David Rydh: Geometry, sheaves, points and functors

Geometry is the study of spaces with various extra structure (metric, manifold structure, sheaf of functions, etc.). In this talk, I will explain and illustrate some of the ways algebraic geometers look at geometry. In particular, I will focus on the functorial point of view and Grothendieck's idea of generalized points. This simple idea has been very fruitful and led to various generalizations of the concept of a topological space.