Materials for some lectures I gave in the 2024 SCMS summer school at Fudan University. I am planning to improve and expand these notes, so please let me know if you spot any typos, or have any suggestions.
Lecture notes: Du Bois complexes and higher singularities
Handouts: Day 1: Introduction to rational and Du Bois singularities
Day 2: Introduction to the Du Bois complexes
Day 3: Survey of higher singularities
Here are some notes, mostly expository, where I make "+ε " improvements to some well-known results that interest me: