Exponential sums, peak sections and Homological mirror symmetry for weighted projective spaces

MSRI 2nd Floor Seminar Room
March 16, 2006    02:00 PM to 04:15 PM
Speaker: Wei-Dong Ruan

Abstract: This talk consists of two parts:

Part I: We will give an alternative proof of Donaldson's almost-holomorphic section theorem and symplectic Lefschetz pencil theorem, through constructions of certain special kind of Donaldson-type sections of the line bundle based on properties of exponential sums.

Part II: In 1994, Kontsevich proposed the homological mirror symmetry conjecture for Fano varieties and Calabi-Yau manifolds that predicts the equivalence of the derived category of coherent sheaves on the manifold and the Fukaya category for the mirror. In this talk, we will consider the case of weighted projective space for all dimension (joint work with A. Bondal). We will prove the homological mirror symmetry in this case through the category of constructible sheaves on the complex side and the Fukaya-Oh Morse category on the symplectic side.