Brussels, January 2002


I walked from Stepney to Waterloo to take the train. Tower Bridge was closed, so I had to go via London Bridge instead. I bought a Big Issue to read but managed to leave it in the terminal while lunching on a bagel.

The train went a different way from usual, via Denmark Hill, Peckham Rye, and Catford, possibly because of big engineering works at the Shortlands junction.

There was a very striking sun corona in a cloud just before entering the tunnel. We were stopped for half an hour because of "illegal people" in the tunnel; they threatened us with going back to Ashford, but in the end we proceeded.

I was met by Philippe Cara and taken to my hotel. Then we went out to eat, and found a bar with good African food: he had west African (in peanut sauce), I had central African (in palm oil), and there was also Somalian (don't know).

After dinner, I wrote up what I had proved in the tunnel while the train was stuck: the determination of all graphs which are k-homogeneous but not (k-1)-homogeneous for k = 2, 3.


Woken by the noise of machinery - the building next door is being demolished, and work starts at 7am while it is still dark. Irritating to hear, but fascinating to watch, as I did for some time.

I got a bit wet on the way to the University; also overshot somewhat and had to backtrack. Seen on the way: a big crane tenderly lifting a baby crane onto the top of a building under construction.

During the day Philippe and I worked on independent generating sets and made some small progress in understanding them for the symmetric groups. Wrote it up back at the hotel. (It looked like another drenching but miraculously the sky cleared and there were little fluffy clouds and vapour trails.)

I now have a full complement of euro notes up to 100 euros and several coins.

Forebore to tell Philippe the joke Hester sent me: What do you call a Frenchman in sandals? Philippe Philippe!

Dinner at a Vietnamese restaurant: Hanoi soup followed by pork with fresh ginger; too much food!


I walked to the University, getting it right this time. Philippe was teaching so I read my email, after which it was time to go across Offa's Dyke to the other country for Alice's private defence.

We kept her for just a bit over an hour, and then agreed to proceed to the public defence (this is supposed to be done several weeks in advance, I believe!)

After lunch, Philippe and I worked some more, until he had to go to a meeting; I worked on my talk for tomorrow and then went home. On the way, I saw how to do the crucial missing step in the classification of minimax sets in symmetric groups.

In my room, I wrote out notes for my lecture and then went out for dinner. I decided to try my luck in town, it being my birthday.

I selected a pleasant-looking restaurant and went in. I was a bit puzzled by the fact that they seemed to be expecting me; they took my coat, brought up a chair, sat me down, and brought a plate of food. But I soon ascertained from the people at the same table that they were a group of Swedish librarians in Brussels in EU business. When I tried to make my excuses, the waiter hushed me up, so I stayed.

We had a great time. The two girls were from Umeå and the man from even further north, on the Arctic Circle. We got through three bottles of wine and then I invited them for a nightcap. We found a nice bar in the Grote Markt and chatted away some more, then called it a night about 11pm after swapping email addresses. Their hotel was very close, mine further away, but I had no trouble retracing my steps.


This morning there is a giant crane outside my window. Work started even earlier (which I didn't need!) so I got up and wrote up the proof of the theorem, as well as I understand it now: still a bit shaky at some points.

Because of the work, I got to breakfast rather early, to find that the bread and croissants hadn't come and the coffee was bitter.

My talk went well enough, and then Jean Doyen took me and a few others including Alice to lunch in the ULB staff club (a splendid fish and prawn salad).

Philippe and I, unsure what to do next, started on PSL(2,p), where Julius Whiston leaves unresolved the question of whether the largest independent generating set has size 3 or 4. According to the Atlas of Geometries, there are geometries for both PSL(2,11) and PL(2,19) corresponding to generating sets of four involutions. We wrote a GAP program to look for such a set in PSL(2,29) - not very efficient but it ran, so we left it going and went over for the public defence.

Alice did well, and it was a very nice occasion, followed by drinks and then dinner for about thirty people at a nearby restaurant. At 11pm I accepted a lift home.


They let me sleep until 6:30 this morning. While getting up, I saw that there is a gap in the proof, and indeed counterexamples: some of the generators may be double transpositions.

I worked on that for a bit, then set off to walk to the station to see how long it took. On getting there, I thought to take the Metro back, but the ticket machines were playing up and the queues too long. So I walked a back way to the university.

Not much time then before we had to go to Ghent, through traffic-jammed back streets, tunnels under Brussels, and then the highway crowded with speed-limited trucks overtaking one another,

A nice pair of talks along with mine - Leo Storme on maximal sets of MOLS from maximal partial spreads, and Hans Cuypers on a local characterisation of the antiflag graphs of projective spaces.

We went to the canonical bar and then to the Irish pub down town, and decided to eat there rather than the (no doubt much better) place Frank had chosen. And so home, a third latish night in a row after too much to eat and drink.


I'd set my alarm (having remembered to change the town to Brussels) and so, of course, slept fitfully, waking finally a few minutes before it went off. I dressed and packed, checked out, and walked through the nearly empty but well-lit streets to the station. Too early to check in so I bought some breakfast and some Belgian beer outside the terminal.

The train left on time and the trip was uneventful; burning across northern France at 300km/h, I watched the changing landscape, while pottering through Kent at 90mph or less I was more aware of the nearpoint (e.g. a field of seagulls). Evergreen trees danced berserk in the wind while the deciduous trees were virtually unaffected.