I am working on a circle of ideas that goes by the name
See there for survey, introduction, details and further links. Expositions, talk notes and lecture notes are listed here. For a list of published articles and of preprints on the subject see at subprojects.
Here is a list of links to lecture notes that I have prepared for various seminars or course that I organized and/or taught.
Joost Nuiten, Cohomological quantization of local prequantum boundary field theory, master thesis (August 2013)
Stephan Bongers, Geometric quantization of symplectic and Poisson manifolds, master thesis (January 2014)
Ragnar Eggertsson, Stacks in Gauge theory, Bachelor thesis (August 2014)
Presently I have two students