Abstract 

Generalised 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 Birkar proof of the Borisov-Alexeev-Borisov conjecture. Recently, the speaker, Hacon, and Xie have proven the cone theorem, contraction theorem, and the existence of flips for generalised pairs in a series of works. These results imply that we can run the minimal model program for generalised 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.

About the speaker 

刘济豪，美国西北大学 Boas 助理教授。2021年3月获得美国犹他大学博士学位，师从 Christopher Hacon。研究领域是代数几何，在双有理几何中的极小模型理论、低维簇的具体界等前沿问题中取得优秀的成果，已有多篇论文发表/接收在Osaka J. Math., Int. J. Math., Math. Nachr.等杂志。