Latest Posts

• Post 17: A Taste of Enumerative Geometry

  In this post, I’ll talk about enumerative geometry. In particular, I’ll talk about the standard questions of interest and how one goes about solving them.

• Post 16: Overview of Infinity Categories

  In this post, I’ll give an overview of the theory of infinity categories. In particular, I won’t get into too many specifics. I will also start with some recollection of ordinary category theory, in case an interested reader has not seen it before.

• Post 15: Perverse Sheaves Finale

  In the final post of my perverse sheaves series, I will discuss some important examples and properties of perverse sheaves.

• Post 14: Perverse Sheaves Part 7

  In this post, I’ll define dimension and constructibility, so we can finally have a full definition of perverse sheaves with field coefficients. In the formalities section, I will also have a crash course on varieties.

• Post 13: Perverse Sheaves Part 6.5

  This post fills in some technical details left out from Part 6. If you are just reading these posts for the intuition, you don’t need to read this.

• Post 12: Perverse Sheaves Part 6

  In this post, I’ll discuss some necessary functors between (derived) categories of sheaves, and some important concepts, such as the dualizing complex.

• Post 11: Correction to Perverse Sheaves Part 4

  You don’t need to read this post if you read Part 4 after January 10 2024.

• Post 10: Perverse Sheaves Part 5

  In this post, I’ll discuss sheaves.

• Post 9: Perverse Sheaves Part 4

  In this post, I will discuss derived functors, the final algebraic ingredient we need to define perverse sheaves.

• Post 8: Correction to Perverse Sheaves Part 3

  You don’t need to read this post if you read Part 3 after January 5 2024.

• Post 7: Perverse Sheaves Part 3

  In this post, I’ll talk about derived categories, the kind of category needed to define perverse sheaves.

• Post 6: Perverse Sheaves Part 2.5

  In this post, I will discuss the formal definition of an abelian category. It isn’t necessary to read if you just want to follow the “intuition” parts of my perverse sheaves posts.

• Post 5: Perverse Sheaves Part 2

  In this post, I will discuss more on categories, abelian categories, chain complexes, and the homotopy category of an abelian category.

• Post 4: Perverse Sheaves Part 1

  In this post, I will give a very “high in the sky” overview of the subject of perverse sheaves. I won’t give many specifics - those will be for future posts.

• Post 3: Lean

  In this post I’m going to talk about the proof assistant Lean, what I’ve done with it, and what I hope to do with it.

• Post 2: Current Research

  In this post I’ll talk about my current research project.

• Post 1: Introduction

  Hi! This post is going to introduce myself and what I do.