Time: 10:00-11:30 October 29, 2024 (Tuesday)
Venue: MCM410
Title: How Are Generalized Pairs Applied in Foliation Theory?
Abstract: The concept of generalized pairs, introduced by Birkar and Zhang, plays an important role in modern birational geometry. This concept has been particularly crucial in proving the Borisov-Alexeev-Borisov conjecture and the McKernan-Shokurov conjecture. In this talk, I will explain how the theory of generalized pairs is applied to foliation theory from various perspectives, including but not limited to: Bertini-type theorems, the canonical bundle formula, the minimal model program (MMP) with scaling, the base-point-freeness theorem, the existence of flips, flops between minimal models, and the explicit adjunction formula. The talk is based on several joint works and ongoing collaborations with one or more of the following scholars: Paolo Cascini, Guodu Chen, Yifei Chen, Jingjun Han, Yujie Luo, Fanjun Meng, Calum Spicer, Roberto Svaldi, Yanze Wang, and Lingyao Xie.
