There has been significant progress recently in the birational geometry of algebraic varieties over the complex numbers. Apart from proving the outstanding conjectures in the Minimal Model Program, one of the main practical problems in the field is that the theory has not been implemented on computer algebra systems, not even for surfaces.
This project aims to make theoretical advancements in the development of a working algorithm as well as to actual implementation of the Minimal Model Program for complex projective klt pairs of log general type. Moreover, we will expand the scope of the famous Cone conjecture beyond the realm of varieties with trivial canonical class.