Mathematical Sciences Research Institute

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Combinatorial, Enumerative and Toric Geometry March 23, 2009 - March 27, 2009
Registration Deadline: March 18, 2009 over 8 years ago
To apply for Funding you must register by: December 23, 2008 almost 9 years ago
Parent Program:
Organizers Michel Brion (U. de Genoble), Anders Buch (Rutgers U.), Linda Chen (Ohio State U.), William Fulton (U. Michigan), Sándor Kovács (U. Washington), Frank Sottile (Texas A&M), Harry Tamvakis (U. Maryland), and Burt Totaro (Cambridge U.)

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"Conference webpage" Algebraic geometry has long been a central subject within mathematics, enjoying deep and substantial connections to other parts of mathematics. In particular, the interplay between algebraic geometry and algebraic combinatorics has led to many important developments in these and other mathematical fields. The last fifteen years have seen an explosion of interest in algebraic varieties with rich combinatorial structures: Schubert geometry of flag varieties and their subvarieties, degeneracy loci, toric varieties, moduli spaces and Gromov-Witten theory, and varieties with group actions. Powerful tools from algebraic topology, combinatorics, commutative and computational algebra, complex and symplectic geometry, and representation theory have been developed to study such objects. In this workshop, we will present the state of the art in combinatorial, enumerative, and toric algebraic geometry. We will highlight this part of modern algebraic geometry within the context of the broader parent program at MSRI, and convey its scope to young researchers. Bibliography (PDF 8KB) 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 March 6, 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: MZ0000. The cut-off date for reservations is February 20, 2009. Room Rate $159/ night.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
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Mar 23, 2009
09:30 AM - 10:30 AM
  On asymptotic invariants of graded sequences of ideals
Mircea Mustaţă (University of Michigan)
11:00 AM - 12:00 PM
  Strong exceptional collections of line bundles on Fano toric DM stacks
Lev Borisov
02:00 PM - 03:00 PM
  Towards a Littlewood-Richardson rule in the Kac-Moody setting.
Nicolas Perrin
03:30 PM - 04:30 PM
  Geometric positivity in the cohomology of homogeneous varieties
Izzet Coskun (University of Illinois, Chicago)
Mar 24, 2009
09:30 AM - 10:30 AM
  Equivariant transversality and K-theoretic positivity
Ezra Miller (Duke University)
11:00 AM - 12:00 PM
  Convex bodies, semi-groups of integral points, algebras of finite type, and geometry of linear series on varieties
Kiumars Kaveh
01:30 PM - 02:30 PM
  What can we learn about matroids from K-theory?
David Speyer (University of Michigan)
03:00 PM - 04:00 PM
  Tropical bounds on nef cones
Diane Maclagan (University of Warwick)
Mar 25, 2009
09:30 AM - 10:30 AM
  Boundary complexes of varieties
Sam Payne (Yale University)
11:00 AM - 12:00 PM
  Compactifications of Subvarieties of Tori
Evgueni Tevelev
Mar 26, 2009
09:30 AM - 10:30 AM
  Quantum K theory of Grassmannians
Constantin Leonardo Mihalcea
11:00 AM - 12:00 PM
  The virtual Betti numbers of the Hilbert scheme of points on a Calabi- Yau threefold
Kai Behrend (University of British Columbia)
01:30 PM - 02:30 PM
  K-theoretic Schubert calculus on the affine Grassmannian
Thomas Lam
03:00 PM - 04:00 PM
  The K-Theory of Symplectic Orbifolds
Tara Holm
Mar 27, 2009
09:30 AM - 10:30 AM
  The Hilbert scheme of the diagonal in a product of projective spaces
Bernd Sturmfels (University of California, Berkeley)
11:00 AM - 12:00 PM
  GIT-cones and applications
Nicolas Ressayre
03:00 PM - 04:00 PM
  Frobenius splitting of matrix Schubert varieties and positroid varieties, with applications to juggling
Allen Knutson (Cornell University)