• Junwu Tu: Categorical enumerative invariants of the ground field proves a result that I've been awaiting impatiently. Namely that the categorical Gromov–Witten invariants of the derived category of a point agree with the usual Gromov–Witten invariants (for all insertions and genera

    As a corollary, the categorical Gromov–Witten invariants for Fukaya categories with semisimple Hochschild cohomology, which is expected for Fukaya categories of Fano varieties with full exceptional collections, agree with the usual ones. I am a very big fan of these results!

    Is anyone up for tracking through this paper (and others) to see how this works for $\mathbb{P}^1$ and some more complicated varieties? I'd also be interested in figuring out whether one can "guess" the necessary splitting data for noncommutative del Pezzo surfaces without a commutative counterpart.

  • Anna Romanov, Geordie Williamson: Langlands correspondence and Bezrukavnikov's equivalence are (extensive!) lecture notes on arithmetic aspects of Langlands and categorifications of affine Hecke algebras. The amount of examples and pictures seem to make it ideal for many types of readers.

  • Igor Reider: Bridgeland stability conditions and the tangent bundle of surfaces of general type is of the same scale as the previous link, except that it is full of new ideas relating stability conditions on surfaces of general type to their tangent bundle, giving a filtration on $\mathrm{H}(S,\mathrm{T}_S)$ inspired by mirror symmetry. Very intriguing, and I'm looking forward to the paper with the examples.