Nicolás Libedinsky (Universidad de Chile) Representation theory and categorification. In the past ten years some spectacular developments in representation theory (of objects like the symmetric group or SL(n)) has arisen. Many things were known in characteristic zero and it was conjectured that in positive characteristic things were controlled by the same kind of objects. But this set of conjectures are now known to be false, and the new understanding of modular representation theory is much richer, deeper, and surprising (although we only know the very tip of the iceberg). For example, there is some fractal behaviour, there are some “dynamical systems” phenomena, strange number-theoretical phenomena and emerging connections with physics, homotopy of spheres and other “distant” parts of mathematics. It is a fascinating and expanding field that we will explore in this course.