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.

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.

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.

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.

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.

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

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.

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 $\tilde X - C$ .

this is the eigth and final post in a series on Katie Mann and Kasra Rafi’s paper Large-scale geometry of big mapping class groups. The purpose of this post is to tie up a loose end. In the third post, we observed that if $\operatorname{Map}(\Sigma)$ is to be coarsely bounded, then any finite, $\operatorname{Map}(\Sigma)$ -invariant set of ends has cardinality at most two, but then went on to discuss the case of self-similarity, where such a set has cardinality one.

This is the seventh post in a series on Katie Mann and Kasra Rafi’s paper Large-scale geometry of big mapping class groups. The purpose of this post is to show that the following surface from the first post has mapping class group generated by a coarsely bounded set. We showed in the fourth post that $\Sigma$ has locally coarsely bounded mapping class group, hence by results of the previous post it suffices to show that $U_S$ for $S$ some finite-type subsurface, together with a finite set of elements $\phi_i$ , generates $\operatorname{Map}(\Sigma)$ .