• Harder–Katzarkov–Liu: Perverse sheaves of categories and non-rationality is a manuscript I stumbled upon after reading Andrew Harder's slides about the same topic. It looks really interesting, and the connection between semiorthogonal decompositions (a subject I really like) and perverse sheaves of categories (also known as perverse schobers) seems very intriguing, but I haven't had the time yet to read it in detail. I'm not sure whether the world is supposed to be able to access this pdf, as it is supposed to be a chapter in an upcoming book, so it might disappear without notice. There are also other versions (1, 2) but I guess I linked to the final one.

  • Brent Pym, Constructions and classifications of projective Poisson varieties is a very nice read about Poisson varieties. Read this if you care about Poisson geometry, deformation quantization or noncommutative algebraic geometry.