Abstract:

We study a quantum mechanical model for fermions that live and move on a lattice. The particles are subject to strong interactions, which are tuned to make the model supersymmetric. Due to this, the states that minimize the energy of the system, i.e. the quantum ground states, are in one-to-one correspondence with cohomology classes of the so-called independence complex of the lattice. I will discuss various recent results and their implications in the physics context.