Perturbative Chern-Simons invariants on lens spaces via BV-BFV quantization

After giving a brief introduction to the quantum BV-BFV formalism developed by Cattaneo, Mnëv and Reshetikhin, I will explain a way of applying it to Chern-Simons theory for split Lie algebras, i.e. quadratic Lie algebras that admit a splitting into isotropic subspaces. I will present applications to perturbative Chern-Simons Invariants, in particular, a computation of the lowest-order Chern-Simons invariant for lens spaces, and explain how the result of this computation agrees with the literature.