The research itself varies a lot; the students work in groups of two with four different professors. I found that there wasn't very much (mathematical) interaction with the other groups. Personally, I had a bad experience research-wise: my partner was a freshman and didn't know any topology at all going in to the program, so I had to do basically everything. I really didn't learn anything or get much research done. Other participants had better experiences, however. The projects were in differential geometry and topology.

The Tulane REU has eight students, with demographics standard for math circles. We live in doubles in a Tulane dorm with other random students who stick around for the center. (The dorm actually looks more like a motel, with all the doors opening to the outside, but I felt safe.) The dorm we were in had a rarely-used common room with comfy sofas and a cable TV; another dorm had a bigger common area with a pool table where people tended to sit around watching TV or movies. There is one drawback to the living arrangements -- there is no meal plan, so you have to cook for yourself. (There's a small kitchen in the dorm.) Luckily (for me), they open half of a cafeteria so you can get food from pizza hut or subway.

Tulane University is located in New Orleans, which is an absolutely wonderful city. You can take public transportation (streetcars) into the French Quarter, which is the heart of New Orleans with its gazillion small shops and pedestrian-friendly streets. You can wander down Bourbon Street; take in the legendary New Orleans jazz scene; have coffee and beignets (basically fluffy dough sprinkled with sugar) late at night; eat up pralines (candied pecans -- a New Orleans specialty) in the French Quarter; or sample the cajun and creole cooking in one of the most culinary cities in the U.S. A couple of people brought cars, so we could drive to the movie theater or take longer outings -- we took a camping trip all the way over to Florida. (Well, actually, when we got to Florida we encountered a hurricane, so we ended up spending the night in Alabama.)

Overall, I had a bad research experience, but I found the rest of the summer to be very fun. Things may have changed since then, but I would suggest going elsewhere if your main concern is your research experience. If on the other hand you just want to have a fun summer, Tulane is a great place to be. Please feel free to email me if you have any questions.