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.

Zoom link: https://osu.zoom.us/j/91638927725

Meeting ID: 916 3892 7725

Password: Mixing

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

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.

Zoom link: https://osu.zoom.us/j/91638927725

Meeting ID: 916 3892 7725

Password: Mixing

Recorded Talk: https://osu.zoom.us/rec/play/h2IKj8dcab78XnCag1DHQ_Qu76CrivFtY5TDxnco_vDe0SuH6LaFQILKy0omyhG8yRAD_WU_461XYiMT.p3_TVFm36rLaZ-KS?continueMode=true&_x_zm_rtaid=y6kPXldWSOq2BEH7eY2rrQ.1631863073516.46b8b6ed0ca4481f5aa60be2f193e0be&_x_zm_rhtaid=291