Houari Benammar (Part 2): An introduction to birational geometry.

Title.
An introduction to birational geometry : running MMP, positivity of direct image sheaf.

Abstract.
We will give an introduction to birational geometry by recalling some basic definitions and natural transformations. We will discuss the history of birational classification of Complex projective varieties starting from Castelnuovo to Mori minimal model program. Thus, we will sketch the result of BCHM. For the second part, we will focus on the notion of the positivity of direct image sheaf, we will present our recent and ongoing work.