Algebraic description of infinite-volume lattice fermions

The operator-algebraic description of quantum mechanical systems can be used to mathematically deal with systems, where the usual Hilbert space description becomes inconvenient or breaks down. In this talk I will discuss how, using this formalism, one can describe a system of interacting lattice fermions directly in the infinite-volume limit. This will allow us to formulate and analyse properties of the bulk of the system, such as the bulk Hall conductivity.