Some good news school-wise. I got a 10 week research fellowship for the summer. We will be trying to answer the question "Which graphs are determined by their spectrum?" I will attempt to explain it in layman's terms, mainly because it might be funny.

Basically, in a branch of math called combinatorics, we study something called graph theory. These graphs are different than those old "x vs y" plot graphs you remember from middle/high school. Actually, they may seem a little easier to understand. In graph theory, graphs are just a set of points, some of which are connected, and some of which are not. So basically, a bunch of dots with lines connecting some of them. Now, given one of these graphs, we can make a matrix called the adjacency matrix, which is actually just a matrix like you may have seen in algebra 2 or linear algebra. The adjacency matrix tells you, for each dot, which other dots it's connected to (hence adjacency). Now, if you're still with me, in linear algebra you learn that, for a given square matrix, we can find a set of something called eigenvalues. I don't suppose I should explain what those are, but rest assured that given a matrix it's well known how to find its eigenvalues. If the matrix is

*n*x

*n*, meaning it has n columns, each with

*n*entries, then it will have

*n*eigenvalues. This set of

*n*eigenvalues is called the spectrum of the matrix. So the question is this: if you tell me a spectrum, can I tell you what graph it came from, or could there be two graphs that have the same spectrum? So we'll be trying to determine which graphs have which answer.

So that's mostly it. I don't think it should be too difficult to understand the way I wrote that, except maybe that eigenvalue part. Probably what you'd really like me to explain is why anyone would care. I'm afraid that's a more difficult question. At any rate, I'm looking forward to it, and maybe I'll keep you all updated on our progress.

For anyone interested, here's my actual project proposal.

One last math related thing. I guess the math department has an intramural indoor soccer team. So I joined it. We've played one game. It was pretty close, 5-6, but we lost. Now, when I say it was pretty close, I mean that both teams played pretty bad, but it was still fun. I get the impression some of our players are a lot better than they seemed in that game. But then, we are all math nerds (and one geologist) so maybe not. Anyway we have 3 more games, and I think it'll be fun. Any team you can play a really bad game for and still have a good time is a good team, I think.

Well, I think those egg rolls are ready, so I am off.

*are we fading?*

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