Du Bois singularities and the Minimal Model Program

Title: Du Bois singularities and the Minimal Model Program
Abstract: Singularities play a crucial role in the classification of algebraic varieties. They naturally arise on degenerations of smooth varieties and on birational models of higher-dimensional varieties. In this talk, I will survey key singularity classes through the lens of the Minimal Model Program, the standard framework for birational classification. In particular, I will discuss its connection with Du Bois singularities, an important class with extremely useful cohomological properties. If time allows, I will also introduce higher Du Bois singularities, a recent generalization motivated by developments in Hodge theory.