Let $X$ be a smooth projective variety over the complex numbers with trivial canonical bundle. Suppose that $X$ is CalabiYau.
Is the automorphism group of $X$ an arithmetic group?
What if $X$ is a K3 surface?
Let $X$ be a smooth projective variety over the complex numbers with trivial canonical bundle. Suppose that $X$ is CalabiYau. Is the automorphism group of $X$ an arithmetic group? What if $X$ is a K3 surface? 


The answer for $K3$ surfaces is no. A counterexample, where the group is not even commensurable with an arithmetic group, was given by Totaro in Example 6.3 of this paper. 

