In the summer semester of 2019 I gave a lecture series on Perturbative Quantization of Chern-Simons Theory at the Kolleg Mathematik Physik Berlin, hosted by the Humboldt-Universität Berlin.
Chern-Simons Theory is a particular gauge theory that has been of interest to both physicists and mathematicians since the late 1980's. On the mathematical side, it has intricate connections to low-dimensional topology, knot theory and representation theory, in physics it is of interest because of its relations to two-dimensional conformal field theory, three-dimensional gravity, and as an effective theory in Condensed Matter Physics describing e.g. the fractional quantum Hall effect. In these lectures we focus on its perturbative quantization in the Batalin-Vilkovisky formalism. The goal is to prove that the partition function of the effective theory on zero modes satisfies the Quantum Master Equation. Mathematically this means that it is a cocycle in a certain complex.
Here is a pdf containing an outline of the course.
I typed up a set of lecture notes available on the arXiv, they were published in Reviews in Mathematical Physics: https://doi.org/10.1142/S0129055X22300035
A small, very non-exhaustive selection of additional references relevant to this lecture series follows below.
Perturbative aspects of the Chern-Simons field theory, E.Guadagnini, M. Martellini, M. Mintchev, 1989. DOI
Perturbative Aspects of the Chern-Simons Topological Quantum Field Theory, D. Bar-Natan's PhD Thesis, 1990. Available here
Chern-Simons perturbation theory I & II, D. Axelrod and I. Singer, 1991 and 1993. arXiv (part I), arXiv (part II)
Feynman Diagrams and low-dimensional topology, M. Kontsevich , 1993. Available here
Integral invariants of 3-manifolds I & II, R. Bott and A. Cattaneo, 1997 and 1999. Available on Project Euclid: part I part II
Remarks on Chern-Simons Invariants, A. Cattaneo and P. Mnev , 2008. DOI
Lectures on Batalin-Vilkovisky formalism and applications, P. Mnev, 2017. arXiv book