Large $N$ limits from a BV perspective

Starting with 't Hooft, physicists have used a ribbon graph expansion to understand certain integrals over spaces
of $N \times N$ matrices in the large $N$ limit. This expansion can be deduced from the Feynman diagram
expansion, which relies on the nice structure of moments of a Gaussian measure. We provide a homological
perspective on this situation: the Batalin-Vilkovisky formalism (which we will outline) provides a homological
approach to computing moments, and the Loday-Quillen-Tsygan theorem (which we will explain) gives a
method for identifying the large $N$ limit. Our talk will focus on finite-dimensional integrals, but we hope
to comment on how our methods extend to gauge theories and connect with string field theory. This is joint
work with Greg Ginot and Mahmoud Zeinalian.