I will discuss two recent applications of the Riemann-Hilbert problem for periods of CY manifolds. One of them deals with the hyperplane conjecture for toric hypersurfaces that goes back to the mid 1990s. The second application provide descriptions for zeros of derivatives of generalized hypergeometric functions. The lecture is based on joint work with A. Huang, S.-T. Yau and M. Zhu.

This video is part of Harvard University‘s conference JDG 2017.