Numerical invariants of singularities and higher-dimensional algebraic varieties

July 31 to August 4, 2006

at the

American Institute of Mathematics, Palo Alto, California

organized by

Lawrence Ein, Robert Lazarsfeld, Mircea Mustata, Nero Budur, and Aleksandr V. Pukhlikov and Vyacheslav Shokurov

This workshop, sponsored by AIM and the NSF, will be devoted to certain numerical measures of the singularities of a divisor or holomorphic function. These invariants -- notably the log-canonical threshold or complex singularity index -- have appeared in recent years in a surprisingly wide variety of mathematical problems. Moreover, conjectural properties of these invariants play a major role in the birational geometry of higher-dimensional algebraic varieties. The idea of the workshop is to bring together researchers working in the various different directions, in the hopes of generating some valuable cross-fertilization.

The workshop will be focused around four specific themes:

  1. The log canonical threshold and related invariants in algebraic geometry.
  2. The p-adic and the motivic viewpoints towards singularities.
  3. Questions and techniques in positive characteristic.
  4. Singularities, stability and existence of special metrics.
Each of the above topics will be represented by a series of three essentially didactic talks, aimed at researchers coming from other viewpoints. Some introductory notes regarding each of the above directions, including the relevant bibliography, will be posted on the workshop website a few months before the beginning of the workshop. Each topic will also be the theme of discussion and working sessions during the workshop.

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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