3264 conics tangent to five conics is a beautiful online interactive implementation of an algorithm that finds the real conics tangent to five conics (these can be input by you!), and also discusses an instance where all of them are real. This is cool stuff!
Olivier Debarre: On the Hodge and Betti numbers of hyperkähler manifolds is a writeup of a lecture given by Olivier Debarre in the joint Bonn-Paris seminar. There are other writeups available too (and the seminar is still in-progress).
Michel Van den Bergh's inaugural lecture (and hopefully the later lectures too at some point) gives a really nice overview of homological mirror symmetry in a down-to-earth setting.