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Workshop

Classical Algebraic Geometry Today January 26, 2009 - January 30, 2009
Registration Deadline: January 26, 2009 almost 6 years ago
To apply for Funding you must register by: October 26, 2008 about 6 years ago
Parent Program: Algebraic Geometry
Organizers Lucia Caporaso (U. Rome III), Brendan Hassett (Rice U.), James McKernan (MIT), Mircea Mustata (U. Michigan), Mihnea Popa (U. Illinois - Chicago)
Speaker(s)

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Description

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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.


Schedule
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Jan 26, 2009
Monday
09:30 AM - 10:30 AM
  The Interpolation Problem
Richard Harris
11:00 AM - 12:00 PM
  Applications of projective geometry to birational geometry
Yuri Tschinkel (New York University, Courant Institute)
02:00 PM - 03:00 PM
  The geography of irregular surfaces.
Rita Pardini
Jan 27, 2009
Tuesday
09:30 AM - 10:30 AM
  Deformations of canonical pairs and Fano varieties
Christopher Hacon (University of Utah)
11:00 AM - 12:00 PM
  Quotients by finite equivalence relations
János Kollár (Princeton University)
02:00 PM - 03:00 PM
  Periods and Moduli
Olivier Debarre
04:00 PM - 05:00 PM
  The Hodge theory of character varieties
Mark de Cataldo
Jan 28, 2009
Wednesday
09:30 AM - 10:30 AM
  Counting curves in 3-folds
Richard Thomas
11:00 AM - 12:00 PM
  Derived cateories and Chow groups of K3 surfaces
Daniel Huybrechts
Jan 29, 2009
Thursday
09:30 AM - 10:30 AM
  The Schottky problem
Samuel Grushevsky
11:00 AM - 12:00 PM
  Refined generic vanishing
Giuseppe Pareschi
02:00 PM - 03:00 PM
  Main components of moduli spaces and log geometry.
Martin Olsson (University of California, Berkeley)
04:00 PM - 05:00 PM
  Algebraic surfaces and hyperbolic geometry
Burt Totaro (University of Cambridge)
Jan 30, 2009
Friday
09:30 AM - 10:30 AM
  Lie algebra actions on the cohomology of hyperquot schemes
Alina Marian (Northeastern University)
11:00 AM - 12:00 PM
  Four-dimensional analogues of K3 surfaces.
Kieran O'Grady
02:00 PM - 03:00 PM
  Syzygies and Geometry
David Eisenbud (MSRI - Mathematical Sciences Research Institute)
04:00 PM - 05:00 PM
  Equivalence problem for minimal rational curves
Jun-Muk Hwang