Harm Derksen - Northeastern University, Mathematics If we take a tensor product of copies of of the same vector space V and its dual, then we have a natural action of GL(V) and any subgroup G (for example the orthogonal group or something more complicated). Wheeled PROPs were introduced by Markl, Merkulov and Shadrin, and seem to be the right framework to study G-invariant tensors, their representations as tensor networks and the algebraic relations among such invariant tensors. This is joint work with Visu Makam.