The Cornell REU
The Projects: Each year, there are (at least--there appear to be three this year) 3 separate research projects, one ran by Robert Strichartz on analysis on fractals, and a few rotating ones. I worked in complex dynamics with John Hubbard on one of the rotating projects. Hubbard is a really great person and mathematician, but he's not going to do the REU again in the near future. Strichartz is a harmonic analyst, and the REU work is part of a grand project of his to develop a theory of harmonic analysis on fractals (defining laplacians, harmonic functions, orthogonal polynomials, etc., by using a definition of laplacian, equivalent in the case of R^n to the usual one, involving some sort of average of the values of nearby points to the one at which you're evaluating the function's laplacian). The undergraduate participants in the REU work out specific cases which hopefully will lead to insights on what the general theory should be. Typical examples were looking at functions on studied fractals which are sent to zero by laplacian^n, n>1, determining how to define laplacians and then determining what functions are harmonic on fractals for which the theory hasn't been worked out, and finding sets of orthogonal functions on fractals for which laplacian and harmonic functions had been worked out (Aside: the nice example for the theory is the Sierpinski gasket, and some of the work when I was there dealt with the Sierpinski carpet, which isn't as nice from this perspective, and a fractal whose early iterates are diamonds that look like the Mitsubishi logo). Anyhow, the way that people were studying these was to look at increasingly high levels in the step-by-step construction of the various fractals. Since that gets complicated quickly, it was all done by computer. Thus, a high proportion of the work was very computational, and generally messy, and some students were unhappy with that. I don't recognize the people running the two other projects this year, although I note that dynamical systems is one of the department's strengths (geometry may be as well--I know their chair is a well-known Euclidean geometer).

The Program: In general, the program is nice. There are twice-weekly lectures by faculty, which are interesting, but superfluous to the program. Each Friday, there is a "jam session" where all groups get together to present their research. It mainly consisted of my research advisor telling the people in the other group that they weren't making sense. I and the others working in the same group met daily for 1-2.5 hours with our advisor to discuss the work and for him to talk about background stuff and whatever else we collectively decided was interesting, and he was very involved in those sessions. The other group's meetings were not as long, and I get the impression that the advisor may not have been as involved (they were early in the morning, so I only attended one and can't say much more than that). There was a decent camaraderie within and between groups, and pretty much everybody was well-prepared and knew what they were doing. Everyone went to Toronto towards the end for the MAA Mathfest Conference, which was an enjoyable trip, even though the attendence for the student paper sessions was minimal. However, at the conclusion of the program, there were presentations in the math department which were attended by about 4 or 5 professors and about 8 grad students and postdocs in the field of dynamical systems. Some people at Stony Brook were interested in the work we were doing, and a trip there was discussed, but it never happened.

The Place: Ithaca's a pretty place, which is to say that it's in the middle of nowhere. It's hard to get around without a car or bicycle (though the bus system isn't bad), and it's even a fair walk to leave campus. There is almost no theatre, opera, or classical music there in the summer, though there is a decent on-campus theatre, the Cornell Cinema (very similar in its offerings to the Brattle). The only decent bookstores (and most other sorts of stores) are in downtown Ithaca (which is about a half-hour run away, as I once discovered by mistake, or about 15 minutes by bus). The Cornell library is excellent, at about 6 or 7 million volumes, with good fiction (especially sci-fi collections). The only way to get to Ithaca is to pay through your nose to fly into Ithaca, or fly/take a train into Syracuse and go on a shuttle (or take the bus, which is about $80), so that will eat up a good chunk of the $3000 stipend if you can't arrange a more economical means of transportation. The dorms on campus, in which I stayed, were expensive ($1000 for the summer) and very mediocre. An apartment nearby would be better, but there is some advantage to being near those with whom you're working--it might not be a bad idea to take the coordinator's suggestion and pool together with your fellow participants to rent a house or something like that for the 8 weeks. The meal plan is expensive but very good (their dining halls put Harvard's to shame), though I usually "cooked" for myself to save money.

I enjoyed my time there, and managed to survive just fine with the culturally bleak surroundings (after all, while it would be nice to have some available, one goes to the program to do math, not to see plays), but your experience will depend heavily on which professor you're working with.
--David Farris (farris@fas)