Time: 2018-5-25 15：00-16：00

Venue: Room 203 Lecture Hall

abstract：Let $E$ be a compact subset of ${\Bbb R}^d$. For $n\in {\Bbb N}$, let $\oplus_nE=E+\cdots+E$ be the $n$-fold arithmetic sum of $E$. In this talk, we consider the general question whether $\oplus_nE$ has non-empty interior for large $n$. We give a confirmative answer under the assumption that the ``thickness'' of $E$ is positive. The assumption is fulfilled by many natural fractal sets. This is based on joint work with Yufeng Wu.