## Seminar 09.09.21 Wolf

Title: Computability of topological pressure on compact shift spaces beyond finite type

Speaker: Christian Wolf – CUNY

Abstract: In this talk we discuss the computability (in the sense of computable analysis) of the topological pressure $P_{\rm top}(\phi)$ on compact shift spaces $X$ for continuous potentials $\phi:X\to\bR$. This question has recently been studied for subshifts of finite type (SFTs) and their factors (Sofic shifts). We develop a framework to address the computability of the topological pressure on general shift spaces and apply this framework to coded shifts. In particular, we prove the computability of the topological pressure for all continuous potentials on S-gap shifts, generalized gap shifts, and Beta shifts. We also construct shift spaces which, depending on the potential, exhibit computability and non-computability of the topological pressure. We further show that the generalized pressure function $(X,\phi)\mapsto P_{\rm top}(X,\phi\vert_{X})$ is not computable for a large set of shift spaces $X$ and potentials $\phi$. Along the way of developing these computability results, we derive several ergodic-theoretical properties of coded shifts which are of independent interest beyond the realm of computability. The topic of the talk is joint work with Michael Burr (Clemson U.), Shuddho Das (NYU) and Yun Yang (Virginia Tech).

Meeting ID: 916 3892 7725

Recorded Talk: https://osu.zoom.us/rec/share/dIchmAETAILph7uojccOdxliuEeNlsH4SfDUEzzVuFwqKQiQi3brEW6GvX_Hpj_4.onMqP6LjZX6OSA6_

## Seminar 08.26.21 Dymek

Title: Topological dynamics of (multidimensional) B-free systems

Speaker: Aurelia Dymek – Nicolaus Copernicus University, Torun, Poland

Abstract: Sarnak turned attention to B-free systems. In particular, he investigated the squarefree subshift. Two multidimensional generalizations of B-free systems have been dealt with by Cellarosi, Vinogradov, Baake and Huck. My talk will be concerned with some similarities and differences between B-free systems in the one- and multidimensional case. This is a part of my doctoral dissertation.

Meeting ID: 916 3892 7725

Recorded Talk: https://osu.zoom.us/rec/play/HkONQZ2ALv6bbdnUaWmJcn0MZj-S2OkT4MOQlHkqmC9IJkZee0I2vxnpHxdGXqxsF-ARe9GuE50A8pJi.8ZNn6D_A7PGsRwPl?continueMode=true

## Seminar program for Fall 2021

This year, our seminar will be a mixture of in person and virtual seminars, with the mix anticipated to trend towards in person later in the year, and virtual early in the year. As usual, we meet on Thursdays at 3.00pm EST unless otherwise noted. In person talks will be in MW154.

For virtual talks, the Zoom link can be obtained from the organizers, Andreas Koutsogianis and Dan Thompson. For most virtual talks, video will be posted afterwards, and will remain viewable on Zoom for 120 days after the talk.

The following is our current schedule, and more talks will be announced soon.

Aug 17th: In person –  Federico Rodriguez Hertz (Penn State)

Aug 26: Virtual – Aurelia Dymek (Nicolaus Copernicus University, Torun, Poland)

Sept 9: Virtual – Christian Wolf (City College of New York)

Sept 16: Virtual – Andreu Ferre Moragues (Nicolaus Copernicus University, Torun, Poland)

Sept 30: Virtual – Pablo Shmerkin (UBC, Canada)

Oct 8 (Friday, 12.00pm, note unusual day and time): Virtual – Ryokichi Tanaka (Kyoto University, Japan)

Oct 19 (Tues, note unusual day): In Person – Keith Burns (Northwestern)

Oct 21: Virtual – Alejandro Maass (University of Chile, Chile)

Oct 28: Virtual – Wenbo Sun (Virginia Tech)

Nov 18: In Person – Dick Canary (Michigan)

Dec 9: Virtual – Giulio Tiozzo (University of Toronto, Canada)