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Graduate Defense: Jacob Miller

March 8 @ 1:15 pm - 2:15 pm

Thesis Defense

Thesis Information

Title: A Survey Of The Classification Of 1-Dimensional Shift Spaces

Program: Master of Science in Mathematics

Advisor: Dr. John Clemens, Mathematics

Committee Members: Dr. Jens Harlander, Mathematics and Dr. Uwe Kaiser, Mathematics


The full shift over a finite set A is the collection of bi-infinite sequences of symbols in A together with the left shift map, which shifts the indexing of the sequence. A shift space is a subset of a full shift defined by a collection of forbidden blocks, i.e., finite words which are not allowed to appear. Many shift spaces arise as the set of bi-infinite walks on a labeled graph, and many dynamical systems can be encoded as shift spaces where the dynamics are replaced by the left-shift map. We introduce shift spaces and their basic properties, then discuss the classification of 1-dimensional shift spaces, the notion of conjugacy via sliding block codes, and several conjugacy invariants. We end with some exploration into the structure of the kernel of a sliding block code and its relationship to the image shift space.