Higher defect state sum models

Quantum field theory is a central part of a modern understanding of physics, especially elementary particle physics and condensed matter physics. A full understanding would also involve a mathematically rigorous and conceptually clear formulation of quantum field theory. The search for this has been a goal of both theoretical physics and pure mathematics for several decades. Our project is part of this endeavour, aiming for a functorial description of so-called topological state sum models. To achieve this, ideas and results of theoretical physics, category theory and algebraic topology are to be employed to construct a general theory of state sum models as an iterative phenomenon that consistently reduces higher-dimensional aspects to lower-dimensional ones. Moreover, this theory will be applied to establish new relations between known topological quantum field theories, to further develop the representation theory of higher algebras, and to describe anomalies of 3-dimensional theories.