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

Original Announcement

This workshop 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.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.