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Bong Lian

2011-10-05
14:00:00 - 15:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

We develop a global Poincare residue formula to study period integrals of families of complex manifolds. For any compact complex manifold $X$ equipped with a linear system $V^*$ of generically smooth CY hypersurfaces, the formula expresses period integrals in terms of a canonical global meromorphic top form on $X$. We also generalize the construction to CY and general type complete intersections. When $X$ is an algebraic manifold having a sufficiently large automorphism group $G$ and $V^*$ is a linear representation of $G$, we construct a holonomic D-module that governs the period integrals. The talk is based on recent joint work with R. Song and S.T. Yau.