Lattice Supersymmetry from the Ground Up

This talk summarizes a series of papers defining and analyzing lattice models with supersymmetry. These models describe strongly-interacting spinless fermions hopping on any lattice or graph. Computing the Witten index and the cohomology of the supersymmetry generator Q allows us to understand a great deal about the ground state. In all one-dimensional and some two-dimensional cases this allows the number and density of the ground states to be found exactly. In two dimensions and up, the ground-state entropy is extensive for generic lattices.