A reading course at HKUST on derived categories, Fourier–Mukai transforms, semiorthogonal decompositions, quotient stacks, and geometric invariant theory. The materials below are from three lectures given in the course.
Lecture 1: Foundations of Derived Categories and Fourier–Mukai Transform
Lecture 2: Semiorthogonal Decompositions and Exceptional Collections
Lecture 3: Quotient Stacks, Derived Categories and Birational Geometry
A student seminar following lectures by Dustin Clausen and Peter Scholze.
A student seminar on continuous K-theory, topological Hochschild homology, and related topics.