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:

• Notes on the Du Bois complexes for quotients
• Notes on G-equivariant cubical hyperresolutions