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.