The affine line is a zero divisor in the Grothendieck group

We will discuss an example of a pair $(X,Y)$ of Calabi-Yau 3-folds such that $[X]-[Y]$ is a non-zero element in the Grothendieck ring of varieties annihilated by the class of the affine line. If the time permits, we will also discuss an example of a pair $(X,Y)$ of non-isomorphic derived-equivalent K3 surfaces such that $[X]-[Y]$ is annihilated by a power of the affine line. This is a joint work in progress with Kenji Hashimoto, Daisuke Inoue, Atsushi Ito, Makoto Miura and Shinnosuke Okawa.