Abstract: 
In firstpassage percolation, one puts i.i.d. nonnegative weights on the nearestneighbor edges, and studies the induced (pseudo)metric. It is wellknown that a metric ball of radius $t$, after rescaled by $1/t$, converges to a deterministic limit shape as $t \to \infty$. However, not too much is known for finite $t$. In this talk, we will focus on the geometry of a ball of radius $t$, by studying its boundary. We will first talk about the size of the boundary of a ball (based on an earlier joint work with M. Damron and J. Hanson), and then we will talk about holes in a ball (based on a recent joint work with M. Damron, J. Gold and X. Shen).
