Part 1 (10:30 ~ 11:45)
-Title: How to Research the Singularity?
-Abstract: Singularities are everywhere. It's not a common situation, so mathematicians try to understand it for their own purposes. In this talk, we present some ideas from singularity theory.
Part 2 (13:15 ~ 14:30)
-Title: Ideals and Spectrum
-Abstract: Algebraic geometry uses rings to understand geometry. Since the singularity is local, we study ideals of a local ring to understand the geometry of the singularity. Spectrum encodes the geometrical information of hypersurface singularities. We illustrate how to recover the information from (higher) multiplier ideals and Hodge ideals.