Diners were Tom Duchamp, Dave Frazzini, Robin Graham, Brian Hopkins, Doug Lind, Paul Tseng, Selim Tuncel, and Ginger Warfield.

Dave launched us in our first direction by commenting that a notable feature to his current existence is its dissimilarity to all previous phases of his educational career--and hence to his expectations. Specifically, after a lifetime of neatly packaged problems that were due at a specific time and done with thereafter, he is now in the midst of a relatively featureless expanse, with theorems here, lemmas there, and no sense of when the next mathematically significant event will occur. While he digested implications of the resulting chorus of "It gets worse from here on!", we got to work on the underlying issue, which is one of communication. Several major areas came up in which graduate students would profit from knowing more, but it is not clear how to convey it. One is what it is like to be a researcher; another is how to recognize research directions that are of value. One helpful item is very small, very specialized seminars in which a professor works closely with several students in his field (to accomplish this, it is helpful if there ARE several graduate students in his field--Brian's problem.) There exist several such seminars, but more would be helpful. Another traditional mode for getting a feeling for the shape of mathematics is to attend colloquia regularly, hanging onto the knowledge that mixed in with the inevitable ones that go zinging straight over one's head there will be others that provide a major insight into a new field, or feeling for how some branch of mathematics operates. Tom still remembers a Terry Rockafeller colloquium from his graduate school days that gave him a whole new perspective. This kind of attendance is not the current culture of the department, but could presumably be worked on.

Another format for communicating things that don't fit anywhere in the sit-down-and-let-me-inform-you category is casual social occasions, of which there is currently a dearth. The pre-season party at the Waterfront Activities Center is great, and there is hope of an end-of-the-year picnic such as we used to have for many years, but that leaves a lot of space between. The Computer Science has a regular Friday session of putting their feet up and drinking beer, which is a nice, relaxed ambience for non-specific communication. We used to have "strong tea" (=sherry parties) weekly back when the lounge was on the fifth floor, but that died out. Selim made some comments which could easily be construed as volunteering to work on reviving some variant on that tradition--basically setting up some predictable time and place where faculty and graduate students could hang out in a relaxed way without feeling obliged to be profound.

According to my notes, we also floated the idea of an event in the first year for students to learn to give talks and to learn what it feels like to do research. AN event? I think I garbled that one. Another of the communication issues led us off in an interesting direction. It started off with "How are you supposed to know when you have enough results to constitute a thesis?" Some nice crisp criteria went by ("enough to constitute two publishable papers") and some wild examples (Doug swears to a seven and a half page accepted thesis--not, alas, his own!) The place where we diverged was the appropriacy of collaborative research between a student and his/her thesis advisor. That one carries lots of interesting issues, with the obvious extremes being that collaboration can mask lack of ability on the part of the student and that rejecting collaboration can block off some darned good research.

Another key question was posed by Robin: "What is the PFF supposed to be doing, anyway?" Expanding the acronym to its full Preparing Future Faculty led us neatly into the issue of what it is that faculty are supposed to be doing (aside from research.) One thing that has become extremely clear in recent years is that one of our obligations is to communicate with the outside world--not just outside of mathematics but all the way outside of academia. This is not always easy--dealing graciously with someone whose idea of a mathematician is someone who can really zip through the income tax form can be distinctly wearing--but it is absolutely essential. We even need to deal graciously with Jean Godden--especially Paul, who lives three doors from her!

The question of the future for which we are preparing our students also led into the issue of industry--what they like, which skills are marketable to them, and how we could improve our communications so as to make available to them the skills and techniques which we have available and which could serve many of their needs. Tom suggested that we need to educate industry to what their real needs are--an awesome thought!

We finished up with a bunch of suggestions for next dinner. One was a repetition of the previous dinner's request for more graduate students. OK,OK! Others took the form of things we didn't get around to discussing and felt were worth some thought (presumably fodder for discussion at the next such occasion): How should the credit issue be handled? (The current system of assigning credit hours to sundry bits and pieces to make the credit-hour accounts balance is getting a bit Byzantine.) How well is the system of potentially replacing one prelim with course work working? What is the impact of the 6-year drop-dead (I did NOT invent that terminology!) policy?