Alexander A. Voronov University of Minnesota BV Quantization, II: Mathai-Quillen's Trick and BV Master Equation Abstract: This is the second talk in a series whose goal is to overview recent, unpublished papers by Losev and Hamilton-Lazarev explaining to the math world a very popular among theoretical physicists procedure of BV quantization. It is basically a certain formalism allowing to reduce integration to fewer variables, namely to the orbit space of a Lie group acting on a manifold. In this talk, I will discuss a formalism, due to Mathai and Quillen, of integrating over a submanifold. Then I will look at the question of integrating along the fibers of a quotient manifold (AKA pushforward of differential forms) and its translation to the BV language.