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Hot Topics: Minimal and Canonical Models in Algebraic Geometry

April 16, 2007 to April 20, 2007
Organized By: Alessio Corti, Jean-Pierre Demailly, János Kollár, Shigefumi Mori
 
Participant List:
View a List of Registered Participants
 
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.
 

Follow this link to read about the new U.S. visa requirements

 

Schedule

Monday April 16, 2007

09:30AM - 10:30AM  Robert Lazarsfeld Lifting Theorems
11:00AM - 12:00PM  Alessio Corti Existence of flips
02:00PM - 03:00PM  Mircea Mustata Existence of flips
03:45PM - 04:45PM  János Kollár Termination of flips

Tuesday April 17, 2007

09:30AM - 10:30AM  Bo Berndtsson A survey of the main analytic tools and their use in algebraic geometry
11:00AM - 12:00PM  Jean-Pierre Demailly Further applications of the main L^2 existence theorems
02:00PM - 03:00PM  Philippe Eyssidieux Analytic approach of the finite generation of the canonical ring
03:45PM - 04:45PM  Jean-Pierre Demailly Extension of non vanishing theorems to higher codimension

Wednesday April 18, 2007

09:30AM - 10:30AM  Yum-Tong Siu Analytic Proof of Finite Generation of Canonical Ring for General Type
11:00AM - 12:00PM  Christopher Hacon TBA
02:00PM - 05:00PM  Short Communications

Thursday April 19, 2007

09:30AM - 10:30AM  Vyacheslav Shokurov Log Termination: Complete and Directed
11:00AM - 12:00PM  Masayuki Kawakita On minimal log discrepancies
02:00PM - 03:00PM  Caucher Birkar TBA
03:45PM - 04:45PM  Hajime Tsuji Extension of log pluricanonical systems and semipositivity of pluricanonical systems

Friday April 20, 2007

09:30AM - 10:30AM  Philippe Eyssidieux KE-metrics on Minimal Models
11:00AM - 12:00PM  Miles Reid Problem Session
02:00PM - 05:00PM  Short Communications

Currently Available Videos

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