Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program I
2025-01-07 15:00 - 16:30 (Asia/Seoul) | B236-1, IBS, Korea, Republic of
Speaker

Sung Wook Jang
IBS CCG

Minimal model program (abbreviated as MMP) is a central problem in birational geometry. The MMP is a sequence of divisorial contractions or flips, which makes the canonical divisor closer to a nef divisor. If the MMP successfully terminates, then we have either a minimal model or a Mori fiber space. We will briefly show how to run an MMP and introduce recent progress concerned with the MMP.

Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program II
2025-01-08 15:00 - 16:30
Speaker

Sung Wook Jang
IBS CCG

We are interested in an anticanonical divisor and hope to establish the MMP for an anticanonical divisor. We believe that the beginning point is the potential log discrepancy that controls singularities of a possible resulting model of MMP for an anticanonical divisor. In this talk, we will give the definition and properties of the potential log discrepancy. We can also define a plc threshold in terms of the potential log discrepancy and show that plc thresholds satisfy ACC.

Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program III
2025-01-09 15:00 - 16:30
Speaker

Sung Wook Jang
IBS CCG

We can run an MMP for an lc pair. However, in general, we do not know whether the MMP terminates or not. Nevertheless, we can show that special MMP terminates. Immediately, we can prove the existence of minimal models for certain pairs. Analogously, for an anticanonical divisor, if we impose appropriate conditions, then we can say that there exists an anticanonical minimal model. Furthermore, we will talk about ongoing project on anticanonical minimal model program.
