October 2016, Manchester, UK

Title: Rationally connected non Fano type varieties

Abstract: The class of varieties of Fano type is a generalization of Fano varieties which is very well behaved under the MMP. It is known that all varieties of Fano type are rationally connected. The converse is true in a sense in dimension 2. I will give counter examples to the converse statement in dimension 3 and higher and use the techniques of birational rigidity and MMP.