## Chicago Action Now rotating workshop

Asaf Katz

University of Chicago

Generalizations of Furstenberg's diophantine result

**Abstract:**In his seminal paper from 1967, H. Furstenberg proved his famous x2x3 theorem which states that for every irrational x, the set 2^{n}3^{m}x is dense modulo 1. I will show a couple of generalizations of this result, which imply density of sparser sequences, using earlier works of D. Meiri and M. Boshernitzan. In particular, I will show density modulo 1 of sequences such as 2^{n}3^{3^{m}}3^{3^{k^2}}x, for every irrational x.I will also discuss another result which is concerned with the case where no group action is present. The talk will be accessible, no prior knowledge is assumed.

Sunday February 18, 2018 at 3:00 PM in SEO 636