Hood Chatham

  • Massachusetts Institute of Technology
  • Department of Mathematics
  • Office 2-390A
  • hood@mit.edu

I am a fifth-year MIT math grad student working in algebraic topology. My advisor is Haynes Miller. I was an undergraduate at Berkeley.

Spectral Sequences

I am curating a collection of spectral sequence diagrams here, I hope they are useful to you. Some of them are pdfs made using my spectralsequences latex package and others are made using an interactive spectral sequence display and editor that I am developing. The source code for the interactive display is on github.

Ext over the Steenrod Algebra

I am working on a minimal resolver which you can find here. It's implemented in Rust and compiled to web assembly. You can find the source code at this gitub repository. They are displayed with my javascipt spectral sequence display. If you clone the repository and install rust, you can run a native binary of the code. It seems to be about 30% faster to run the code natively. Currently it can produce a resolution of an arbitrary finite dimensional or finitely presented Steenrod module over any sub Hopf algebra of the Steenrod algebra using either the Milnor or Adem basis. It also works for the complex motivic Steenrod algebra at p=2. The old C resolver can do unstable resolutions though it doesn't use the correct instability condition at odd primes. I believe that it's the fastest currently available resolver, and is certainly the most convenient. It is possible to save the output and interactively add differentials to it. For example, I made charts of the Adams spectral sequence for S(2) and the Adams spectral sequence for S(3) in this way.

The Adams Spectral Sequence for $\tmf_{(2)}$

Dexter Chua has documented the calculation of the Adams spectral sequence for $\tmf_{(2)}$ here. He used the Ext resolver to compute the $E_2$ page and products and to propagate differentials by the Leibniz rule.

Steenrod Calculator

In the process of creating the ext calculator, I had to implement the Adem and Milnor bases for the Steenrod algebra. This simple interface parses an arbitrary arithmetic expression using any mixture of Adem and Milnor monomials, addition, multiplication, and parentheses. It can output both into the Milnor basis and into the Adem basis. For simple use cases itis probably both faster and easier to use in than the Sage steenrod algebra implementation.

Papers

Talk Notes

Programming

I am a pretty good TeX programmer. My packages: