Other writing


The Clebsch cubic surface (left) and the Kummer quartic surface (right).

Etale cohomology

Here are some notes from a topics course of the same name:

  1. Introduction and Flat Morphisms
  2. Faithfully Flat Descent
  3. Unramified and Etale Morphisms
  4. Sheaves in the Etale Topology
  5. Local Notions in the Etale Topology
  6. Etale Cohomology
  7. Tate and Hodge Conjectures
  8. Tate and Artin Conjectures
  9. Zeta Functions and the Weil Conjectures
  10. Chow Motives

Noncommutative motives

These are lecture notes for a reading seminar with my adviser and another student:

Review of pure motives

  1. Cycles and Equivalence Relations
  2. The Category of Pure Motives
  3. The Standard Conjectures
  4. Finite Dimensionality
  5. Finite Dimensionality II

Noncommutative motives

  1. Introduction to DG Categories

Miscellaneous notes

Here are a variety of notes and and documents that I have written up (mostly for myself) over my time in graduate school. They vary in length and sophistication, and certainly contain many errors (always my own), so I can make no promises on their usefulness.

  1. The derived McKay correspondence in dimension two. This is a summary of a proof of the derived McKay correspondence, first proven by Kapranov and Vasserot. These notes also contain an introduction to equivariant derived categories (warning: still technically in progress, there are many things to fix and adjust).
  2. The Calabi conjecture and complex Monge-Ampere equations. This was a talk given as part of a topics course in several complex variables.
  3. Conjectures on Bridgeland stability for derived Fukaya categories. This is a presentation I gave for a topics course on Fukaya categories. My talk was on the conjectures of Joyce for stability conditions in symplectic topology.