5 problems

Let $L$ be a Lorentzian lattice with a Weyl vector, and let its signature be measured as in the source. Maximal-signature conjecture. The maximal signature for a Lorentzian lattice…

Let $\even_{1,25}$ denote the even Lorentzian lattice of signature $(1,25)$. A largest Lorentzian lattice with a Weyl vector is understood in the source's sense of maximal size amo…

Let $L$ be a Lorentzian lattice, and let a modular form be reflective when the singularities of its singular theta transform occur along the reflection hyperplanes of $L$. Reflecti…

A Lorentzian reflection group with Weyl vector is a reflection group associated with a Lorentzian lattice and admitting a Weyl vector. The maximal-dimension conjecture. The maximal…

Automorphism invariance conjecture. Any automorphism $f\in\operatorname{Aut}(\Lambda)$ preserves $\Lambda_i^0$ for $i=1,2$.