Title: Some remarks on the `eventually always hitting’ property

Speaker: Dmitry Kleinbock – Brandeis University

Abstract: Eventually always hitting (EAH) points are those whose long orbit segments eventually hit the corresponding shrinking targets for all future times. This is a uniform version of the classical hitting property in ergodic theory with shrinking targets; the terminology is due to Dubi Kelmer. Unlike its classical counterpart, not much is known about conditions on the targets for which almost all vs. almost no points are EAH. I will talk about systems where translates of targets exhibit near perfect mutual independence, such as Bernoulli schemes. For such systems tight conditions on the shrinking rate of the targets can be stated so that the set of eventually always hitting points is null or co-null. This is a joint work with Ioannis Konstantoulas (Upsala) and Florian Richter (Northwestern, formerly OSU).

Zoom link: https://osu.zoom.us/j/98033590349

Meeting ID: 980 3359 0349

Password: Mixing

Recorded Talk: https://osu.zoom.us/rec/play/eICdcrGw2A_-x1WmjS6UgyzYCVDZADy-KfA8uye4jX7kPIoePqaYYBF0c7ISHF9viCWfdaeMUedK5id-.dV8lQAD0FV7drJ33?continueMode=true&_x_zm_rtaid=DXAGijRmQ7q5uDvEGc2Npg.1619747814944.5ef3cf2ca7136822f71c937da2797fba&_x_zm_rhtaid=397

Title: Rough similarity, rigidity and the Manhattan Curve for metrics on
hyperbolic groups

Speaker: Steve Cantrell – The University  of Chicago

Abstract: Consider a hyperbolic group equipped with two hyperbolic metrics
that are left invariant and are quasi-isometric to a word metric. A
natural question to ask is: when are these metrics roughly similar, i.e.
when are they within bounded distance after scaling by a positive
constant? In this talk we’ll discuss rigidity statements that characterize
rough similarity in terms of the properties of the so-called Manhattan
Curve. We’ll see how to study this curve using a blend of ideas coming
from ergodic theory and geometric group theory. This is based on joint
work with Ryokichi Tanaka.

Zoom link: https://osu.zoom.us/j/98033590349

Meeting ID: 980 3359 0349

Password: Mixing

Recorded Talk: https://osu.zoom.us/rec/play/oojIKeNTtJYj2_BDzTMoq_B838qwHXhn_iL8nILR-obhxHVOVdSq9i-yd1-KTAT3QgRolQBWdTVY5Nx_.tCVmCXOuKzaXbsN_?continueMode=true&_x_zm_rtaid=Vd768-G5T-qQzFi8nIZqcw.1619131951571.08574cec3bd38c984e60711df5327a21&_x_zm_rhtaid=146

Title: Multiplicative recurrence with additive averaging

Speaker: Joel Moreira – University  of Warwick

Abstract: Motivated by the question of whether Pythagorean triples are partition regular, one is naturally led to study sets of recurrence in the semigroup of natural numbers under multiplication. However, for sets with “additive structure”, the usual tools (such as the van der Corput trick) don’t seem to be useful in this context. As an alternative, we propose to study sets of averaging recurrence, where the averaging is taken additively. We present some results in this direction, and some applications to number theory. This is based on joint work with Sebastian Donoso, Anh Le and Wenbo Sun.

Zoom link: https://osu.zoom.us/j/98033590349

Meeting ID: 980 3359 0349

Password: Mixing

Recorded Talk: https://osu.zoom.us/rec/play/J1MkxyEaOGUHGcdGM84cNOQXt7thTW47Im6oWulA6EIbn4c5tpI0vGFW1eR7u_vDHqpnpLQCKVQso5SK.86O6eYU5IyOTjLxX?continueMode=true

Title: Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds

Speaker: Jonathan DeWitt – The University of Chicago

Abstract: Suppose that M is a closed isotropic Riemannian manifold and that R_1,…,R_m generate the isometry group of M. Let f_1,…,f_m be smooth perturbations of these isometries. We show that the f_i are simultaneously conjugate to isometries if and only if their associated uniform Bernoulli random walk has all Lyapunov exponents zero. This extends a linearization result of Dolgopyat and Krikorian from S^n to real, complex, and quaternionic projective spaces.

Zoom link: https://osu.zoom.us/j/98033590349

Meeting ID: 980 3359 0349

Password: Mixing

Recorded talk: https://osu.zoom.us/rec/play/JjhZEG2ebLvvPOuNY89RaqBxiOLNqabVfSbbvaymyAjAjed4F9Po-6ta7hsUClSnRLRfzvmuGAQ3FWA.kllkqpyJemaIrY1W?continueMode=true&_x_zm_rtaid=BC-VSS-jTo6_ENY8NMDZJw.1617934286899.261230408b5271ecf9eadf5e3924f1e2&_x_zm_rhtaid=413