Emmy-Noether-Seminar: Higher algebras and topological quantum field theories

Higher algebras and topological quantum field theories

Nils Carqueville (Wien)

Abstract: Topological quantum field theory is a place where algebra, topology, category theory and theoretical physics meet. We give an introduction from a representation theoretic perspective, and then discuss how actions of (higher) groups and (higher) fusion categories naturally appear in this setting. A unifying umbrella for such examples are algebraic structures called orbifold data. We explain their basic topological origin and explore some applications.