A rapid course on generated Jacobian equations

The general framework for Generated Jacobian Equations (GJE) was first studied in a systematic fashion by Neil Trudinger in 2014, motivated by near field geometric optics problems. These equations involve the prescription of the Jacobian of a transformation derived from a scalar potential, which itself arises as the envelope of a some family of "generating" functions. As such, they also appear in areas such as economics, geometric optics, and optimal transport --which, to use the economic literature terminology, corresponds to the special case of "quasilinear" generating functions. I will discuss these examples as well as the elements of the theory of GJE, and provide a partial overview of the growing literature on the field.Non UBCUnreviewedAuthor affiliation: University of Massachusetts AmherstResearche