- Ballico–Barmeier–Gasparim–Grama–San Martin, A Lie-theoretical construction of a Landau–Ginzburg model without projective mirrors is the paper about which Elizabeth Gasparim talked in the Antwerp conference. I'm trying to understand a little more about Landau–Ginzburg models, and this paper seems like an interesting example to understand how to deal with these things. If anything, they deserve the award for silliest notation of the month, denoting the mirror of the Landau–Ginzburg model $\mathrm{LG}(2)$ by using
\reflectbox, see theorem 8.1.
- Speaking about Landau–Ginzburg models, Favero–Kelly: Fractional Calabi–Yau categories from Landau–Ginzburg models is another very interesting looking paper about these objects. It can be seen as the analogue of Kuznetsov's Calabi–Yau and fractional Calabi–Yau categories, where smooth projective varieties are studied.
- Beren Sanders, The compactness locus of a geometric functor and the formal construction of the Adams isomorphism is in some sense a followup of Grothendieck–Neeman duality and the Wirthmüller isomorphism by Balmer–Dell'Ambrogio–Sanders. In this paper they prove a trichotomy result for functors between rigid monoidal triangulated categories: such a functor is either part of a triple of adjoint functors, a quintuple of adjoint functors, or has infinitely many adjoints on both sides. In this new paper, the failure for a triple to extend to a quintuple is studied, and it is shown that after taking a quotient it is possible to find more adjoints. Cool! And the pictures on pages 22, 30 and 31 are worth a look.
- Simon Crawford, Singularity categories of deformations of Kleinian singularities is a very pretty paper about noncommutative deformations of Kleinian singularities, as introduced by Crawley-Boevey and Holland. I've had the intention of reading that paper for a while now, and with the appearence of this preprint explicitly describing their singularity categories I am even more intrigued by these objects.