The Geometry of Forms on Supermanifolds

Online-talk.

In this talk, I will discuss some features of the geometry of forms on supermanifolds. In particular, I will introduce differential and integral forms via a double complex construction, that allows for easy cohomological computations. Further, if time permits, I will address some peculiar aspects of the geometry of forms on complex or algebraic supermanifolds — such as the degeneration of the Hodge-to-de Rham spectral sequence —, and on odd symplectic (super)manifolds — such as the relation with BV formalism for quantization of gauge theories. The talk is based on arXiv:2111.12841, arXiv:2202.08136 and on arXiv:2004.10906 (w/ S. Cacciatori and R. Re), arXiv:2312.05224 (w/ K. Eder, J. Huerta).