PhD Thesis Defense: "Hodge theoretic completion of period maps"

Abstract: After Griffiths’s fundamental works on the theory of periods, completions of period maps coming from algebraic geometry have been studied for decades. There are many well-known results for period domains of classical types on which the Griffiths Transversality condition is trivial, for example, Baily-Borel and Ash-Mumford-Rapoport-Tai. However, completing period maps of non-classical types remains as a widely open field.

In this talk, I will briefly review the general literature as well as Kato-Usui’s recent work which aims at giving a toroidal-style compactification generalizing Mumford's results to period maps of non-classical types. I will analyze some key properties and obstructions of Kato-Usui’s construction, and then introduce an application to a non-classical motivic variation with 2 parameters worked out by the speaker. Some related works and future directions will also be discussed if time permits.

Host: Matt Kerr