This is a repository of notes I’ve made that people might find useful. Nothing here is original – I have tried as much as possible to give due references. Comments are welcomed.

Motivic/Étale Homotopy Theory

• On Po Hu’s Exotic Picard Element in Motivic Homotopy.
• Some notes on the Milnor Conjectures via Cobordism.
• Friedlander’s Proof of the Adams Conjecture.
• Morel’s Stable Connectivity Theorem.

Algebraic Topology

• May’s recognition principle out.
• The Atiyah-Segal completion theorem.

Algebraic Geometry

• Basics of étale cohomology.
•  On the degree-genus without cohomology.
• Zariski’s main theorem.
• Bezout’s theorem on curves.
• Morphisms and generic point.

Higher Category Theory

• Quick overview on -categories.