Research

The Minimal Log Discrepancy (MLD) is an invariant of singularities in birational geometry. In this talk, we will discuss some conjectures on MLD focusing on my research. In the 1980s, the Minimal Model Program (MMP), which is a specific program for classifying algebraic varieties, was proposed. One of the most important open problems in birational geometry is the conjecture of "termination of flips", which asks whether this program stops after a finite steps. The MLD is an invariant of singularities introduced by Shokurov to attack this conjecture. It is known that "the termination of flips" follows from two conjectures on MLD, the ACC conjecture and the LSC conjecture. In this talk, I will explain known results on these two conjectures with my recent research.