# Integral Structures in Geometry and Representation Theory

Integral structures are found in many places throughout mathematics: as lattices in Euclidean space, as integral models of reductive groups and algebraic schemes, or as integral representations of groups and associative algebras. Even questions about the most basic example of an integral structure, the ring of integers $\mathbb{Z}$, quickly lead us into the fields of analysis, algebra, or geometry. In the same vein, investigations of integral structures are most successfully treated by viewing them from different perspectives, often requiring the usage of the most advanced mathematical methods and frequently leading to unexpected connections.