Relating test ideals and multiplier ideals

This workshop, sponsored by AIM and the NSF, will be devoted to the the connection between two prominent and distinct means of measuring singularities: the multiplier ideal in complex algebraic geometry, and the test ideal in positive characteristic commutative algebra. These two concepts are related via "reduction to characteristic p" techniques. The subsequent interplay of geometric methods in characteristic zero and Frobenius techniques in positive characteristic continues to inspire new questions and results throughout numerous areas of mathematics, including algebraic geometry, commutative algebra, representation theory, and number theory.

Potential focus topics of this workshop include recent progress, new applications, and remaining open questions in the following areas:

• Understanding F-jumping numbers of test ideals as the characteristic p > 0 varies.
• Computing test ideals via finite extensions and regular alterations.
• Test ideals and multiplier ideals in non-Q-Gorenstein rings.

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.

For more information email workshops@aimath.org

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