Minhea Popa Simons Fellow Application

General goals: One of the recent themes in my research has been to apply the powerful but still somewhat mysterious mixed Hodge module theory developed by Morihiko Saito to concrete problems in algebraic geometry. There has been some success already (see for instance [PS2] and [PS3] in the past research statement), but this should only be the beginning; my main plan for the sabbatical year is to pursue further applications to families of varieties, vanishing theorems, and singularities. In the reverse direction, there are constructions and statements that only came to the surface due to Saito's theory (like the extension of multiplier ideals that I will mention a bit later), but where more standard tools from birational geometry might prove to be the key for substantial progress. All of this constitutes what I am mainly planning to pursue during my sabbatical year. University of Michigan and Stony Brook are ideal places for collaborations that will lead to such developments, as I will explain in more detail below.