An observation I made a while ago while peeking over people's shoulders (with their consent, of course) is that even when they're writing TeX in a powerful text editor, like Emacs or Vim, most people don't really harness the extensive programmability of their text editor (especially MM¹). For instance …

Another 9 months have gone by without a blog post, and this time I don't even have lack of time as an excuse my lack of writing. This summer turned out to be quite different from what I had planned, which probably goes to show one shouldn't plan too far …

In the previous post, we proved Sullivan's shadow lemma, which gave us concrete estimates for special subsets of the boundary, namely shadows. Recall that the shadow of a ball of radius \(r\) based at \(y\), with the source at \(x\), denoted by \(\mathcal{O}_r(x, y)\), is the set …

In the previous post, we saw how to get an asymptotic count of orbit points under a lattice action, i.e. a finite covolume Fuchsian group. To do so, we needed the fact that the geodesic flow on the associated quotient was mixing with respect to the Liouville measure. That …

After 10 months of being unable to come up with anything interesting to post on the blog, I realized it might be a good idea use this blog to keep track of the math I've been working on. That way my blog can act as a public version of my …

One of the things a math major learns in their first proof based course is that one must prove existence of objects before going on to prove any properties about them. After a few years, this becomes almost second nature, and most pure mathematicians are wary of making claims about …