**Title: **Odd polynomials, Diophantine approximations and applications to ergodic theory

**Speaker: **Rigo Zelada Cifuentes – The Ohio State University

**Abstract:** Let v(x)=∑Nj=1ajx2j−1 be an odd real polynomial. We will start by describing new Diophantine results pertaining to sets of the form {n∈ℕ|‖v(n)‖<ϵ}, where || || denotes the distance to the closest integer. The second part of the talk will be devoted to applications of these Diophantine results (and the techniques behind them) to ergodic theory. Among other things, we will discuss a new version of Khintchine’s recurrence theorem, a new characterization of weakly mixing systems and a result on strong mixing of all orders. The talk is based on a joint work with Dr. Bergelson.