Where are you going?

As if keeping up with the lectures were insufficient challenge, Michaelmas term is also the time when Part III’s have to think hard about if and where they are going to go for further studies. During the time I had responsibilities for Part III, this issue was a major headache.  I hope there are more resources, and better publicised now. 

Deal with the if first. The year is young but the first few weeks may well have brought previously held answers to the “if” question into doubt. In the face of uncertainty, one must still apply now. How to deal with this: there are several options. For most, the usual plan is go ahead and apply as if new doubts had not arisen, but apply to a broad range of places. For those who don’t feel the pressure of passing years, delaying applications until you have the results of Part III may be a reasonable strategy.  There are creative ways of spending an interim year.

Putting the “if” aside, the problem of “where” can be a daunting one. There is a cohort within Part III who will not have trouble with this.  For those expecting top distinctions the present arrangement whereby subject advisers offer advice is generally satisfactory. They will have sufficient friends in top schools world-wide to offer a such a student a sensible list of ten to choose from, six to go for.  For the rest, getting truly useful information is not straightforward.  Advisers’ knowledge of schools that might not be top rank in all subjects is not encyclopaedic. So how do you find out about these schools?

Cambridge has a great resource in this respect that Part III students are maddeningly slow to discover and take advantage of: their colleagues. Over half of Part III students come from other schools, and therefore have a very good idea of what it is like to study in those places, which faculty would make good supervisors, and (important) which to avoid. Similarly, the vast majority of the staff in CMS have spent time in other universities. I tried for over ten years to get a tidy database of contacts within CMS that can be searched by discipline or schools without success. Unfortunately, assembling tidy databases was never my strong point, and as far as I know it never happened.  Now that it is no longer me trying to do it, perhaps someone will have succeeded. I live in hope.

However, you all have tongues in your heads and sit next to colleagues in lectures. Those who come from elsewhere will know about the strengths of subjects and the faculty in their home university.  I did notice that the map was posted during the first week of term.  If the map and records were kept, that might be useful. Start talking.

Before you decide where to apply, you need also to have considered what makes a school a right one for you? Some desirable features are obvious ones; it wants to have a reasonable number of staff and PhD students in the area you want to work in. Less well known schools can nevertheless provide very effective launch-pads for a career.  It might be worth doing the research to find out what jobs their recent phd’s have moved on to.  

The problem of deciding which schools to apply to becomes very much more difficult when the decision requires a choice of PhD supervisor. Fortunately there are increasingly PhD options which involve a year of study before choosing a PhD supervisor. If not, take all possible steps to reduce the risk of finding yourself with a supervisor who, while she/he might be at the top of the field you want to work in, nevertheless turns out to be completely incompatible as a supervisor for you. Visit the school.  Meet and talk with the potential supervisor. (it is risky for her/him too - she/he probably is as anxious to have the chance to talk to you are you are to talk to her/him. Or should be.) Talk to her/his students. 

Some years ago, to give you a chance to meet and talk with students doing PhD’s elsewhere we started  inviting students from other universities to come and talk to us about their work (ok, it was my doing). Students, not faculty; this was important.  You will not necessarily get useful information asking a faculty member which of their colleagues make good supervisors. There are things colleagues cannot say about colleagues. Students can speak more freely. Take advantage of this opportunity (Thursday 2 Nov.). You need to know. You really need to know. See cautionary tale below.

————— story time.

I served for half a dozen years as PhD ombudsman in DPMMS. The experience I brought to the job was primarily that of having made most of the egregious errors myself.  In the choice of supervisor the error was a three star one.

I liked algebra, the representation theory stuff. I liked coalgebras and Hopf algebras even better.  I liked topology, simplicial complexes, homology and homotopy theory, although I was less enamoured of spectral sequences which were all the rage at the time. Therefore, algebraic topology was probably not going to work. Algebraic geometry had a very strong group with lots of students, but I wasn’t all that handy with commutative algebra (in my case it was all self-taught) and Riemann Roch seemed a bit of magic without mitigating intuition.  That left only one obvious choice of supervisor: Bertram Kostant. I read some of his recent papers; they had coalgebras in. I set about finding him. 

Eventually I tracked him down. We had a short discussion in his office, what was I interested in (coalgebras) what was my background (I told him), “fine, fine fine, we should be able to work together.” 

The common room was nearly adjacent to his office; I repaired there for a triumphal cup of tea. While a wisp of steam was still rising from it, one of his other grad students came in: “you didn’t just ask Kostant to be your supervisor did you?” she asked. "Yes", I had. “Don’t” she replied.

She was right. Kostant was by no means a bad supervisors; he had many very successful students.  I just was not one of them. I discovered during our first serious mathematical discussion that while he might count himself an algebraist, his intuition ran entirely along analytic lines, and analyticity and I had at that time no working relationship at all.  It was a disaster.  I hid.

It was not hard to hide at MIT, and Kostant was not a difficult man to hide from. He was not often in his office, and less often with his door open. He was a benign, absent minded man, and soon forgot I was his student, all of which suited me.  His other students occasionally reminded him, more for a laugh than any serious attempt to initiate a more effective supervisor-student relationship. I came in to work every day, and worked hard, just not on any agreed topic. I hung out with the topologists and went to their seminars. I was an honorary algebraic geometer; when that gang went off to Vermont for the weekend they took me along. I behaved exactly like a PhD student should, except that I never spoke to my supervisor

If it had come to my attention during my years as PhD ombudsman that one of our students was behaving that way, I would have sought the student out and kicked her/him around the block. It was a seriously stupid strategy.

I have wondered from time to time why I got away with it, whether MIT just had a very hands-off approach to graduate students. Possibly not. I was still obviously engaged with mathematics, and well integrated into both the topology and the algebraic geometry camps and the Powers that Be had informants.  Moreover I was not without contact with faculty. Every week I would take my morning tea down to Dan Kan’s office. We didn’t discuss mathematics as such, but we talked about doing mathematics. He was one who had only encouragement for a student who had decided that she had a better chance of solving a problem that she herself had come up with than one that someone else had set. Equally important, Ed Miller had a spectacularly helpful habit of wandering the halls in the afternoon, catching graduate students and asking “so what have you thinking about?”  Nor was it a short-answer question; it was a genuine invitation to trot out my most recent ideas.  It was exceedingly helpful. When you all get to be young faculty, please do the same.

Perhaps, with Dan and Ed keeping an eye on me thus I was not so short of supervision as I imagined. I certainly didn’t feel neglected. And eventually I got a thesis, although that is something of another story which you might hear some day.