#
ACC for minimal log discrepancies and termination of flips

May 14 to May 18, 2012
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Tommaso de Fernex and Christopher Hacon

## Original Announcement

This workshop will be devoted to two
closely connected conjectures in the minimal model program.
The minimal model program generalizes the classification of surfaces
to higher dimensional varieties. After the recent proof of the existence
of flips (due to Birkar-Cascini-Hacon-McKernan), one of the main
remaining open problems in the field is the Termination of Flips
Conjecture. This is an important conjecture with many applications to
questions related to the minimal model program. As shown by Shokurov,
termination of flips can be reduced to a question on minimal log
discrepancies, an invariant that gives a sophisticated measure of
singularities. Minimal log discrepancies are known to improve after
each flip, and Shokurov conjectured that these invariants have no
accumulation points from below, that is, that they satisfy the
ascending chain condition (ACC). This conjecture, together with a
conjecture on the semicontinuity of these invariants, is known to
imply the termination of flips. Results on minimal log discrepancies
are of independent interest as these invariants are important in the
study of singularities.

The above conjectures constitute the main topics for the workshop:

- Termination of flips.

- ACC for minimal log discrepancies.

These topics are closely related to other central questions in this
area of research such as the ACC for log canonical thresholds, the
Borisov-Alexeev-Borisov Conjecture, and the Abundance Conjecture. In
view of recent spectacular results in this area, we hope that this
workshop will help to spur further progress on these conjectures.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop: