• Billiards and tilting characters for SL3 is a beautiful video illustrating the billiards conjecture for $\mathrm{SL}_3$ as formulated by Lusztig–Williamson in Billiards and tilting characters for $\mathrm{SL}_3$. If you don't wish to read the article you can also watch Geordie's ICM address which builds up to this video.

• Olivier Debarre: Hyperkähler manifolds is an overview article on (you guessed correctly) hyperkähler manifolds, with an emphasis on those which are deformations of $\operatorname{Hilb}^n\mathrm{K3}$. These have remained quite magical to me (I mostly think about the case where $\omega_X^\vee$ is ample, not trivial), but this overview definitely helps in understanding the relationship between algebraic geometry and lattice theory which appears in this setting.