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Workshop

Intersection Theory on Stacks March 11, 2002 - March 15, 2002
Registration Deadline: March 15, 2002 almost 17 years ago
To apply for Funding you must register by: December 11, 2001 about 17 years ago
Parent Program:
Organizers K. Behrend, W. Fulton, L. Katzarkov, M. Kontsevich, Y. Manin, R. Pandharipande, T. Pantev, B. Toen, and A. Vistoli
Speaker(s)

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Description
The intersection theory on stacks was pioneered by H. Gillet and A. Vistoli. Later the work of M. Kontsevich and Y. Manin on the algebraic Gromov-Witten invariants required the full intersection theory machinery on Deligne-Mumford stacks. Several foundational results in this direction were obtained by Behrend-Fantechi and Fulton-Pandharipande. The theory was further developed by K. Behrend, D. Edidin, T. Graber, W. Graham, A. Kresch, R. Pandharipande and B. Toen. Many fundamental results with far reaching geometric applications were obtained. Among these we may mention: the Kunneth formula in quantum cohomology proven by Kontsevich and Manin; the localization formula for virtual classes proven by Graber-Pandharipande; the Lefschetz trace formula proven by K. Behrend; and the Riemann-Roch and GAGA theorems for Deligne-Mumford stacks proven by B. Toen. A connection with deformation theory was established by Kontsevich. All these topics as well as new applications will be discussed.                      Group photo of participants
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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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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A block of rooms has been reserved 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 MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

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Schedule, Notes/Handouts & Videos
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Mar 11, 2002
Monday
08:00 AM - 05:00 PM
  A 2-Categorical Approach to Differential Graded
Kai Behrend (University of British Columbia)
10:30 AM - 11:30 AM
  Intersection theory on algebraic stacks: The approach of Totaro, Edidin and Graham
Angelo Vistoli (Scuola Normale Superiore)
11:45 AM - 12:45 PM
  Can one do arithmetics intersection theory on stacks?
Henri Gillet
02:00 PM - 03:00 PM
  Multigraded Hilbert schemes
Bernd Sturmfels (University of California, Berkeley)
04:10 PM - 05:10 PM
  Gorenstein tautological rings
Rahul Pandharipande (ETH Zurich)
Mar 12, 2002
Tuesday
09:30 AM - 10:30 AM
  Intersection theory on Artin stacks: Chow groups for Artin stacks
Andrew Kresch
11:00 AM - 12:30 PM
  Gromov-Witten theory of P1, part I
Rahul Pandharipande (ETH Zurich)
02:00 PM - 03:30 PM
  Gromov-Witten theory of P1, part II
Andrei Okounkov (Columbia University)
04:00 PM - 05:00 PM
  Riemann-Roch for quotients and Todd classes of simplicial toric varieties
Dan Edidin
Mar 13, 2002
Wednesday
10:00 AM - 11:00 AM
  Degeneration formula of Gromov-Witten invariants
Jun Li (Stanford University)
11:30 AM - 12:30 PM
  Quot schemes for Deligne-Mumford Stacks
Jason Starr
01:00 PM - 02:00 PM
  Intersection theory on toric hyperkahler varieties
Tamas Hausel
03:30 PM - 04:30 PM
  Cohomology ring of crepant resolutions of orbifolds
Yongbin Ruan (University of Michigan)
Mar 14, 2002
Thursday
10:00 AM - 11:00 AM
  Toric stacks of pavings
Laurent Lafforgue
11:30 AM - 12:30 PM
  Logarithmic geometry and algebraic stacks
Martin Olsson (University of California, Berkeley)
02:00 PM - 03:00 PM
  Vanishing of cohomology classes on the moduli space of curves
Ravi Vakil (Stanford University)
03:30 PM - 04:30 PM
  How many Gromov-Witten invariants of rational curves are there, really?
Aaron Bertram (University of Utah)
05:00 PM - 06:00 PM
  Differential graded schemes in algebraic geometry
Mikhail Kapranov (Kavli Institute for the Physics and Mathematics of the Universe )
Mar 15, 2002
Friday
10:00 AM - 11:00 AM
  Higher intersection theory on algebraic stacks
Roy Joshua (Ohio State University)
11:30 AM - 12:30 PM
  TBA
Kai Behrend (University of British Columbia)
02:00 PM - 03:00 PM
  K-theory of algebraic stacks
Bertrand Toen (Centre National de la Recherche Scientifique (CNRS))
03:30 PM - 04:30 PM
  On symmetric degeneracy loci
William Graham