Lieven Le Bruyn has posted his vacation reading. I was planning on eventually writing something about Victor Ginzburg’s Lectures on Noncommutative Geometry, which is a survey of noncommutative geometry. Berest and Chalykh’s A∞ modules and Calogero-Moser Spaces. A∞ algebras are a generalization of algebras where the multiplication goes horribly wrong. Calogero-Moser space is a space that parametrizes right ideals in the Weyl algebra. These are two topics that I’d like to learn, so it looks interesting.