Notes for a summer school in KIAS, June 2023. Minor revisions March 2024.
An introduction to stacks using the language of ∞-categories.
A cohomological approach to intersection theory on schemes and stacks.
An introduction to ∞-categories and a modern account of perfect complexes and higher algebraic K-theory following Thomason–Trobaugh.
An introduction to algebraic K-theory and Chow rings of smooth algebraic varieties.
Lectures on the Grothendieck–Riemann–Roch theorem for derived schemes.
An overview of some descent results in the algebraic K-theory of derived schemes.