**Seonhee Lim**

Seoul National University

February 22, 2018

**Hausdorff dimension in inhomogeneous Diophantine approximation**:
Homogeneous dynamics is often helpful to solve some problems in number theory. We will explain a particular example of the setting in homogeneous dynamics, useful for Diophantine approximation. We will then show why the set of epsilon-badly approximable target vectors in inhomogeneous Diophantine approximation is not full for almost every approximating vectors. We further explain the situation in dimension 1, which is almost settled with the aid of continued fraction expansions. The main part is a joint work with Uri Shapira and Nicolas de Saxce.