# UBC Ergodic Theory Seminar: Sophie MacDonald

## Topic

Encoding subshifts through sliding block codes

## Details

A number of results in symbolic dynamics, principally Krieger’s embedding theorem and Boyle’s lower-entropy factor theorem, give conditions for the existence of an injective or surjecive sliding block code from one subshift to another, in terms of entropy and low-order periodic points. I will present a recent result answering the following question of Tom Meyerovitch: given a surjective sliding block code from a mixing shift of finite type X to a mixing sofic shift Y, for which subshifts Z of strictly lower entropy than Y does there exist a sliding block code from Z into X such that the composition (from Z into
Y) is injective? The result can be seen as a deterministic analogue of various results in information theory, giving conditions, in terms of entropy and periodic points, on the sources which can be transmitted without error through a deterministic channel (i.e. a sliding block
code) despite deterministic noise (i.e. non-injectivity).

## Additional Information

**Time**: 3:00pm Pacific

**Hybrid** (if in person, please wear a mask)

Join Zoom Meeting

https://ubc.zoom.us/j/62427563725?pwd=RzJvTCtzVSs2MGFUTDYxd1JmYzh5UT09

Meeting ID: 624 2756 3725 Passcode: 269638

Sophie MacDonald, UBC

This is a Past Event

Event Type

**Scientific, Seminar**

Date

**November 25, 2022**

Time

**-**

Location

University of British Columbia