This is the personal area of Urs Schreiber within the nLab.
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.
Previous students:
Herman Stel, ∞-Stacks and their function algebras , master thesis, (August 2010)
Joost Nuiten, Bohrification of local nets of observables , bachelor thesis (August 2011)
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
Felix Wellen is writing a thesis on formalization of cohesive synthetic differential geometry in homotopy type theory. See at Formalizing Cartan Geometry in Modal HoTT.
Vincent Schlegel is writing a thesis on cohesive derived geometry and BV-quantization