Pre-talk title: How the minimal model program works

Abstract: In this pre-talk, I will explain how to run the minimal model program and introduce some basic concepts in the minimal model program.

Talk title: Minimal model program for generalized pairs

Abstract: Generalized pairs, an analogue of pairs and varieties, were first introduced by Birkar and Zhang in the study of effective Iitaka fibrations and had later played a crucial role in Birkar’s proof of the Borisov-Alexeev-Borisov conjecture and other important questions. This structure naturally appears in birational geometry via the canonical bundle formula. The minimal model program (MMP) for generalized pairs is a central topic in modern day MMP. In this talk, I will show that we can run MMPs for generalized pairs with log canonical singularities by establishing the cone theorem, contraction theorem, and the existence of flips for generalized pairs. This extends the MMP to its wildest category of structures which naturally appear in birational geometry. If time admits, I may provide some proofs and applications of the results. The talk is based on joint works with Christopher D. Hacon and Lingyao Xie.