Seminar 12.09.21 Tiozzo

Title: Hitting measures for random walks on cocompact Fuchsian groups

Speaker: Giulio Tiozzo – University of Toronto

Abstract: A recurring question in the theory of random walks on hyperbolic spaces asks whether the hitting (harmonic) measures can coincide with measures of geometric origin, such as the Lebesgue measure. This is also related to the inequality between entropy and drift.  For finitely-supported random walks on cocompact Fuchsian groups with symmetric fundamental domain, we prove that the hitting measure is singular with respect to Lebesgue measure; moreover, its Hausdorff dimension is strictly less than 1. Along the way, we prove a purely geometric inequality for geodesic lengths, strongly reminiscent of the Anderson-Canary-Culler-Shalen inequality for free Kleinian groups.  Joint with P. Kosenko.

Meeting ID: 916 3892 7725

Recorded Talk: https://osu.zoom.us/rec/share/dcqrRfiTn8n_stVOUUooY9q8cCpzFwreq0L3ih3lUrgoR-rdbQefsdxYwfUJu-Y.p0RYOqWCdsYDR1iA

Seminar 10.28.21 Sun

Title: Joint ergodicity conjecture for systems with commuting transformations

Speaker: Wenbo Sun – Virginia Tech

Abstract: It is well know by the Mean Ergodic Theorem that for any measure preserving system $(X,\mathcal{B},\mu,T)$ and $L^{\infty}$ function f, the time average of $T^{n}f$ converges to the integral of f if and only if T is ergodic. It is a natural question to ask when the average of products of polynomial iterates of  $L^{\infty}$ functions (known as multiple ergodic averages) converges to the product of the integrals of the functions. This question is called the Joint Ergodicity Problem. In this talk, I will introduce some recent advances in this problem. This talk is based on joint works with Sebasti\’an Donoso, Andreu Ferr\’e Moragues and Andreas Koutsogiannis.

Meeting ID: 916 3892 7725

Recorded Talk: https://osu.zoom.us/rec/play/dk–MjWHHK8ex0sdF0ILXOXT338U71LQ1awWnexrtUuyYiEtC-noT76YCLpX4bnCvTAT2mU-xxTPv9d1.OUHqT_H7CAgbLfFM?continueMode=true

Seminar 10.21.21 Maass

Title: Spectral analysis of topological finite rank systems

Speaker: Alejandro Maass – University of Chile

Abstract: Finite topological rank Cantor minimal systems represent a broad class of sub shifts of zero entropy or odometers [Downarowiz-Maass], it contains well studied systems like substitution sub shifts or linearly recurrent systems. In this talk we will present the study of measure-theoretical and topological eigenvalues for such class of systems, given formulas characterizing them. This work is motivated by the seminal work of Bernard Host where it is proved that measure-theoretical and topological eigenvalues of substitutions systems coincide. This is a joint work with Fabien Durand and Alexander Frank.

Meeting ID: 916 3892 7725

Recorded Talk: https://osu.zoom.us/rec/share/6x1GYGHuPkjR4KFdpi4usJMP1ert17FX_RHSF_MVaxIkD6PrLXjLO83fXN_-CR8u.0rZGFYbboMqO4Ps7

Seminar 10.08.21 Tanaka

Title: The Manhattan curve and rough similarity rigidity

Speaker: Ryokichi Tanaka – Kyoto University

Abstract: For every non-elementary hyperbolic group, we consider the Manhattan curve, which was originally introduced by M. Burger (1993),
associated with any pair of (say) word metrics. It is convex; we show that it is continuously differentiable and moreover is a straight line if and only if the corresponding two metrics are roughly similar, that is, they are within bounded distance after multiplying by a positive constant. I would like to explain how it is related to the central limit theorem for uniform counting measures on spheres, to ergodic theory of topological flows built on general hyperbolic groups, and to the multifractal structure of Patterson-Sullivan measures. Furthermore, I will present some explicit examples including a hyperbolic triangle group and compute the exact value of the mean distortion for a pair of word metrics by using automatic structures of the group.
Joint work with Stephen Cantrell (University of Chicago).

Meeting ID: 916 3892 7725

Recorded Talk: https://osu.zoom.us/rec/share/LPAREOkf7DJ5zT6tKMPY1dZP_Vs824-zAEFnAJ7CTzXJKS-pMk_Bx8o2eD6QXg-y.lFp9Na68FCmloePw

Seminar 09.30.21 Shmerkin

Title: Beyond Furstenberg’s intersection conjecture

Speaker: Bablo Shmerkin – University of British Columbia (UBC)

Abstract: Hillel Furstenberg conjectured in the 1960s that the intersections of closed ×2 and ×3-invariant Cantor sets have “small” Hausdorff dimension. This conjecture was proved independently by Meng Wu and by myself; recently, Tim Austin found a simple proof. I will present some generalizations of the intersection conjecture and other related results.

Meeting ID: 916 3892 7725

Recorded Talk: https://osu.zoom.us/rec/share/qQEteZ_GglmdyYvMPoZyFwipOFOENgKYvoYIar9tCmhxLm82JhuYaLNr7bNqoFxb.pHzsX46hQRGFTR2y

Seminar 09.16.21 Ferre Moragues

Title: Polynomial ergodic averages for certain countable ring actions

Speaker: Andreu Ferre Moragues – Nicolaus Copernicus University, Torun, Poland

Abstract: Inspired by a recent result of Frantzikinakis that allows one to establish joint ergodicity of general integer valued sequences, we will take a look at the ring actions setup. I will present new joint ergodicity results for families of independent polynomials when the acting ring is a field of characteristic zero, their corollaries in combinatorics and topological dynamics, and the methods of proof. Based on joint work with Andrew Best.

Meeting ID: 916 3892 7725

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)