I will discuss an invariant of singularities that plays
an important role in birational geometry, the log canonical threshold.
Depending on the time available, I plan to cover some of the following
topics:
1) Definition and examples. Connection with multiplier ideals and vanishing
theorems
2) Shokurov's ACC conjecture, and its connection with Termination of Flips
3) A proof of the conjecture on ambient smooth varieties
4) Asymptotic invariants for graded sequences of ideals
5) Connection with invariants in positive characteristic defined via
Frobenius