Differential Equations and Mixed Hodge Structures

Explore a cutting-edge development in asymptotic Hodge theory in this 59-minute lecture by Matt Kerr from the University of Washington. Delve into the connections between Golyshev-Zagier and Bloch-Vlasenko's work and the Gamma Conjectures in Fano/LG-model mirror symmetry. Focus on Hodge and period-theoretic aspects through two main examples. Examine variations of Hodge structure on Zariski open sets in P^1 and learn how to compute periods of limiting mixed Hodge structures at punctures. Discover how these asymptotic invariants are encoded in the motivic Gamma function, determined by the underlying Picard-Fuchs operator. Explore closed-form solutions for hypergeometric cases and predictions for special values of normal functions in non-hypergeometric settings. Gain insights into this collaborative research with V. Golyshev and T. Sasaki, advancing our understanding of differential equations and mixed Hodge structures.