• Making of Mathematical Instruments is yet another beautiful modern reworking of a classical illustrated book. I've been linking to this website for a while now, and I'll continue doing so, as it keeps on surprising me. Go check it out!

  • Benjamin Gammage, Maxim Jeffs: Functorial mirror symmetry for very affine hypersurfaces solves Auroux' conjectural picture for how toric varieties and their anticanonical divisors fit into a homological mirror picture together with natural functors between their derived categories. Cool! Auroux gave a beautiful lecture about this at Noncommutative Shapes (before this preprint was posted), you can watch the recording.

  • Tom Coates, Liana Heuberger, Alexander M. Kasprzyk: Mirror Symmetry, Laurent Inversion and the Classification of $\mathbb{Q}$-Fano Threefolds is another beautiful illustration of the Fanosearch program, which tries to classify Fano varieties using mirror symmetry. Whilst we know the classification of Fano 3-folds (warning: product placement) the analogous classification for appropriately singular Fano 3-folds is not known yet. There exists a list of Hilbert series that such Fano 3-folds might possess, yet it is not clear whether a given Hilbert series is realised by one, many or no deformation families of singular Fano 3-folds.

    Thus what they do in the paper is take the ansatz that Fano 3-folds ought to be mirror to suitable Laurent polynomials, and see which ones are realised. The amazing thing that appears is that there is something like a mismatch: the distributions of possibilities in Figure 1 for Hilbert series vs. Laurent polynomials are very different. The former is much more bottom-heavy (so high codimension), and extends all the way to genus $-2$, whereas the latter only gives genus 2 or 3 onwards, and more in low codimension. This is this 0, 1 or many comment coming into play.