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

This workshop, sponsored by AIM and the NSF, 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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

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