Simultaneous Diophantine approximation on the Veronbese curve

2:00pm, Wednesday, 25-th October

Abstract

Measuring the set of simultaneously well approximable points on manifolds is one of the most intricate problems in metric theory of Diophantine approximation. Unlike the case of dual case of well approximable linear forms, the result here is known to depend on a manifold. For example, some of the manifolds do not contain simultaneously very well approximable points at all, while for the others the set of such points always has positive Hausdorff dimension. In this talk, we will closely look at the Veronese curve $\{x, x^2, x^3, \ldots, x^n\}$ and discuss what is known about the sets of simultaneously well approximable points on it.