Algebraic Geometry Seminar

Please see the following for more related talks:

• geometry/topology seminar
• string theory seminar

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• Monday, November 23, 2009, 4:30pm, 205 Physics, Elliptic Curves Working Seminar
  Who wants to be a millionaire?
  Shahed Sharif (Duke University)

   

  The Mordell-Weil theorem shows that the rational points on an elliptic curve defined over the field of rational numbers is a finitely generated abelian group. The Birch and Swinnerton-Dyer conjecture relates the rank of this group to a number of analytic and algebraic invariants of the curve. (More generally it considers an elliptic curve defined over a number field.) The conjecture is one of the Millennium Prize problems and the Clay Institute is offering a reward of 1 million dollars for a solution. This talk will be an introduction to the conjecture. In following weeks we will have lectures explaining each of the terms in the formula.

• Monday, November 30, 2009, 4:30pm, 205 Physics, Algebraic Geometry Seminar
  Essentially self-dual vector bundles on algebraic varieties
  Asher Auel (Emory University)

   

  Vector bundles isomorphic to their dual after tensoring with a line bundle are called essentially self-dual. Indecomposable essentially self-dual vector bundles support a line bundle-valued symmetric or skew-symmetric bilinear form. The computation of Witt and Grothendieck-Witt groups of line bundle-valued forms has only recently been completed for certain projective homogeneous varieties using derived category techniques. I'll review the history of this problem and discuss a new characteristic class in mod 4 etale cohomology for line bundle-valued symmetric forms.