We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with $n$ nodes can be drawn on a $\sqrt{n}\times \sqrt{n}$ grid. We also show that testing whether a given binary tree has an upward embedding with a given combinatorial embedding in a given grid is NP-hard.
(Based on a paper by Hugo A. Akitaya, Maarten Löffler, and Irene Parada from Graph Drawing 2018.)