The primary research interest of the author is Spectral Algebraic Geometry. This page also contains less recent, but more extensive, work on higher category theory, along with some early studynotes from various elementary textbooks. Please be advised that the majority of notes and documents presented here are unpolished, and in particular, not errorfree.

An exposé on stable
categories  Colimits and Kan extensions
 Euler chararacteristic
 Simplicial sets
 The fundamental groupoid
 Mapping spaces in higher category theory

The Thomason model structure on
𝕒 𝕥 
A comprehensive study of

Joins in
,𝕒 𝕥 , and Set𝕠 𝕡 
Properties of
 Enrichment in category theory
 Monoidal categories
 An outline for studying higher category theory
 Notes from Goldblatt's Topoi book
 Morphisms of schemes
 Properties of schemes
 Schemes II
 Schemes I
 Sheaves
 Algebraic Geometry: Homework
 Notes from Hartshorne
 Abelian Categories
 Category Theory: Homework
 Adjunctions
 Universal Arrows, Yoneda Lemma, Limits
 Natural Transforms, Products, Free Categories
 Modules of fractions, Primary decomposition
 Commutative Algebra: Homework
 Rings: Homework
 Rings and Algebras
 Linear Algebra
 Ideals, Modules, Tensor products
 Cellular Homology
 General Topology
 Fundamental Group, Singular Homology, Excision