Long overdue, so here goes.
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later is a beautiful retrospective by the creator of the OEIS, an absolutely amazing resource. Section 4 is a highly recommended read.
Wen Chang, Fabian Haiden, Sibylle Schroll: Braid group actions on branched coverings and full exceptional sequences disproves a conjecture of Bondal–Polishchuk, which says that the braid group acts transitively on the set of exceptional collections. Maybe it was an ambitious conjecture, given how little evidence for it there was, but then again, it might have been a matter of "why wouldn't it be true", in light of the existing evidence.
They use full exceptional collections arising in symplectic geometry, and not algebraic geometry. So maybe there is something special about exceptional collections arising in algebraic geometry? Who knows!
Daniel Halpern-Leistner: The noncommutative minimal model program sets out a precise version of a programme (inspired by mirror symmetry) on the structure of derived categories of varieties. It is not an easy read, but it is very interesting to see what Dan thinks are the correct precise versions of various mirror symmetry heuristics, building upon and improving works of others. I'm looking forward to seeing more details being worked out!