Â鶹ÒùÔº

Ìý

Project title: The automorphism group of a subshift of finite type

Ìý

Ìý

Informally, a dynamic system is any physical system that evolves with time (e.g., a pendulum, a planet orbiting the sun, the weather, etc). From a more mathematically precise perspective, one can consider a function mapping a space to itself. For example, f(x)=x^2 defined on the set of real numbers. Using this formulation, time is represented by iterating the function. In the example f(x)=x^2, if the initial value is 2, then after one unit of time, the value is f(2)=4, after two units of time, the value is f(f(2))=f(4)=16 and so on.

Ìý

We will study a class of dynamical systems called subshifts of finite type. These systems are examples of chaos. Roughly speaking chaos is characterized by the property that "the present determines the future, but the approximate present does not approximately determine the future." The study of subshifts of finite type involves combinatorics, graph theory, linear algebra, and group theory.

Ìý

The goal of this project is to study the automorphism group of a subshift of finite type. This will involve using Sage and Gap to construct interesting shifts, the construction of explicit examples of automorphisms, and the study of invariants both at the shift and automorphism group level. No knowledge of shifts or automorphism groups is required to apply to this Math Lab.

Ìý

Number of undergraduate students: 2-3

Ìý

Committment: Ìý5 hours/week for pay or course credit

Ìý

Due date: ÌýJan 20 2025

Ìý

Ìý

Ìý

Send applications to robin.deeley@colorado.edu with "Subshifts Spring 2025 App" for the subject line

Ìý

Back to the Experimental Mathematics Lab.

Ìý