On block gluing and related properties of Hom-shifts

Hom shifts form a class of multidimensional shifts of finite
type (SFT) and consist of colorings of the grid Z^2 where adjacent
colors must be neighbors in a fixed finite undirected simple graph G.
The gluing gap measures how far any two square patterns of size n can be
glued. In this talk I will focus on possible values of gluing gap and
algebraic properties of objects related to this problem. I will also
comment on algorithmic complexity of possible solutions.
(Based on joint work(s) with Nishant Chandgotia, Silvere Gangloff and
Benjamin Hellouin de Menibus.)