Holonomic Rank Problem (II) and the Residue Formalism for Relative Cohomology.


Tsung-Ju Lee ( National Taiwan University )
2015-06-05  09:10 - 11:00
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

In the first part of this talk, I will introduce the recent result for the holomonic rank problem, which is due to A. Huang, B. Lian, and X. Zhu. They proved the holonomic rank conjecture in a more general setting. The result is also more abstract, involving the perverse sheaves.

For the second part of the talk, I will discuss the residue formalism for relative cohomology, which is used to construct the inhomogeneous Picard-Fuchs equations.

Ref: 1. Period integrals and the Riemann-Hilbert Correspondence, A. Huang, B. Lian, and X. Zhu. 2. Picard-Fuchs Equations for Relative Periods and Abel-Jacobi Map for Calabi-Yau Hypersurfaces, S. Li, B. Lian, and S.-T. Yau.