Speaker: Dr. Jihao Liu (Northwestern Univ)
Time: 14:00-15:00 April 18, 2023 (Tuesday)
Place: MCM410
Title: Minimal model program for generalized pairs
Abstract: 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.
Speaker: Dr. Yalong Cao (RIKEN)
Time: 15:30-16:30 April 18, 2023 (Tuesday)
Place: MCM410
Title: From curve counting on Calabi-Yau 4-folds to quasimaps for quivers with potentials
Abstract: I will start by reviewing an old joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten, Gopakumar-Vafa and stable pair invariants on compact Calabi-Yau 4-folds. For non-compact CY4 like local curves, similar invariants can be studied via the perspective of quasimaps to quivers with potentials. In a joint work in progress with Gufang Zhao, we define a virtual count for such quasimaps and prove a gluing formula. Computations of examples will also be discussed.
附件：