In this seminar we will argue why noncommutative geometry provides a very interesting mathematical framework to the study of the Batalin-Vilkovisky formalism.

After a brief review of the BV formalism, where we will recall its original physical motivations and the main points of the construction, from the introduction of ghost fields to the definition of the BV/BRST cohomology complexes, we will then focus on the mathematical formalism: noncommutative geometry and the key notion of spectral triple.

A spectral triple can be seen as a noncommutative generalisation of the classical notion of a compact Riemannian spin manifold. However, beyond their relevance from a purely geometrical perspective, spectral triples also play a relevant role in the mathematical formalization of gauge theories, as each spectral triple naturally induces a gauge theory.

Knowing the motivations and having described the tools, we will then present our main result: we will see how the BV construction can be inserted in the formalism of noncommutative geometry. A key role will be played by the "BV spectral triple", whose notion we introduce to encode in a noncommutative manifold the ghost sector of a BV- extended gauge theory.