Workshop

The workshop will concentrate on the recent advances on canonical and minimal models of algebraic varieties. We plan to study the proofs, survey applications and related results and chart future directions for research. Two algebraic varieties are said to be birational if their fields of rational functions are isomorphic. There is a unique smooth projective curve in each birational equivalence class of curves. For surfaces, the situation is a little more complex, but was completely understood in by the early 20th century: most surfaces have unique "minimal" models, and when this is not the case the set of minimal models is easy to understand. Shigefumi Mori won the Fields medal in 1990 for proving a similar theorem for 3-folds, and there has been intense work on extending the "Mori Programme" to higher dimensions, ever since. A closely related problem is the finite generation of the canonical ring of a variety of general type and thus the existence of "canonical" models for these varieties. Very recently Yum-Tong Siu on one hand and Birkar, Cascini, Hacon and McKernan on the other announced proofs of this finite generation. This has as a consequence the extension of the Mori Programme to all dimensions, and also has many other applications. A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: TR0000. The cut-off date for reservations is March 16, 2007. A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). A calendar will appear showing the MSRI rate on all room types available. Enter the following Group Code in the "Comment" field: CG418. Please note: The Original Queen room type does not have an in-room T1 connection, but they do have WIFI available in the main lobby area. The cut-off date for reservations is March 26, 2007.