalent (say, C^∞ conjugate) to the one you started with. Flows (actions of ℝ) are not locally rigid, but actions of larger groups containing ℝ might be locally rigid. For example, many algebraic actions actions of ℝᵏ (for k≥2) are locally rigid (Katok and Spatzier, 1997). 

I am investigating some "standard P-actions" of rank-one Lie groups (roughly speaking, matrix groups containing a diagonalizable copy of ℝ but no diagonalizable copies of ℝ²). In my thesis, I show that standard P-actions related to complex-hyperbolic geometry are locally rigid. The analogous actions in real-hyperbolic geometry is already known to be sometimes locally rigid (Asaoka 2015). I believe my approach will also apply to the quaternionic-hyperbolic and Cayley-hyperbolic settings, and I hope to solve these next.

My research statement (last updated October 12, 2025) has more details and a less-rushed exposition. Comments, questions, and corrections are welcome.

I do not yet have a shareable draft. If you would like updates, please contact me!

Teaching

I find working with students to be enriching, rewarding, and frequently inspiring. Here are some of my teaching experiences at Northwestern University:

Instructor of Record for Math 220-1 (Single-Variable Differential Calculus)

Teaching Assistant for many courses (including calculus-es, linear algebra, proofs, graph theory, complex analysis, and dynamical systems)

Mentor for our Directed Reading Program, a Research Experience for Undergraduates, and our Causeway Program.

I also completed the Searle Center's Reflective and Effective Teaching program.

Music

I joined my elementary school's orchestra when I was ten years old, and I have been playing cello ever since.

I currently play in the Evanston Symphony Orchestra. Here is us performing Tchaikovsky 6! In recent years, we've performed some of my favorites: Mahler 1, Pictures at an Exhibition, Copland's Billy the Kid suite, the Mozart Clarinet Concerto, and Beethoven 9.

I also enjoy chamber music and am open to starting and joining casual chamber groups. Feel free to hit me up!