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 …

Last Wednesday, the conversation in my office veered towards the words we hated the most in math. Not surprisingly, the list included the usual suspects like normal, simple, and regular. It's probably the same reason that these words also make it to the top five of this MathOverflow post. These …