# Fortnightly links (106)

Ivan Cheltsov, Victor Przyjalkowski: Fibers over infinity of Landau-Ginzburg models states an interesting conjecture in homological mirror symmetry for Fano varieties, suggesting another aspect of the relationship between the geometry of the Fano (namely $\mathrm{h}^0(X,\omega_X^\vee)$) and the singularities of the mirror Landau–Ginzburg mirror (namely the number of irreducible fibres over $\infty$ in a log Calabi–Yau completion).

Gavril Farkas, David Jensen, Sam Payne: The Kodaira dimensions of $\overline{\mathcal{M}}_{22}$ and $\overline{\mathcal{M}}_{23}$ is not even remotely close to something I usually think about. But somehow I greatly enjoy the statement of this problem. Consider $\overline{\mathcal{M}}_g$, the compactified moduli space of genus $g$ curves, which is projective of dimension $3g-3$. What is its Kodaira dimension? It is known that it is $-\infty$ for $g=2,\ldots,15$, and equal to $3g-3$ for $g\geq 22$ (where $g=22$ and $g=23$ are new).

So if you want to achieve fame, you should tackle the cases $g=16,\ldots,21$ before anyone else does!

Joshua Ciappara, Geordie Williamson: Lectures on the Geometry and Modular Representation Theory of Algebraic Groups looks like a really good introduction into modular representation theory, written by one of the leading figures in the field, and containing many pictures and explicit details, as per usual in lectures of Geordie. I also look forward to their announed more detailed treatment!