Abstract: Differential calculus on Euclidean spaces can be generalized in different ways. A diffeological structure on an (arbitrary) set is given by maps from open subsets of Euclidean spaces to the set (satisfying some axioms); a differential structure is given by maps from the set to R; a Frolicher structure is given by maps from R to the set as well as maps from the set to R. We describe relations between these structures and present examples, including good subsets, bad quotients, and infinite dimensional spaces of smooth maps.

Speaker's web page: http://www.math.toronto.edu/karshon/