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Classical Algebraic Geometry Today

January 26, 2009 to January 30, 2009
Organized By: Lucia Caporaso (U. Rome III), Brendan Hassett (Rice U.), James McKernan (MIT), Mircea Mustata (U. Michigan), Mihnea Popa (U. Illinois - Chicago)
 
Parent Programs:
Algebraic Geometry
 
Participant List:
View a List of Registered Participants
 
Click here to see a list of confirmed speakers.

Algebraic Geometry is one of the most diverse areas of mathematics. Due to the breadth of the subject it is often a challenge for graduate students and people from other fields to get a global view of current developments in the field. Algebraic Geometry has grown dramatically over the past century, with new subfields constantly branching off. The core of the field is now universally called Classical Algebraic Geometry, an exciting area itself full of fundamental unsolved problems and at the same time providing a theoretical foundation for the areas that have developed in recent years.

The main theme of the workshop will be to explore modern approaches to problems originating in Classical Algebraic Geometry, and at the same time offer an introduction to various subfields to the younger participants in the semester-long program. Topics will include:
  1. Birational geometry: minimal model program, singularities of pairs, linear series, classification of surfaces of general type.
  2. Moduli spaces of curves: intersection theory, cones of ample and effective divisors, limit linear series.
  3. Moduli spaces of vector bundles: intersection theory on Quot schemes, Strange Duality, generalized theta divisors.
  4. Abelian varieties: Schottky problem, analytic methods, Fourier-Mukai transform.
  5. Rational curves on algebraic varieties: rational connectedness, behavior in families, rationality.

Bibliography (PDF 27KB)

Accomodations:

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). By using this code a new calendar will appear and will show MSRI rate on all room types available.
The cut-off date for reservations is January 9, 2009.

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: M00000. The cut-off date for reservations is December 26, 2008. Room Rate $159/ night.
 

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

 

Schedule

Monday January 26, 2009

09:15AM - 09:30AM  MSRI Welcome
09:30AM - 10:30AM  Joseph Harris The Interpolation Problem
10:30AM - 11:00AM  Coffee, Tea in the atrium
11:00AM - 12:00PM  Yuri Tschinkel Applications of projective geometry to birational geometry    (See Abstract)
12:00PM - 02:00PM  Lunch
02:00PM - 03:00PM  Rita Pardini The geography of irregular surfaces.    (See Abstract)
03:00PM - 03:30PM  Coffee, Tea in the atrium
04:00PM - 05:00PM  Robert Lazarsfeld Positivity Properties of Divisors and Higher Codimension Cycles

Tuesday January 27, 2009

09:30AM - 10:30AM  Christopher Hacon Deformations of canonical pairs and Fano varieties    (See Abstract)
10:30AM - 11:00AM  Coffe, tea in the atrium
11:00AM - 12:00PM  János Kollár Quotients by finite equivalence relations
12:00PM - 02:00PM  Lunch
02:00PM - 03:00PM  Olivier Debarre "Periods and Moduli"    (See Abstract)
03:00PM - 03:30PM  Coffee, tea in the atrium
04:00PM - 05:00PM  Mark de Cataldo The Hodge theory of character varieties    (See Abstract)
05:00PM - 06:00PM  Reception in the atrium

Wednesday January 28, 2009

09:30AM - 10:30AM  Richard Thomas Counting curves in 3-folds    (See Abstract)
10:30AM - 11:00AM  Coffee, Tea in the atrium
11:00AM - 12:00PM  Daniel Huybrechts Derived cateories and Chow groups of K3 surfaces    (See Abstract)

Thursday January 29, 2009

09:30AM - 10:30AM  Samuel Grushevsky The Schottky problem    (See Abstract)
10:30AM - 11:00AM  Coffee, Tea in the atrium
11:00AM - 12:00PM  Giuseppe Pareschi Refined generic vanishing    (See Abstract)
12:00PM - 02:00PM  Lunch
02:00PM - 03:00PM  Martin Olsson Main components of moduli spaces and log geometry.    (See Abstract)
03:00PM - 03:30PM  Coffee, tea in the atrium
04:00PM - 05:00PM  Burt Totaro Algebraic surfaces and hyperbolic geometry    (See Abstract)

Friday January 30, 2009

09:30AM - 10:30AM  Alina Marian Lie algebra actions on the cohomology of hyperquot schemes.    (See Abstract)
10:30AM - 11:00AM  Coffee, Tea in the atrium
11:00AM - 12:00PM  Kieran O'Grady Four-dimensional analogues of K3 surfaces.    (See Abstract)
12:00PM - 02:00PM  Lunch
02:00PM - 03:00PM  David Eisenbud Syzygies and Geometry    (See Abstract)
03:00PM - 03:30PM  Coffee, Tea in the atrium
04:00PM - 05:00PM  Jun-Muk Hwang Equivalence problem for minimal rational curves    (See Abstract)

Currently Available Videos

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