@article { , title = {Wavefront sets and polarizations on supermanifolds}, abstract = {In this paper we develop the foundations for microlocal analysis on supermanifolds. Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for superdistributions which generalizes Dencker's polarization sets for vector-valued distributions to supergeometry. In particular, our super wavefront sets detect polarization information of the singularities of superdistributions. We prove a refined pullback theorem for superdistributions along supermanifold morphisms, which as a special case establishes criteria when two superdistributions may be multiplied. As an application of our framework, we study the singularities of distributional solutions of a supersymmetric field theory.}, doi = {10.1063/1.4975213}, eissn = {1089-7658}, issn = {0022-2488}, issue = {2}, journal = {Journal of Mathematical Physics}, publicationstatus = {Published}, publisher = {American Institute of Physics}, url = {https://nottingham-repository.worktribe.com/output/846028}, volume = {58}, keyword = {Supermanifolds, Pseudodifferential operators, Polarized wavefront sets, Microlocal analysis, Propagation of singularities}, year = {2017}, author = {Dappiaggi, Claudio and Gimperlein, Heiko and Murro, Simone and Schenkel, Alexander} }