An introduction to derived algebraic geometry

Notes for a summer school in KIAS, June 2023. Minor revisions March 2024.

A modern introduction to algebraic stacks

An introduction to stacks using the language of ∞-categories.

Cohomological intersection theory

A cohomological approach to intersection theory on schemes and stacks.

Descent in algebraic K-theory (SS 2020)

An introduction to ∞-categories and a modern account of perfect complexes and higher algebraic K-theory following Thomason–Trobaugh.

Algebraic K-theory and intersection theory (WS 2019/20)

An introduction to algebraic K-theory and Chow rings of smooth algebraic varieties.

The Grothendieck–Riemann–Roch theorem (SS 2018)

Lectures on the Grothendieck–Riemann–Roch theorem for derived schemes.

Descent in algebraic K-theory (WS 2017/18)

An overview of some descent results in the algebraic K-theory of derived schemes.