Algebraic Geometry Seminar: "Period integrals of vector bundle sections"

Abstract: Tautological systems introduce by Lian-Song-Yau and Lian-Yau are Picard-Fuchs type differential systems to study period integrals of complete intersections in varieties with large symmetry group. It is a generalization of Gelfand-Kapranov-Zelevinsky hypergeometric systems. The work of S. Bloch, A. Huang, B. Lian, D. Srinivas, S.-T. Yau and X. Zhu gives complete descriptions of Riemann-Hilbert type problems for these differential systems arising from hypersurfaces in generalized flag varieties. I will describe the generalizations of tautological systems to vector bundle sections, and discuss the solution rank formulas and geometric realizations of solutions. In particular, we conjectured the solutions for complete intersections in homogenous varieties are given by Euler type integrals, which is proved recently by T.-J. Lee, B. Lian and D. Zhang. This is based on joint work with A. Huang, B. Lian and S.-T. Yau.

Host: Matt Kerr