The EU network EAGER (European algebraic geometry research training network) will run a EuroConference on higher dimensional complex geometry as the climax of the Cambridge Isaac Newton Institute's 2002 program on algebraic 3-folds. Algebraic geometry is the study of geometric locuses defined by polynomial equations; whereas the one dimensional case (algebraic curves or Riemann surfaces) was well studied in the 19th century, and the two dimensional case (algebraic surfaces) from around 1900, the theory of algebraic 3-folds involves many subtleties, and it is only in the last 25 years that a theory has taken shape.
Mori theory offers rewarding new insights into classical results on algebraic surfaces and is essential in advances such as mirror symmetry and the McKay correspondence. The Mori category consists of varieties with mild singularities; this leads to a remarkable wealth of problems that can be treated by explicitly calculations, for example, hundreds of families of Fano 3-folds.
The 3 main scientific topics of the conference are:
1) Mori theory and the birational geometry of 3-folds,
2) the McKay correspondence for resolutions of orbifolds,
3) Calabi-Yau 3-folds and mirror symmetry.
The conference sets itself the task of making available to European algebraic geometers the new ideas and methods arising in each of these topics and exploiting their many applications to other areas of geometry and physics.