Welcome! My name is Dustin Clausen and I'm a mathematician at the University of Copenhagen. This is the website for a class I'm teaching on algebraic de Rham cohomology.
Lecture 1: de Rham cohomology of real manifolds
Lecture 2: Interlude on D(R)
Lecture 3: Interlude on sheaves with values in D(Z)
Lecture 4: de Rham cohomology of complex manifolds
Lecture 5: Grothendieck's theorem, part 1
Lecture 6: Grothendieck's theorem, part 2
Lecture 7: Kahler differentials, smooth maps, and the de Rham complex
Lecture 8: Derived quasi-coherent sheaves
Lecture 9: Globalization and Deligne's theorem on degeneration
Lecture 10: Deligne's theorem, part 2
Lecture 11: de Rham cohomology in characteristic p: pathological?
Lecture 12: Equivariant de Rham cohomology: set-up and definition
Lecture 13: Totaro's theorem on Hodge cohomology of classifying stacks
Lecture 14: Chern classes and Thom classes
Lecture 15: Cycle classes and deformation to the normal bundle
Lecture 16: Poincare duality