Numerical invariants of singularities and higher-dimensional algebraic varieties
July 31 to August 4, 2006
American Institute of Mathematics,
Palo Alto, California
and Aleksandr V. Pukhlikov and Vyacheslav Shokurov
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
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
The workshop will be focused around four specific themes:
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 log canonical threshold and related invariants in algebraic geometry.
- The p-adic and the motivic viewpoints towards singularities.
- Questions and techniques in positive characteristic.
- Singularities, stability and existence of special metrics.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.