Chunyi Li, Laura Pertusi, Xiaolei Zhao: Derived categories of hearts on Kuznetsov components answers a natural question when one knows both of Bridgeland stability conditions (which involves t-structures, and thus abelian categories) and the Beilinson's realisation functor (which gives a functor from the derived category of the heart of a t-structure to the original triangulated category). Namely: is it an equivalence in interesting settings? This came up originally in the setting of perverse sheaves, but makes perfect sense in the setting of stability conditions too.
This preprint covers the case of K3 categories in cubic fourfolds or Gushel–Mukai varieties, showing that there is indeed an abelian category (namely the heart of a stability condition on the Kuznetsov component) for which this abstractly constructed triangulated category is indeed the derived category. Cool!
Giovanni Staglianò: Explicit computations with cubic fourfolds, Gushel-Mukai fourfolds, and their associated K3 surfaces discusses a Macaulay2 package to work with K3 surfaces associated to cubic fourfolds and Gushel–Mukai varieties (staying in the theme of the previous link). It's great to see this interplay between Hodge theory, algebraic geometry and computer algebra.
Peter Spacek, Charles Wang: Towards Landau-Ginzburg models for cominuscule spaces via the exceptional cominuscule family constructs Landau–Ginzburg mirrors for the Cayley plane and the Freudenthal variety. There is a lot to unpack in there, and it would be great to see exceptional collections (which we don't have for the Freudenthal variety yet!) mirror to exceptional collections in the Fukaya–Seidel categories of these mirrors.