Recent Posts

Combatting bitrot

August 27, 2023

This is just a small note that I've changed the backend organization of this website around. You might notice old links are likely dead, for which I'm sorry. Whereas previously it was built with Jekyll, we're now using Hugo. Jekyll itself, which is built on Ruby, has been pretty good to me. I was able to do the design work on this website over the course of maybe about a week in summer 2019; writing blog posts in Markdown and now Org mode was simple.

Listening to Chaos

July 7, 2023

I spent the past four months based in Montréal for a semester program in Geometric Group Theory. During that time, Abdul Zalloum, Mariam Al-Hawaj and Giulio Tiozzo organized a special session at the annual meeting of the Canadian Mathematical Society and invited me to give a talk. The purpose of this post is to recap a couple of cool things I learned at the special session and to share an application of that stuff, a "

The Seamstress Event Loop in Zig

June 21, 2023

I've been working on a program called seamstress for the past couple of months. I think it's in a pretty good spot, even if it's early days. The program is heavily inspired by monome's norns, specifically its matron program, which embeds the Lua programming language to speak with monome's grid and arc controllers, MIDI, OSC, a screen, the norns' keys and encoders, and so forth. One big difference between seamstress and matron is, besides the fact that seamstress is designed for desktops/laptops rather than a purpose-built device, is that seamstress is written in Zig, a young C-like programming language.

Failing to Prove a Matroid Algorithm

May 7, 2023

I have a new paper up! It's about "one-endedness" and "semistability at infinity" of certain outer automorphism groups of free products; more about this almost certainly soon. What I want to talk about today is an algorithmic process I wanted to include in the paper but was unable to provide a proof of its correctness. The statement that I needed was that a certain collection of subforests of a graph (with special vertices—this is a graph of groups) forms what's called a matroid.

SyncTeX With Kitty

January 21, 2023

I’m a big fan of the terminal. I do almost all of my writing inside kitty, a terminal program, running a text-editor called neovim. As a mathematician, I’m usually writing LaTeX. One of the nice features of LaTeX is called “SyncTeX”, which allows a PDF generated by LaTeX to remember a bit about the source files that compiled it, so that you can jump from the PDF to the source code.

Learning to Run

December 25, 2022

Happy holidays! One of my goals for this past year was to record and release an album of music, totalling at least thirty minutes and ten tracks. I accomplished that goal! You can listen to and buy the album on Bandcamp and it is also available on most streaming platforms as well. I wrote about the album on Lines, a forum centered around music, computers and synthesis that I am a moderator of.

A Polish Milnor Schwarz Lemma

November 6, 2022

Perhaps the fundamental observation in geometric group theory, the Milnor–Schwarz lemma (an independent discovery of both Milnor and Schwarz, sometimes romanized Švarc, hence sometimes titled with the names transposed) says, very roughly, that if you have a group of symmetries of a geometric object that satisfies certain properties, then the group of symmetries may be regarded as a geometric object in its own right and if you “squint,” the geometry of the group and the object are the same.

Anderson's Trick

October 30, 2022

This week I had the pleasure of attending a seminar talk Nick Vlamis gave at CUNY, where he taught us a very pretty trick due to Anderson which one can use, as Anderson did, to prove that the groups of orientation-preserving homeomorphisms of the $2$ - and $3$ -spheres are simple. The purpose of this post is to reproduce Nick’s exposition of the trick. Suppose $g$ is a homeomorphism of a surface $S$ (for me a surface is a Hausdorff and second countable $2$ -manifold) whose support


October 13, 2022

Perhaps my main non-mathematical joy is music. I took piano lessons from when I was eight through the end of college, and this year I wrote and recorded an album of pop songs, about which more certainly sometime soon. Anyway, I lost most of my weekend to a musical math problem. The purpose of this post is to explain the problem and the solution, partly so that I will have fewer steps to retrace, should I need to in the future.

Another Mathematical Postcard

September 3, 2022

I submitted another “mathematical postcard” (see below) to the Nearly Carbon Neutral Geometric Topology conference. The purpose of this post is to offer a little more context and explanation for it. For some reason I end up discussing things like ends of groups and finiteness properties rather than sticking strictly to Bieri–Eckmann duality. Here is the postcard: The text reads as follows: A space $\tilde X$ is $n$ -connected at infinity if for all $K \subset \tilde X$ compact, there exists $C \subset K$ compact such that every map $S^n \to \tilde X - K$ is nullhomotopic in $\tilde X - C$ .