Coming Spring 2025!
Faculty supervisor: Jeffrey Danciger
Graduate student mentor: Aaron Benda
Description – A classical approach to understanding certain dynamical systems involves converting information between discrete-time versus continuous-time systems. For theoretical reasons, hyperbolic geodesic flows (continuous-time systems, with geometric significance) can be encoded as symbolic systems, namely subshifts of finite type (discrete-time systems, which are dynamically well-understood). A Markov coding is a way to convert between these two kinds of systems. Broadly speaking, the goal of this project is to produce pictures or animations indicating how this coding takes place in certain specific cases. The hope is that unpacking this process by visualizing Markov partitions in a concrete way will lead to deeper understanding and insights regarding problems of current research interest.
Desired qualifications:
– Strong coding skills (Python or any language of roughly equivalent strength is fine)
– Solid foundational understanding of calculus, linear algebra, differential equations at a minimum
– Ideally, some experience with (smooth) topology and dynamical systems theory