Abstract: According to Hayden and van Dam, embezzlement of entanglement describes the possibility of converting any pure bipartite entangled state into any other in the presence of a (finite) catalyst — to unlimited accuracy, without the use of any communication, quantum or classical. Based on some ideas of Werner and Scholz connecting embezzlement to the type classification of von Neumann algebras, we show that among hyperfinite factors with separable predual, the type III_1 factor is uniquely characterized by the property that any of its normal states can serve as a catalyst, inducing embezzling families of states in the sense of van Dam and Hayden. We also discuss connections with the flow of weights. This is joint work with L. van Luijk, H. Wilming, and R.F. Werner.

Abstract: Quantum field theory describes large parts of physics, in particular high energy physics. It mathematical status, however, is still not satisfactory, in spite of impressive attempts from several directions. I want to report an a
recent approach based on algebraic relations found in formal perturbation theory. The talk is based on joint work with Detlev Buchholz and more recent work with Romeo Brunetti, Michael Dütsch and Kasia Rejzner.