Progress in the study of minimal varieties has had a profound impact on numerous areas of geometry and physics. This conference will bring together mathematicians and physicists working on minimal varieties and their applications.

The conference will have four main themes:

• Minimal Submanifolds in Riemannian Spaces
  • Classical theory in Rⁿ and other homogeneous spaces;
  • Minimal surfaces in 3 and 4 manifolds; applications to topology.

• Calibrated Geometry
  • Special Lagrangian geometry, mirror symmetry;
  • Calibrations and gauge theory;
  • Calibrations and M-theory;
  • Manifolds with special holonomy, in particular G₂-manifolds.

• Complex Subvarieties--Algebraic Cycles
  • Boundaries of complex analytic varieties;
  • Algebraic cycles;
  • Spaces of algebraic cycles, relations to topology;
  • Voevodsky theory;
  • Cycles and forms --secondary classes in algebraic geometry (Arakelov theory, singular connections, differential characters).

• The Dirac Operator
  • Relation to minimal hypersurfaces and positive scalar curvature;
  • Applications to geometry and topology.

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  There will be three minicourses:

  • Minicourse I: Minimal surfaces in 3-manifolds (Colding and Minicozzi).
  • Minicourse II: M-theory and calibrations (Papadopoulos).
  • Minicourse III: Voevodsky Theory (Dugger).

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  Contact Addresses:

  Varieties Department of Mathematics SUNY at Stony Brook Stony Brook, NY 11794, USA E-mail: varieties@math.sunysb.edu Fax: (631) 632-7631 c/o Varieties

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  This event is sponsored by the James H. Simons Math-Physics Endowment and the National Science Foundation.

  The four-ended surface was discovered by Michael Callahan, David Hoffman and Bill Meeks. The image displayed above was created by James T. Hoffman.

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  The State University of New York at Stony Brook is an affirmative action/equal employment opportunity educator and employer.