Math 264X: Algebraic Cobordism

This is the class webpage for my topics class at Harvard (Spring ’19). The goal is to give an overview of Levine-Morel’s algebraic cobordism via various perspectives (Levine.

  1. Lecture 1: overview
  2. Lecture 2: a primer to derived algebraic geometry I: affine derived schemes, tor-amplitude
  3. Lecture 3: a primer to derived algebraic geometry II: derived stacks, schemes, the cotangent complex
  4. Lecture 4: a primer to derived algebraic geometry III: quasi-smoothness, virtual dimension, derived pullbacks
  5. Lecture 5: Chow groups and the formalism of oriented Borel-Moore theories
  6. Lecture 6: the definition of derived algebraic cobordism

Detailed syllabus.