Federico Lazzeri: The 0-Hecke algebra

Abstract: We will define the q-Hecke algebra as a deformation of the symmetric group algebra, and we will specialize it in the case q=0. This particular algebra is not semisimple, so we will have to do some work in order to study its representation theory. In this task, combinatorics will help us, just as it does with the representations of the symmetric group. Finally, we will see the connections with algebraic geometry and we will introduce open problems inherent this topic.