Invited Talk 3: Tensor Networks and Counting Problems on the Lattice

An overview will be given of counting problems on the lattice, such as the calculation of the hard square constant and of the residual entropy of ice. Unlike Monte Carlo techniques which have difficulty in calculating such quantities, we will demonstrate that tensor networks provide a natural framework for tackling these problems. We will also show that tensor networks reveal nonlocal hidden symmetries in those systems, and that the typical critical behaviour is witnessed by matrix product operators which form representations of tensor fusion categories.