Mini-course

Lecturer: Aimee Johnson (Swarthmore College)

Title: Symbolic Dynamics and Factor Maps

Abstract: Symbolic dynamical systems developed as a useful tool in studying general dynamical systems and as a model of data storage for computers. In this context, the symbolic models consist of one-dimensional arrays of symbols and a shift map that maps one such array to another. One can ask the same questions of these systems as one asks for any dynamical system: for instance, when are two such systems conjugate? When can we map from one system to another? One wonderful result in this vein says that if the entropy of the symbolic dynamical system is at least log(n), then one can find a map from the system to the full shift on n symbols. We will discuss this result and consider the analogous situation for higher dimensional symbolic systems. We will follow the story of what happens for this situation, delving into the details and proofs as much as possible.

Lectures:
1. Introduction to higher dimensional symbolic dynamical systems.
2. Factoring onto the full shift when we have an extra mixing condition and enough entropy: the work of Johnson and Madden.
3. The complete story for factoring onto the full shift in the above situation: the work of Desai.
4. The equal entropy situation: the work of Boyle and Schraudner.
5. What can happen without the mixing condition: the work of Pavlov.

Program

There will be introductory talks aimed at students and non-specialists on Thursday's evening (2 March), but the main part will start on Friday morning. There will be other talks, but we would like not to overload the program. The detailed program will appear on our website shortly before the meeting.

Venue

Friday morning session will be held in an old villa belonging to the Institute of Mathematics of Polish Academy of Sciences at Mikolaja Kopernika 18 (see photo).
All other lectures will take place at the main campus of Wroclaw University of Science and Technology in the buidling of Faculty of Pure and Applied Mathematics (C11) at Janiszewskiego 14a

Registration

There will be no conference fee, but we do ask people to register in advance. To register write to

frej@pwr.edu.pl

Please, inform us if you would like us to provide an accommodation and whether you wish to give a talk during the meeting.
We will probably be able to cover the accommodation of some number of participants (with the strong emphasis of young people and researchers without financial support of their organizations).

About

Wandering Seminar is an initiative which aims at integrating ergodic theory and dynamical systems research groups in Poland. The idea is to organise mini-conferences/workshops a few times each year. These meeting are to be devoted to actual research topics in our area. Contrary to what the title suggests, this should be a recurring event, which only wanders geographically across Polish universities with dynamical systems research groups.
The workshop will be partially funded from the resources of WCMCS for small meetings.

Organizers

• Bartosz Frej (PWr)
• Dawid Huczek (PWr)
• Dominik Kwietniak (UJ)
• Michal Rams (IMPAN)

Partners