Seminar 3.2.17 Ramirez

Title: Some questions about inhomogeneous approximation

Speaker: Felipe Ramire (Wesleyan)

Abstract: Khintchine’s Theorem (1924) states that almost all (respectively, almost no) real numbers can be approximated by rationals at a given rate, provided that the rate is monotonic and corresponds to a divergent (resp. convergent) series. In 1941, Duffin and Schaeffer showed by way of example that the monotonicity condition cannot be removed. They formulated the famous and resistant Duffin—Schaeffer Conjecture in response to this example. I will discuss an analogue of this situation for inhomogeneous approximations. From the point of view of dynamics, this talk is about toral translations.