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Workshop

Hot Topics: Minimal and Canonical Models in Algebraic Geometry April 16, 2007 - April 20, 2007
Registration Deadline: April 09, 2007 over 7 years ago
To apply for Funding you must register by: January 16, 2007 almost 8 years ago
Series: Hot Topic
Organizers Alessio Corti, Jean-Pierre Demailly, János Kollár, Shigefumi Mori
Speaker(s)

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Description

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.


Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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MSRI has preferred rates at the Rose Garden Inn, depending on room availability. 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). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code 123MSRI. Our preferred rate is $139 per night for a Deluxe Queen/King, based on availability.

MSRI has preferred rates of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

MSRI has preferred rates of $110 - $140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

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Schedule
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Apr 16, 2007
Monday
09:30 AM - 10:30 AM
  Lifting Theorems
Robert Lazarsfeld (University of Michigan)
11:00 AM - 12:00 PM
  Existence of Flips
Alessio Corti (Imperial College, London)
02:00 PM - 03:00 PM
  Existence of Flips
Mircea Mustata (University of Michigan)
03:45 PM - 04:45 PM
  Termination of Flips
János Kollár (Princeton University)
Apr 17, 2007
Tuesday
09:30 AM - 10:30 AM
  A Survey of the Main Analytical Tools and Their Use in Algebraic Geometry
Bo Berndtsson
11:00 AM - 12:00 PM
  Further Applications of the Main L^2 Existence Theorems
Jean-Pierre Demailly (Université de Grenoble I (Joseph Fourier))
02:00 PM - 03:00 PM
  Analytic Approach of the Finite Generation of the Canonical Ring
Philippe Eyssidieux
03:45 PM - 04:45 PM
  Extension on Non-Vanishing Theorems to Higher Codimension
Jean-Pierre Demailly (Université de Grenoble I (Joseph Fourier))
Apr 18, 2007
Wednesday
09:30 AM - 10:30 AM
  Analytic Proof of Finite Generation of Canonical Ring for General Type
Yum-Tong Siu (Harvard University)
11:00 AM - 12:00 PM
  TBA
Christopher Hacon (University of Utah)
02:00 PM - 03:00 PM
  TBA
Bo Berndtsson
03:45 PM - 04:45 PM
  TBA
Osamu Fujino
Apr 19, 2007
Thursday
11:00 AM - 12:00 PM
  On Minimal Log Discrepencies
Masayuki Kawakita (Kyoto University)
02:00 PM - 02:30 PM
  TBA
Florin Ambro
02:30 PM - 03:00 PM
  TBA
Ivan Cheltsov
03:45 PM - 04:45 PM
  Extension of Log Pluricanonical Systems and Semipositivity of Pluricanonical Systems
Hajime Tsuji
Apr 20, 2007
Friday
09:30 AM - 10:30 AM
  KE-metrics on Minimal Models
Philippe Eyssidieux
11:00 AM - 12:00 PM
  Problem Session
Miles Reid
02:00 PM - 03:00 PM
  Noncommutative Deformations of K3 Surfaces
Paul Hacking
03:45 PM - 04:15 PM
  TBA
Shunsuke Takagi (Graduate School of Mathematical Sciences)
04:15 PM - 05:00 PM
  TBA
Chuanyi Xu