Finite groups grading and actions on fusion categories

In this talk we will present two dual notions: finite group actions and finite group gradings
on a fusion category. We will explain how to use these notion to construct new fusion
categories from old ones. We will describe the equivariantization category, and extension theory
for fusion categories. We will also describe the Tambara Yamagami fusion categories, and use
them to give examples for non-group theoretical fusion categories.