Local and global well-posedness for the generalized Parabolic Anderson Model

I will present some tools used in the study of the generalized Parabolic Anderson Model (gPAM) in the singular regime. After quickly introducing the multi-index approach to gPAM and the model used, I will explain how to obtain local well-posedness in the full subcritical regime. I will then detail some recent global well-posedness results by Ajay Chandra, Guilherme de Lima Feltes and Hendrik Weber and our attempts to sharpen them. This talk is based on an ongoing internship project with Felix Otto and Rhys Steele.