Abstract:

The minimal model program is a program which produces a good representative in each birational equivalence class of algebraic varieties. The termination of flips is one of the important problems in this program, and it is reduced to certain boundedness properties of the  singularities. The minimal log discrepancy is an invariant of singularities which plays an essential role from this point of view. I will explain the recent progress in the study of minimal log discrepancies.