We will use Representation Theory to calculate systematically and efficiently the topological invariants of compact Lie groups and homogeneous spaces.
 

Most of the talk is covered by our second paper on ArXiv with John Jones and Adam Thomas, who are both at Warwick. The paper is part of the ongoing project to study the topological invariants of the four exceptional Rosenfeld projective planes.

In this talk I will review how the BV formalism is used in quantizing theories with local gauge symmetries within the framework of perturbative algebraic quantum field theory. The latter is a mathematically rigorous approach to QFT that combines the locality idea going back to Haag and Kastler with Epstein-Glaser renormalization. In my talk I will also show how these methods can also lead to the construction of a factorization algebra.