Warren Cattani, Franco Giovenzana, Shengxuan Liu, Pablo Magni, Luigi Martinelli, Laura Pertusi, Jieao Song: Kernels of categorical resolutions of nodal singularities is a nice preprint, painting a pretty picture on the categorical resolutions of nodal singularities. Highly recommended reading for an accessible introduction to how one can use Lefschetz collections to get resolutions, and then study these from a categorical point-of-view!
Yuki Mizuno: Some examples of noncommutative projective Calabi-Yau schemes constructs more examples of noncommutative Calabi–Yau projective varieties using Artin–Zhang style noncommutative projective geometry, a subject close to my heart. They are all constructed using skew polynomial algebras with roots of unity. If anyone is interested in what I think about noncommutative Calabi–Yau projective varieties outside the finite-over-the-center case, just ask!
jOEIS is "a collection of pure Java programs implementing sequences from The On-Line Encyclopedia of Integer Sequences (OEIS)". This is an amazing project, currently implementing 115000 sequences! I would love to see something written about the experience of doing this: which mistakes in the literature were found, what was particularly challenging?
Also, what about having this available within Sage? That would be great!