**Team:** 2-4 students

**Supervisors:** Dr. Robin Deeley, Rachel Chaiser, Levi Lorenzo

**Time Commitment:** 5 hrs per week

**Pay or Credit:** Pay ($15/hr) or 2 credit hours in independent study (MATH or possibly CS), or a combination.

**Description:**

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.

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, and linear algebra. The goal of project is the computation of invariants such as the entropy and dimension group of a subshift of finite type. After understanding these systems and their invariants abstractly, we will create code that explicitly computes invariants given the adjacency matrix of a subshift of finite type.

**Application: ** **DUE AUGUST 19th, 2022.**

Send application materials to robin.deeley@colorado.edu with the subject line "Subshifts Fall 2022 App". A complete application consists of:

- Cover letter or personal statement indicating your interest in the project, including how it will help you in your educational path, and how you can contribute.
- Unofficial transcript
- CV
- Statement (included in cover letter is fine) about availability during the semester, e.g. how many other responsibilities will you have and how available are you for daytime meetings? I find students have a tendency to over-commit, so please think about how this project will fit into your weekly routine and how you will prioritize it. We will need to find a one-hour weekly meeting time. The time committment is 5 hrs/week including that meeting.

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