The Punisher for Congress (in Ecuador)

We should have candidates like this in the U.S. I'd like to vote for Robin Hood and a masked crime fighter.

Shimura-Taniyama-Weil Conjecture

There's an excellent article by Henri Darmon which was published in 1999 in the Notices of the American Mathematical Society. The article reports the announcement of the proof of the full Shimura-Taniyama-Weil conjecture, but I post it here because it is an excellent overview of the sort of mathematics I am studying. ("Diamond" in the article is my supervisor, Fred Diamond.) I think it's quite readable, though that may just be because I have been studying these things for years.

My work concerns Serre's conjecture, which isn't mentioned explicitly in the article, but is what he's referring to when he talks about establishing connections between automorphic forms and Galois representations (in the Langlands Program section). Basically, the idea is that the Galois representations also have a sequence of numbers associated to them, and you want to be able to determine precisely for which Galois representations there exists a modular form such that the sequence of numbers Darmon describes for the modular form matches the sequence associated to the given Galois representation.

The proof of Serre's original conjecture is pretty much complete by now. Here's a layman's notice from 2005 on Khare's proof. My thesis will (hopefully) be a formulation of the conjecture (in particular, the so-called "weight part" of the conjecture) over imaginary quadratic fields along the lines of the formulation over totally real fields by my supervisor and two others (at conferences I've heard it referred to as the "BDJ conjecture" and the "Buzzard-Diamond-Jarvis paper" even though it hasn't actually been published yet), and then to also provide some evidence that the conjecture is the correct one.

成语 (chéng yǔ)

One of the 成语 we've learned is 四面楚歌, where
四 = sì = four
面 = mìan = side
楚 = chǔ = country/area
歌 = gē = song

There's a story that goes along with it, which I believe Chunyan said comes from some historical occasion. There were these two regions at war and the army of one had fought its way into the region of the other, but had gone too deep too quickly. (I wouldn't be surprised if this is used as a Go proverb.) The invading army was surrounded and their opponents (if I have the story correct -- we were a bit confused about this) started singing a song from the homeland of the invaders to demoralize them.

The expression is used to mean that you're "facing hostility on all sides". I remember it by a misreading of the literal translation: there's country music on all sides.