Seminar

After the recent breakthrough in the Minimal Model Program, one of the
few parts that is still missing in the program is the Termination of
Flips Conjecture. It turns out that this conjecture is related to the
behavior of certain sophisticated invariants of singularity, one of
which is the "log canonical threshold". This invariant, defined by a
suitable integrability condition, has become a fundamental measure of
singularities in birational geometry. It is generally believed that
the set of all log canonical thresholds in any fixed dimension should
carry some interesting structure, and there is a conjecture of
Shokurov, motivated by the Termination of Flips Conjecture and known
as the ACC Conjecture, which predicts that there are no strictly
increasing sequences in these sets. In this talk I will discuss some
recent progress towards this conjecture.