So I've finished my first week of summer research, which I began on Tuesday (as Easter Monday was a holiday). I am re-revisiting the spreading and covering numbers, those devilish little fiends from combinatorial commutative algebra that plagued me last summer. You can read about last summer's research here. I shall try to blog often about this summer's efforts as well.
This week was very much about settling in and trying to get my mind into a math research mode. I am starting earlier than I did last year, because I will be returning to school in late August. We professional year students have to start early to finish classes in time for student-teaching in November! Unfortunately, this means that I didn't get much of a break between the end of classes and starting research. I have tried to seize as much downtime as I could. Still, as far as summer jobs go, I won't complain about doing research. It's pretty choice.
I'm in the same office as I used last year, and you can see photographs in this blog post. I'm in the desk in which Aaron is sitting in those photos, as my former desk is still occupied by a sessional professor's things. Aaron, who is not in concurrent education, has also finished his math degree and is going on to graduate school here at Lakehead. He promises he will be getting a key to the office, however. Also, Rachael is returning to academic research starting next week, so it will soon feel like old times!
There is a new face in the office this year: Tim also has an NSERC grant to do some math research; he's a third year student who has switched to math from biology, and so far his project involves recurrence relations.
There is one material difference in the office this year: books. The math resource room is getting new carpet, so Tim and I spent some time this week removing all of the books from the metal bookcases, packing them in what boxes were available, and stacking those boxes in our office. We cannot reach the chalkboard any more; moreover, we ran out of boxes, so there are a lot of freestanding stacks right now. It's messy and musty and dusty and kind of cool, though I want my chalkboard back.
I didn't take any photos; I shall do that on Monday and update this post.
I shall not say too much about how my research is going right now, because there's not much to say. I'll be using Macaulay2 and SHARCNET again. So far we're looking at the orbits of vertices of my graphs; these are the equivalence classes created by the action of the symmetric group on the graph's vertex set. We hope to find some relationship between the orbits and the size of the maximum independent set and thereby find a way to compute the spreading number. Next week I'll be investigating this further.