Kato-Usui Type Extension of General Period Map

Explore a comprehensive lecture on the extension of general period maps, presented by Haohua Deng from Duke University at the "Periods, Shafarevich Maps & Applications" conference. Delve into the complexities of extension theories for period maps, comparing well-known classical types with their non-classical counterparts. Examine the Kato-Usui theory, which offers a method for extending general period maps into logarithmic manifolds, contingent on the existence of specific fans. Understand how this theory aligns with toroidal compactification in classical cases. Review an example demonstrating the practical application of Kato-Usui's theory and, time permitting, discover ongoing research and future directions in this field of mathematics.