Dr.Jihao Liu,Northwestern Univ

Generalized pairs are a natural structure in birational geometry that first appeared in Kodaira’s canonical bundle formula for elliptic fibrations. They were formally introduced by Birkar and Zhang in 2014 as part of their study of effective Iitaka fibrations and have since become a central topic in modern-day birational geometry. In particular, they have been essential in the study of the Borisov-Alexeev-Borisov conjecture [Bir19,Bir21]. Recently, the speaker, Hacon, and Xie have proven the cone theorem, contraction theorem, and the existence of flips for generalized pairs in a series of works. These results imply that we can run the minimal model program for generalized pairs. In this talk, I will discuss these results and their applications in the structure of Du Bois singularities and the minimal model program for foliations.