# Fortnightly links (135)

Elizabeth Gasparim: Intrinsic mirrors for minimal adjoint orbits computes the Landau–Ginzburg models that arise from the intrinsic mirror symmetry program of Gross and Siebert for the Landau–Ginzburg models that were mentioned in fortnightly links #22. They do not have a smooth projective mirror, but rather as is argued in this paper one has to produce a new Landau–Ginzburg model. It's great to see the intricacies of the Gross–Siebert program in a case that is close to my heart!

Akihiro Higashitani, Kenta Ueyama: Combinatorial classification of (±1)-skew projective spaces proves a combinatorial Torelli theorem for a special type of noncommutative projective spaces, in arbitrary dimension. It is shown how geometric data (namely the structure of the point scheme, interpreted combinatorially) completely determines the noncommutative projective space, provided that only coefficients in $\{1,-1\}$ are used. It gives a full classification of these varieties too, with the relevant integer sequence being OEIS:A002854.

This brings back fond memories of one of my first papers, and it makes me wonder to which extent something similar can be done for more general skew polynomial algebras. We (= Kevin De Laet, Lieven Le Bruyn, and I) never figured out the possible number of point varieties for instance (which are just very special unions of linear subspaces in $\mathbb{P}^n$), or came up with the appropriate Torelli theorem (which will likely involve automorphisms of point varieties).

Andrei Caldararu, Yunfan He, Shengyuan Huang: Moonshine at Landau-Ginzburg points proposes a conjecture involving series expansions arising in mirror symmetry and enumerative invariants, whilst Letong Hong, Michael H. Mertens, Ken Ono, Shengtong Zhang: Proof of the elliptic expansion Moonshine Conjecture of Căldăraru, He, and Huang provides a proof. I like how to come up with the conjecture mirror symmetry was used (which using Daniele Amati's words feels like a piece of 21st century mathematics that fell in the 20th century) whilst the proof uses manipulations of hypergeometric functions, which to an outsider like me feel like the type of mathematics originating in the 19th century but still not understood by this 21st century mathematician!