6/19

1: TeX/Midterm
2: Today

1: The TeX workshop thing helped a lot. I know how to do slides now anyway, so I'll probably work on that next week for my midterm presentation (that I haven't yet picked a day for--should do that tomorrow I guess). I'm not sure how result-oriented (or introductory/broad) our presentation needs to be. Half the people have seen a lot of the introduction stuff and half haven't. But, thirty minutes gives you a lot of time to talk, so it's probably about half/half? Anyway, I've got plenty of introduction and not a lot of results, but I guess I could show some graphs from Matlab? Also, I'm not sure what part of my "research" I should emphasize, local or infinite. Or how one applies to the other. I haven't really proved much for either, and I haven't really found any sources for local dimension as I've defined it for myself.

2: Besides the workshop, today the only thing I really did was read (and read and read). Prof Day suggested a inf-dim space I could look at and I tried doing some things with it and didn't really get anywhere. Infinity is confusing (seriously). I almost finished rereading my topology textbook from 426. I don't think we ever went over "Jordan Curve Theorem" and homology in class though (at least I don't remember this stuff), so I'm not sure if I should bother finishing these sections (but I see stuff about homology a lot when I'm looking for sources, so maybe I should?). That kind of helped as a review of topologies and bases and open/closed and products and such. I also went back to look at the Conley Index stuff too which makes a little more sense I guess. I guess you use it to help identify and prove the existence of fixed and periodic points and other "invariant objects" in your set, but I'm not sure how I would use it (for this project), but in Prof Day's thesis, she talks about some sort of projection into a finite space that preserves certain properties of infinite dimensional objects. I don't know if I should look at that? Maybe not yet. I really didn't do anything with Matlab today--looked at some things but didn't really change or fix anything.