5 problems

Let $p,q\geq 3$ satisfy … For the Ising model on the corresponding Lobachevsky lattice, let $\mathcal{G}_\beta$ denote the set of Gibbs states, let…

Let $M$ be an even lattice of signature $(l,2)$ with $l\geq 3$, and let $c$ be a primitive norm-zero vector of $M$. Write … A hyperbolic lattice is an even lattice of signature…

Let $L$ be an even hyperbolic lattice with infinitely many simple $(-2)$-roots. Say that $L$ has the Borcherds property if it admits an isotropic vector whose inner products with a…

Hyperbolic point-group representation conjecture. For a $\{4g,4g\}$ hyperbolic lattice, Eq. above remains valid, with $M$ a representation of $G$ valued in $SL(2g,\mathbb{Z})$.

We consider a hyperbolic lattice and a disk of large radius $R$ centered at an origin vertex. Boundary sites are vertices outside the disk connected to at least one vertex inside i…