On the Completions of General Period Mappings

 Constructing completions of period mappings with significant geometric and Hodge-theoretical meaning is an important topic in Hodge theory and its applications. There are rich theories for the classical case in which the period domain is Hermitian symmetric. In this talk I will talk about recent breakthroughs in the non-classical settings, particularly the generalized toroidal completion in the sense of Ash--Mumford--Raport--Tai and Kato--Nakayama--Usui. Joint works with Colleen Robles and Jacob Tsimerman.