An important problem in Hodge theory and its application to the study of moduli is to generalize the Satake-Baily-Borel compactification and Borel’s extension theorem to arbitrary period mappings. I will outline some of the difficulties that arise, and explain how the problem can be reduced to an extension problem (a la Ohsawa-Takegoshi, but without the need for bounds on the L2 norms). If you wish to join by Zoom, please contact Haohua Deng [haohua.deng@duke.edu] who has generously agreed to facilitate remote attendance.
Department of Mathematics