Two trips to Canada, May and July 2009

Ottawa and Montréal | Banff

1. Ottawa and Montréal, May 2009

The purpose of the trip, squeezed in during the exam period, was to attend two conferences: the Ottawa Discrete Mathematics Days, a small two-day meeting organised by Mike Newman, who had been a post-doc in London a few years ago, and CanaDAM, a huge four-day conference in Montréal. The exam for the course I taught this year was sat while I was away, and on return I would be faced with nearly a hundred and forty scripts, with just three and a half days to mark them.

21 May

I'm not at all prepared for this trip. I realised, on the tube to the airport, that I had no Canadian currency and no label for my bag. All the trains came expeditiously and (given that I had already checked in) I was, as usual, at the airport far too early.

A sunny day with elder and broom in full flower and luxuriant vegetation.

At Heathrow, no need to queue since I only had hand baggage; the queues for the bag drop seemed as long and slow-moving as normal check-in queues. The passage through immigration and security seemed even more trying than usual. I was asked to take everything out of my pockets and remove my belt (the trousers I was wearing don't stay up without it) and even got into an argument about whether the white toy is a laptop. It wasn't clear whether we had to go through the shoe check or not: some exits from the X-ray machines led to it, others didn't.

No luggage labels at any of the Smiths' at the airport. Of the two before security, each tried to send me to the other. The one past security only had books, so I did buy one (having, of course, left behind the one book I had bought for the journey).

I sat down to wait. Fortunately someone left a Telegraph on the seat beside me, so I picked it up and read it. It also had some puzzles (the regular and quick crossword and the Telegraph Toughie, a couple of sudoku, a killer sudoku, a codeword) which kept me going until halfway across the Atlantic.

Boarding started after a short delay, and we pushed back right on time. But some further unexplained delay in starting the engines meant it was half an hour before we were airborne. The man in the window seat beside me introduced himself as a dentist who had studied in Manchester and now lives in Canada, going to Montréal for his son's graduation. He kept the shutters down for almost the whole flight.

When I had done the puzzles, I listened to music for a while (the Band, Motown classics, and Sonny Boy Williamson), and then tried to find where we were, but was told "flight data unavailable". Clearly only a local problem, since other people were watching it.

We landed about ten minutes late, and there was a further delay. First we were told that we would park off-terminal and be taken to the terminal in buses. Then they changed that: we went to a gate in the domestic terminal and were taken by buses from there (directly off the plane). By great good fortune I was at the back of the plane, the end which deplaned first, and got through immigration and customs quickly. (The immigration officer was a bit fierce but the customs man very good-humoured.) Outside I asked someone for the bus stop for the transit bus to the station, and found I was almost at it and the bus came almost immediately.

The trip was a bit nail-biting, since there was a lot of rush-hour traffic and some very long-period traffic lights. As the bus pulled up, there was a train pulling in to the station. I assumed it was the one I wanted, but went to the ticket office anyway; the man assured me that the Ottawa train was next, five minutes later, and sold me a ticket, even giving me a discount for being a Senior! So I caught it with plenty of time.

We were off, through the outskirts of Montréal, and across what may have been the Thousand Islands, lots of fast-flowing channels breaking up the land. Then the country, first dead flat cultivation (with hills in the distance), then forest, then what seemed to be pasture but there were no animals in sight. Little towns had churches with elaborate spires. At a level crossing coming into one town, firemen were standing around a blackened and soaked car, where they had presumably just put out a fire. The sun shone brightly at first, but then sank into some lovely cirrus clouds. As we came suddenly into Ottawa station, it was just setting.

Ottawa station

The station seems to be cut off from anywhere by huge roads. So I didn't even try to walk, but took a taxi. The first half of the journey again involved getting round huge traffic interchanges with slow traffic lights, but once we were on the way, it was quite quick. I got my hotel key, went to my room, and went to bed and slept.

22 May

I woke early, but had no trouble getting back to sleep until nearly six, when it started getting light. So I got up, took a bath, and went down to breakfast.

It was a morning of several discoveries. First, I had come without the second pair of trousers that I had intended to pack (and was fairly sure I had done so), so I have only the ones I travelled in to last me a week. Plenty of shirts, though.

Second one came when I tried to walk down the stairs to breakfast. The stairs ended in an alarmed door. So I walked back up to the second floor (North American style), and took the elevator down. I got in and fumbled for the right button (which happens to be L), and was helped out by a German couple who just got on. The door closed and the elevator moved, and when it stopped we got out, to discover that it had taken us to the fourth floor! So we jumped back on (along with a lot of other people) and tried again.

The breakfast room opens at 6:30. It was almost deserted at 7 but filled very rapidly, mostly with elderly German couples (no idea why). The buffet was only slightly more expensive than having juice, coffee and one breakfast dish from the menu, so I went for that; really worth it.

Back in my room, third discovery was a pleasant one. I had brought an adapter but not a transformer. So I was delighted to find, in the small print on the white toy's power lead, that it can cope with 110 volts at 60 cps. I just plugged it in, and away it went. The hotel has free internet access; you can even take your choice of wireless, a high-speed cable, or surfing the web on the television (using the handset as a keyboard). So I was able to read my email, check out the Save LMS blog, and bring the CSG web page up to date.

It was time to set off, but I didn't really know the way, and ended up going by a rather indirect route. I arrived just after 9, the official starting time (for registration and coffee). The registration consisted simply of picking up a name badge from the desk in the front of the lecture room.

Many old friends were there beside Robert and Mike, including the girl who won the competition at the IPM conference in Tehran in 2003 to find out the invited speakers' middle names (she simply asked us all!), and people like Luis Goddyn whom I met in Burnaby when I visited Dugald there.

It was a day of very nice talks; not a bad one among them, and a great deal of variety. The three main talks were by Ron Canfield (in two parts, the first on the problem of whether the Stirling numbers of the second kind can repeat their maximum value (for given n), the second, a curious thing about the number of non-negative integer matrices with constant row and column sums, involving giving an exact formula, an approximation, and a confidence interval (whatever that means!); by Patric Östergård, on the "Russian dolls" method for clique search problems; and by Heather Jordan, on generalisations of Skolem sequences and their use in constructing cyclic cycle systems(!). The contributed talks were all good too. It is invidious to pick one out, but I have to mention Alois Panholzer, who gave a lovely talk about his very detailed analysis of the asymptotics for the parking problem.

For lunch we went to a restaurant on campus but found (as expected) that it was full, so we went on to a nice pub, the Royal Oak, just off campus. It was warm enough to sit outside. I had a pint of ale from a Toronto microbrewery (and still didn't fall asleep in the afternoon) and a California chicken club sandwich (the first word means "with avocado").

After the talks, there was a reception in the lounge of the Maths department. Nice light food (actually all I needed after a big lunch), no alcohol (supposedly by regulation, although it was wryly remarked that there is an alchol-fuelled Christmas party in that room every year). I talked to several people, especially Robert and Rod Canfield. Robert had been asking Rod about something which will go in our survey paper, but we talked a lot about more general things.

Several people asked me if I have been to Ottawa before. I think I have, but am not completely sure! (I am old enough that I suppose this is allowed). If so, it was for a very short visit a long time ago. I have a faint recollection that I was visiting Mike Atkinson, which would probably narrow it down.

After a while, I made my excuses and left. I was a bit tired, but mainly I wanted to explore a better way of walking from the hotel to the conference. I found a tunnel under the busy road (this involved a bit of a backtrack search, but it comes up very near the building where the conference is), crossed the canal on a footbridge, and walked down the left bank towards the centre of the city. This was a bit difficult, because of obstructions, some to do with a marathon coming up shortly which will finish here, and some caused by building works. But eventually I found my way to the spectacular flight of eight huge locks which take the canal down to the river. The sun was getting low, and there was a lovely light over everything. Two people came under a bridge on the other side, casting huge wavering shadows, but I didn't get my camera out quickly enough.

Rideau Canal

I walked down to the bottom, and crossed over the bottom lock and went up the other side. I found I would have had to follow the two people I saw earlier on a very narrow ledge under the bridge, so I crossed back over the top lock and up onto the road, and crossed back on the bridge. Then I found a way down to the other towpath, walked down to the next bridge, where a circular staircase took me up and a short walk brought me back to the hotel as the sun was setting.

I read my email again, wrote up my diary, looked over my notes for the next day (I am the first speaker), and then it was bedtime.


23 May

In the night I woke up with a burning throat. I wasn't sure whether it was a cold coming on or just the effect of the stale air-conditioned air of the hotel. But by morning it was clearly the former.

I had a bath, and did a sudoku while soaking - in fact it was what is called an "engdoku" in the student paper, using Greek letters instead of numbers. This makes it much harder: looking for where to place an alpha is OK, but figuring out what is missing in a row is quite challenging. It mut be much harder for people who are not mathematicians and don't know Greek; apart from anything else, having names for the letters helps thinking about them.

After breakfast I read my email, then set off for work, intending to look for vitamin C (as well as toothpaste) on the way. There was a Sears with a huge shopping centre behind it; some things were open, but when I finally found the "Shoppers Drugstore" it didn't open until 9. Escaping from the shopping centre was not easy either, and I found myself almost back at the hotel. So I started again and followed my chosen route, which worked very well. (Mike says that the reason that bridge is so long is that it used to go over the railway as well as the canal, but a town planner who didn't like trains replaced the railways with four-lane roads where people drive like maniacs, in the name of creating a proper capital city.) There was also a drugstore on campus, but it didn't open until 10.


On the way I did see some wildlife. Birds, like blackbirds or thrushes (they hopped; the males fought) but with chestnut breasts, probably American robins; and a black squirrel straight from Mirkwood.

My lecture was first. Mike gave me a stunningly generous introduction; if I had felt better, I might have done a better job of living up to the picture he painted. As usual I had a lot of material, but did finish on time, and got a lot of questions (and hopefully created some interest). I failed to answer Luis Goddyn's question, because my brain had gone to sleep. After coffee we had lectures from Robert and John Arhin (wearing a Bethnal Green T-shirt, introduced by Mike in a Hackney T-shirt) and Anthony Bonato, who posed a question about the Urysohn space which I think I can answer.

At lunchtime I felt more ill and not hungry, so went to the campus pharmacy. I got 1000mg vitamin C, which were a fraction of the price of the 500mg ones, also toothpaste and some stuff to help flu symptoms (which I hope I won't need). I found the local issue of the Epoch Times, which I remembered fondly from Auckland, and so picked up a copy. Definitely more anti-Chinese here than in Auckland.

Then I went back to the SITE building. Lots of people were eating Chinese food but I couldn't find where it came from and didn't feel strong enough to look very hard. So I took a vitamin C and sat and wrote my diary while I waited.

The afternoon lectures were a trial. By now my temperature was way up, and my throat sore, and most of the talks didn't catch my attention enough to overcome this. Bill Sands gave a nice talk about the following problem: Given n, find all minimal intervals such that the following is true: for any set of n cards, each with n non-negative real numbers summing to 1, there is an ordering of the cards such that the sum of the first number on the first card, the second number on the second card, ... lies in that interval. It is solved for n=3 and n=4; curiously, both cases fit the pattern that the intervals are [i/(n-1), 1+i/(n-1)] for i=0,1,...n-1. But he can't prove it in general.

I told Mike that I was not feeling up to a party, but he was very insistent. So I went back to my hotel room, took a painkiller, and lay down for a nap. I woke up at 7:30, the start time of the party, feeling sufficiently much better that I could face going. So I walked there (in 35 minutes, mostly along the canal). Runners were finishing a race on the other side, either 5km or 10km; they were going very slowly. I went round the bend in the canal, under the expressway bridge, across the next bridge, and found my way to Mike's place, crossing over what looked like the end of a canal basin.

I stayed for an hour and a quarter, talking mostly to an economist who works on transport planning policy, and to Robert. Then I decided to go; I wasn't feeling bad but was quite tired. I went back to the hotel a different way (straight up O'Connor Street and over the bridge) and went to bed.

24 May

I woke feeling a little better. I checked out the CanaDAM website: I am talking on Wednesday morning, and I was supposed to have booked accommodation myself. Never mind, I went to the student residences webpage (now re-branded as a hotel with soft-focus pictures) and made a booking, getting confirmation almost immediately.

Then I took another vitamin C and went down to breakfast.

The headline in the local paper described the competitors in the race as "runners, joggers, and shufflers". It was certainly the shufflers that I saw!

Conference poster

Back in my room, I wrote out some notes for Robert on what the distinguishing number (which Anthony Bonato talked about yesterday) has to do with our project. I decided that the base size of a wreath product in the product action is bounded above by the sum of the base size of the bottom group and the logarithm of the distinguishing number of the top group rounded up, where the base of the logarithms is the degree of the bottom group. I am sure this is not new, and pretty sure it is right for the automorphism groups of cubes.

Then I packed, took a painkiller, went downstairs, and checked out. I went outside. It was a glorious day: clear blue sky, dazzling sun, light cool breeze. I went over the road to Sears, to try to buy a pair of trousers, but they don't open until 11 on Sunday. So I went instead to the ByWard market.

The market seems to specialise in flowers and plants, especially hanging baskets which they had in great profusion, with a certain amount of gourmet food and some Canadian souvenirs. It has many cafes, so I had a coffee and sat for a while killing time.

ByWard market

Observations on Canadian French: "OK" is a very common expression; and rather than "courgette" they say "zuckini" if one stall is to be believed!

Then I went up York Stairs, dodged through the marathon runners, and went into the nice little Major's Hill Park overlooking the river and the canal locks with a fine view across the gap to the Parliament building. I read about Colonel By (who built the Rideau Canal and founded Ottawa).

I walked out of the park to the start of the Alexandra Bridge, a long and somewhat decrepit bridge leading over to Gatineau on the Quebec side of the river. Pedestrians were on an outside deck, the main lane of the bridge being used by runners, though by this stage they were not even shuffling, rather staggering. At my speed, which was a gentle tourist stroll on a sunny day, I was overtaking them. I felt this to be rather disgraceful: why enter a marathon if you can't do better than this? At the end of the bridge, two paramedics were treating a casualty, who was wrapped up in aluminium foil as if ready for the oven.

Marathon victim

Back along the canal, and into the Rideau Centre, where I went into Sears and bought a pair of stripy(!) trousers. They were 30% off in the sale, and a further 10% with their "scratch 'n' save" scheme. All of the toilets were broken, but I had another coffee before going on my way. Sad to say, it was so watery and tasteless that I couldn't drink it.

I bought a bus ticket and went across the road to wait for the bus to the station. There were Robert and Andrea Burgess also waiting for the bus, which was just as well since it was not at all clear which bus to catch (it didn't have a number) or where we had to get out. The bus routes have been disrupted by the marathon, it seems.

At the station, we bought tickets and lunch and I told Robert about my thoughts on distinguishing number. Then it was time to queue up to get the train.

I sat in the sunshine, eating my lunch and enjoying the view, as we rolled acrss Quebec. Little fluffy clouds rode in the sky, and yellow flowers shone in the meadows; a heron started from a stream, and a deer bounded across a meadow.

We arrived in Montréal (the train makes a very long detour and approaches the city from the east). We trooped after Robert looking for a metro station; finally some locals took pity on us and sent us back into the train station. It was quite easy from there, one change only, and a short walk to the residences.

First glitch, they didn't have my reservation in their printout, and I had forgotten to write down the booking confirmation number. But they found it on the computer eventually, and we went to our rooms on the 14th floor (of which you have to walk up to the 7th before catching the elevator).

We found that the rooms had not been cleaned: the floors unswept, no clean towels, beds not made. Robert phoned and complained, and they offered to change our rooms, which meant traipsing back down to reception to get new keys and then back up again.

The new room had a nicer feel to it, and was on the side with a view over the back of the city, with the Olympic stadium clearly visible. However, needless to say, the internet connection didn't work! So I had a rest, for longer than I had intended, and went out at about 8 for something to eat.


I walked towards Côte des Neiges. The sun was setting over the flat suburbs of Montréal and everything was bathed in golden light. I found a pizza restaurant and went in. It wasn't quick, but the pizza when it came was tasty, and they brought chili oil to help penetrate my bunged-up taste buds. Walking home, it was not quite dark; the street lights shone on new maple leaves.

Back in my room, I discovered a quirk of the lights. Two buttons by the door where light switches should be have no effect; the lights, in the middle of the room, are controlled by small chains.

Cote des Neiges

25 May

I had a quite dreadful night. My throat hurt, made worse by an irritating cough; my nose ran. The fridge kept switching on and off, and the room was unbearably hot. Finally I realised that the last two things were connected and fixable, so I got up, turned the fridge right down, and opened the window a bit. The view of the city lights was quite wonderful.

Then, having realised I can do a bit more on bases for wreath products, I wrote that up before going back to bed. The bound is attained if the bottom group is transitive on its bases and its degree is at least as large as the distinguishing number of the top group. I also realised that the bottom group being an IBIS group is not enough.

I dozed as the light came up, and went down to breakfast quite early. A low band of cloud at sunrise had turned int a speckling of clouds across the sky, and the air was quite chilly.

There were quite a few people I knew at breakfast, and others who were quite obviously mathematicians. But, sad to say, I'd lost my voice, and so was unable to be very sociable.

After breakfast I wandered over to the university, and found some other people heading that way; but they seemed to have not much more idea where to go than I did, and tried to get through the main building (which is quite impossible). But eventually we found our way there.

It turned out that, not only had I not reserved accommodation, but I had not registered either. Perhaps they emailed me about it and it went astray; certainly I have diligently searched through all my emails and not found anything relevant. Anyway, that was done without fuss, and I had time to try out the wireless network (it works flawlessly), and send the file to Robert (and even check that it compiled) before the opening.

After some speeches, Sylvie Corteel gave the first talk. Unfortunately, the projector was misaligned and the only way she could get the entire slide on was to make it very small; in addition, the screen flickered; and the microphone was feeding back. So I'm afraid she didn't get my full attention.

After that, I talked to David Richter about a nice idea connecting Euclidean nets with Tait colourings of cubic graphs, then went off to hear Christophe Reutenauer's talk, only to find it had been cancelled. So I logged on to the Save LMS blog and posted Alice Rogers' letter (having got her permission to do so), before going off to hear Karen Meagher and Mike Newman. After Karen's talk I was able to report what David Ellis had said in London last week, and my voice was almost audible (a good sign!)

I had noticed a little cafe in the building where the plenary talk had been, so headed there for lunch. They had a nice cheap hot meal: poached salmon with rice and vegetables. After lunch I talked to Robert about the base size for Hamming graphs with alphabet size 3 (the exact result is known; our simple bound is met a fixed proportion of the time and never off by more than one).

The afternoon plenary had the problems of the morning one, somewhat modified, and in particular the sound was dreadful. It was by a biologist, who lost her place rather dramatically once with the memorable line "That's not my talk!" and hunted through the files on her computer; finding nothing better, she continued with the one she was using.

After the break, I intended to go to a couple of talks, but with a few minutes to go I sat down in a comfortable armchair in full sunlight (through the plate glass) in the company of Richard Nowakowski, Cathy Baker, and Antony Bonato. That was the end. I stayed there until Antony left and Richard decided the sun was too hot (Cathy and I, both having lived in Brisbane, were perfectly happy).

So we moved to a table in the shade, where Peter Winkler joined us and got out two puzzles, both very beautiful and very fiendish in their way. One involved packing four awkward-shaped tetrominoes into a frame slightly less than 6 by 5 units, which Richard and Cathy tackled without success. (I had a quick go and failed too). Peter didn't know how to do the other one, which consisted of two identical pieces in dark metal like bronze with a patina, trapping a neatly-fitting shiny ball. It came with no instructions, the puzzle presumably being to take it apart. I noticed that the shiny ball had a curved line engraved on it which seemed to have a very small amount of give. Peter discovered that by aligning the lines on the ball very carefully with the curves on the outer pieces, it was possible to make the ball come apart. Then taking the whole puzzle apart was all too easy and soon accomplished, and Peter was left with the harder job of putting it back together.

Peter Winkler

While we were doing this, the reception started, so after a while we got up and circulated. I found myself having a long conversation, mainly about the LMS, with Robert and Ross Kang. After a while Ross went and I made an excuse to circulate. I ran into Karen Meagher, and Robert joined; unfortunately the sun was in Karen's eyes and she didn't really want to hear about a foreign squabble, so she went off and left me to Robert.

I was starting to fade by this point. Antony had invited me to dinner at an Indian restaurant twenty minutes' walk away; I said probably not but I would come if I felt up to it. But clearly I didn't, so I went home. It will be a very great pity if, as seems likely, I don't get to walk anywhere in this lovely city!

I took a high path through the wood and came down at the back of the tower blocks. Unfortunately the key letting me in to the main door didn't work on the doors here, so I had to scramble down a bank to reach the door I could open.

I got to my room and lay down on the bed. Next thing I knew, I was woken by a shout; it was pitch dark. So I undressed and got into bed.

26 May

For the first part of the night I was tormented by nightmare fantasies about the LMS or events in the novel I am reading. My temperature was quite high. But this passed (the crisis of the fever, I hope) and I slept well. In the morning my throat was still in bad shape and my nose blocked but I felt more human than in recent days. Dare I hope I'm on the mend?

But when I tried to talk to people at breakfast, I found that my voice was in worse shape.

On the way to breakfast, I found that a big hole had appeared on the path; so I had to scramble down another bank.

After breakfast I walked over to the conference. I read my email and found one from Maurice Dodson to post on the Save LMS blog. Editing is difficult on this small screen since for some reason WordPress obeys line ends (unlike normal HTML) and on the small screen they are hidden by menus. I wonder if he and Alice actually think that the people who read that blog will take any notice of them - but I am all in favour of letting them have their say, as a small contribution to reducing tensions.

Joel Spencer gave a lovely talk about the history of the Ramsey number R(3,k). Its asymtotics are determined up to a constant, but there are still interesting things to say, including a plug for the next talk, by Robin Moser, on a constructive version of the Lovász Local Lemma.

Between the talks, Geňa took the conference photograph from a walkway at the top of the stairs, with much hilarity. Vasek Chvatal told me that he has tried out the elementary walk-counting argument which proves the Friendship Theorem on arbitrary strongly regular graphs, and found that it gives nothing at all that the eigenvalue methods don't give (a pity!).

Gena Hahn

After Moser's talk there was nothing that really drew me so I sat out for a while. I got lunch at the same place as yesterday: they had sesame chicken today, again cheap and good. Then I thought some more about bases for wreath products. I now understand it completely, and have a general theorem which includes all known results as special cases. Trouble is, it is not quite a formula, though it can be converted into one in many special cases (and I think probably for any IBIS group). I just emailed it to Robert when he walked in and sat down, so I told him abut it. Several times this week I have wondered why I bothered coming to CanaDAM - it is far too big a conference, and not a high enough density of interesting stuff - but I think this is sufficient reason.

I had a busy afternon; first a talk by Carsten Thomassen, then two I wanted to hear in the Design session (Clement Lam trying to construct strongly regular graphs with specified automorphisms, and Patric Östergård on analysing his catalogue of the eleven billion Steiner triple systems on 19 points), then back to the Graphs session to hear Luis Goddyn talking about excluded minors for bicircular matroids, and finally Joan Hutchinson doing a tribute to Mike Albertson who died in March (of thyroid cancer). I wanted to hear that since he had introduced the concept of distinguishing number for graphs, but I didn't learn anything new.

I walked down the hill past the residences. Today there have been lots of starlings around, and a few sparrows, and I also saw a grey squirrel.

I decided to look for a sandwich in the other direction. I vaguely remembered a convenience store from an earlier trip, but either I was wrong or it has disappeared. Bd Eduard-Montpetit winds and turns into Bd Mont-Royal, lined with houses much too posh to allow a convenience store in the neighbourhood. Then it meets the big road and all of a sudden it is a slum, with a few fast-food joints. At least there was a petrol station that could sell me a sandwich. I walked back along a different road, went to my room, ate the sandwich, and went over my talk ready for the morning, then turned in early.

27 May

I slept fairly well, woke up early, and finished reading the book. (Had I been feeling bouncy, I would probably have stayed up late eating and drinking; this will be better since I will have to get straight to work when I get home with no time to adapt to the jetlag.)

Not the best novel I have read, but I like novels from which I learn something, and that was the case in this one: a snippet of the history of Ferguson tractors. Apparently Ferguson made an agreement with Henry Ford to make tractors with Ferguson's three-point linkage (these were the Fordsons). But when Henry Ford died, his son tore up the agreement (if you can tear up something made with a gentleman's handshake), and Ferguson had to make a new deal with Vauxhall to get his tractors produced. There was a later deal with Massey-Harris (which impinged on my life) but she doesn't get to that.

The fact that I can think about going home, rather than just surviving this ordeal, may be a sign of recovery. It was such a comedown from a nice hotel in Ottawa to this squalid dump where many things don't work; home seems very attractive even if there is a long unpleasant flight first. (But when I looked in the mirror, the person who looked back was rather gaunt.)

I've been to Montréal many times, and have had some really good and some really bad experiences here (the latter mostly health problems). Just past where I walked last night was a park where the Hare Krishna people were having a carnival on one of my visits. Of course there was a wonderful meal in a bakery-cum-gallery organised by Geňa, and another time when at his apartment we made music almost until dawn. But this time it looks like I will see nothing nice: just this sordid residence and featureless lecture rooms.

I must have been a bit earlier at breakfast: there was no juice, no fruit, and no paper napkins. They all eventually appeared.

They had forecast heavy rain for today, but it hadn't arrived; so I put my waterproof in my bag after breakfast, and set out for the lecture rooms to read my email. I saw the news from Peter Cooper about Brian Davies retiring as LMS president, and was inspired to put a little rant on the blog. Surely people will see now that this has gone too far?

The first talk was by Jesus de Loera, who gave such a good talk in Auckland. This one was a bit more showy, and probably further from my interests, but still a most entertaining performance.

I did't stop for coffee but went straight to the room where I was to speak. There was no computer, so I tried out the white toy which worked fine. Then an organiser came along with a computer, so I decided to use that instead. The first speaker wasn't there (as neither were the fourth and fifth), so we sat around until it was time for me to start.

Adrenalin is such a remarkable drug. I was able to squeeze enough volume out of my voice to be more or less comprehensible, and I covered a lot of ground. There was a bit audience - the room almost completely full - and I could see that many people were following.

Afterwards I stayed on for the rest of the session and heard talks by Bruce Richmond and Ed Bender.

Had a nice lunch, and a long chat to Geňa, who was recording a radio programme but was able to take his headphones off once he was sure that the recording was progressing. I also saw Robert Woodrow and Ivo Rosenberg.

After lunch, the first speaker was talking about interesting stuff on the relation between discrete geometry and combinatorics of words. I must admit that I fell asleep. (Another good sign, I think; I have felt too lousy to sleep through lectures at the meeting before now.)

Then I heard my co-author Jason Bell in one session, sat out for a while (talking to Robert about our paper) and went to hear about adiabatic quantum computing. Learning what this is was probably more valuable to me than the detail of the talk. I stayed for the following talk, which had an implicit challenge which my brain was too tired to cope with. Given a symmetric matrix over GF(2) with ones on the diagonal, show that its row space contains the all-1 vector.

The next event was on the other side of the mountain, in an old house belonging to McGill: a problem session, beer and pizza, and a talk by Jason Brown on mathematics and music. The programme made clear that the last of these was open to all, but hinted that the others were for students and postdocs only. But I had been encouraged to submit a problem, and did so, hoping that if nothing else it would be my entry ticket to beer and pizza. It was still raining but only gently; so I donned my hat and waterproof and set out, up Cote des Neiges past the cemetery, down the other side, turning off onto Dr Penfield, and then a short distance up McTavish. (I had checked the route on Google Maps, which told me that it was 4.5km and would take me 57 minutes - an overestimate - and volunteered the information that a short stretch of the road had no pavement.)

When I arrived, there was a totally unsuitable room almost full of mathematicians, and somebody trying inaudibly to present a incomprehensible problem. (Brett Stevens had put problems sent to him into a beamer file, which at least was legible, though had some misprints.) After what seemed a very long time this ordeal was over. Someone (probably Geňa) had produced a microphone, which helped. I said mine, rather quickly, and was asked several intelligent questions about it.

The session finished at 8 and Jason came on. It was an interesting talk. I didn't agree with a lot of things in the more theoretical part (such as what makes a "nice" chord in a scale of n notes), but there is no doubt that he had ingenious explanations for the blues chord sequence, bossa nova rhythm, and so on. But he was good on the Beatles (though again I didn't agree with him about why "I want to hold your hand" was the song that launched the Beatles in America). The piece de resistance was his analysis of the famous opening chord of "A hard day's night". He sampled it and put it through an oscilloscope. After discarding harmonics and noise, he was still left with more notes than even the 22 strings used by the Beatles could make. But three of these were very slight variants on the same F, and he realised that this must be a piano, and not only that, but a piano small enough that this F would have three (rather than two) strings, and must have been added by George Martin (and perfectly mixed in so that no-one would notice). He really was the Fifth Beatle!

At the end the pizza appeared, and clearly it was for everyone. Beer also, though there was a crush around the bar. So I had a couple of slices of pizza and set off. On the way out I caught up with Robert Woodrow who had found the noise too much. He was staying with Geňa, so our ways parted quite soon. I walked back over the hill and through the university to the residences. Four young people were very noisily playing a ball game in the communal area; the flimsy walls don't keep the sound out.

28 May

The kids went on screaming for a while, then they stopped and the wind took over. Even a gentle wind howls ominously around the tower blocks. But I slept until 6 despite all. I got up and showered, leaving the shampoo and shower gel (pilfered from the hotel in Ottawa) to the next client (I doubt the cleaners will go into the bathroom). The water was hot even if it did drain badly and spread over the floor.

I got a shock when I arrived at breakfast. There were about 30 teenagers, talking loudly and playing music, already bright-eyed and bushy-tailed at this early hour. The queue was long and slow-moving because they all wanted their sliced bread toasted, and the arrangement meant that the queue for the toaster blocked access to cereal, croissants, bagels, fruit, etc. As soon as I could reach something without impoliteness I took it and went. (Juice and coffee were at a different table, fortunately.)

I went back to my room and packed, and threw away the remaining vitamin C and Tylenol. I have decided that I am better, and don't need any more drugs. But I shall try to get some pastilles at the airport, since the Canadians are more concerned about swine flu than most nations and would probably lock me up if I snuffle on their plane. Robert showed me an email from the organisers of the workshop in Waterloo next week: if he has a cold he shouldn't come; in any case he will have a medical examination in an isolated room before they admit him to the meeting. Is this in store for all of us?

I went back down to the reception desk by the breakfast bar to hand in my key and computer cable. The girl, of course, asked whether everything was all right, and I explained that the internet connection didn't work. She of course said that I should have gone down to the desk to report it, and a technician would have come and fixed it. But I had foreseen that in my enfeebled state, if the technician threw up his hands at the idea of connecting a non-windows computer to the internet, I wouldn't have had the strength to protest. Anyway, it is surely the mark of a third-rate hotel to say "if you report it we will fix it" rather than trying to get it right without a report.

I tried to walk up the other side of the residences, but hit a dead end, and had to backtrack all the way down.

On the way up the hill, I saw a couple of starlings. I might have to change my identification of them. The other ones I saw were in a group, but these two were on their own; they hopped and flew like blackbirds, even though they had characteristic starling plumage.

When I arrived at the conference building, another shock was in store. The accounts had all been cancelled and I was unable to check-in online as I had hoped.

But I went to the first talk: Qing Xiang was talking about the stunning new results that he, his student and Peter Sin have about the p-ranks (and even Smith normal forms, in some cases) of incidence matrices of points and k-spaces in projective space or symplectic polar space over a finite field of characteristic p. Essentially, they get the complete submodule structure of the space of functions on the points of projective space as GL(V) module (some way beyond what Bob Guralnick and I did in a restaurant in Pasadena one lunchtime), and then identify the module spanned by a k-space; then they just have to read off its dimension. It is a sum of t-th powers (where q=pt) of eigenvalues of a certain matrix whose entries are dimensions of various modules. A bit lost on the audience though, since Steinberg's tensor product theorem was not as familiar to most of the combinatorialists as he thought. (Shame on them!)

In the break, the accounts had been restored; I checked in but of course was unable to print out a boarding card. But there were plenty of people to talk to - in fact it is a sign of my recovery that I can walk around the lobby and strike up conversations with all sorts of people. Very nice.

I went to hear Robert Bailey give a nice talk about a tough topic. The talk after his was cancelled so I went back to the lobby. After a while Robert came back, and we talked about the paper for a while. He is having a bit of trouble with Evdokimov and Ponomarenko. They ask readers to recall a fact which is in a paper of theirs in Russian, which didn't appear in English translation until a year later; and they assume without the least comment that their definition of a base in a coherent configuration (or cellular algebra) and Babai's agree, or at least have some relation, a fact which is rather unobvious. I told Robert I would think about it.

We went and got lunch, and he showed me some pictures from his round-the-world trip (mainly Sydney and the train from Seattle to Vancouver).

It came time for the next plenary talk, by Shafi Goldwasser, about programs that run once and then disappear without leaking any information about how they work. Possibly interesting and even useful for the applications she has in mind (such as delegation of an electronic signature to someone else for a short period), but I wouldn't put it past Bill Gates to find a way of forcing everyone to buy more of his stuff.

After the talk I set out, but was delayed by many farewells and conversations, and it was nearly 3:30 when I finally got away. I took the metro to the bus station at Berri, and got the airport bus before the one I was aiming for.

Maybe as well. It wandered aimlessly around the traffic jams of downtown, crossing its tracks a couple of times, before setting off more purposefully. At a huge piece of concrete spaghetti, I noticed that the road forked, and we passed up the one to Trudeau airport and took the one to Mirabel instead. Robert had told me that Mirabel has completely closed (another white elephant from the 1972 Olympic Games), so I was surprised that so many signs to it still exist, even on the doorstep of Trudeau (formerly Dorval). For we did, of course, go there. But we spent a lot of the intermediate time stuck in a very slowly moving line of traffic on a freeway, and the 45 minute journey took 75. The extra time did allow me to sort out that the two types of basis for coherent configurations are the same thing. [In fact I was wrong about that, but it is true that one implies the other.]

The automatic machine recognised neither the barcode on my itinerary nor my booking number, so I had to queue up. The queue moved OK until I was almost at the front, when almost all the people behind the desks went off duty, so the last bit was tediously long. But no problems. Also a long queue for the security check, but it was much less of a hassle than London, and there was no passport check at all. So I was actually in the departure lounge two hours before the plane was due to leave.

I started writing up the argument for Robert until it was time to board. The boarding was slow, and departure from the gate even more so, but finally we were underway. I finished typing up the proof before the meal came around.

The woman beside me is married to a Chelsea fan; he is in Europe at the moment, and they are going to meet up in London and go to the Cup final.

After dinner I had a few hours' good sleep, and woke when the light was coming in over the west of Ireland. We landed at Heathrow right on time. There were long delays in immigration, nearly an hour (with notices on the screens suggesting that they are proud of the fact that it takes longer, rather than recognising it as the result of incompetence). But finally I was through and on my way home in the morning rush hour.

2. Banff, July 2009

Banff, a small town in the Rocky Mountains, is the centre of the oldest National Park in Canada (and third oldest in the world). On the outskirts of the town, under Tunnel Mountain, is the Banff Centre, an arts centre supported by the Alberta provincial government. Almost as an afterthought, the centre includes BIRS (the Banff International Research Station for Mathematical Discovery and Innovation) which runs week-long conferences on the Oberwolfach model. In the period 19-24 July 2009, there was a meeting on "Permutation Groups", my real mathematical subject, to which I was invited (though because of being too busy at work, I hadn't been able to get myself into the right frame of mind for the trip).

19 July 2009

Getting underway took several attempts since I first wanted to have the limo schedule at Calgary to hand and then I realised I had forgotten my hat.

The District Line is not running east of Aldgate East, so I had a fair walk on setting out. The sky was cloudy but the sun was shining as I walked down through a very uncrowded Whitechapel. There was some wait for the tube, but eventually it came and I got a seat.

When we emerged into the daylight again at Barons Court, it had been raining; the tracks were wet. The second tube to come took me to Heathrow. Since I had checked in online, I went to the departure gate. But the scanner wouldn't read my boarding pass, so they sent me back downstairs to have another one printed out. That, fortunately, worked OK.

I sat in the departure lounge and worked on a new chapter for my counting notes (on permanents, SDRs, and Latin squares) until the gate was announced. At the gate, they didn't like my passport; the picture was not printed with waterproof ink, and has smudged from a bit of water getting into it in Galway. (What a relief that I didn't spend a lot of money getting a UK resident stamp put into it!) But they accepted my old passport as ID and let me in.

The flight was late leaving. They announced that this was caused by delay to the incoming plane, and that we would be boarding in five or ten minutes. Fifteen minutes later they repeated this announcement, word for word. But the second time it was actually correct. Then, when we were ready to go, the pilot was told by air traffic control that there was a further fifteen minutes' delay. We messed around on the tarmac for quite a long time, and in the end were almost an hour late leaving. There is now almost no chance of catching the limo; I should have booked a later one.

On taking off, there was a lot of turbulence, so they didn't turn off the seat belt sign for quite a while. I listened to "Highway 61 revisited" for a while, until lunch came. The flight data system is not working so I cannot get updates on our position or even find out for sure how many hours Calgary is behind London (I think it is seven).

After lunch and coffee, I got the white toy out and typed up the chapter I have written. I am not sure yet how much to say about Falikman's proof of the van der Waerden conjecture, so I have deferred that decision and written up the rest.

Then I read for a while (travel diaries, then a book), and listened to music, while time passed. None of the other music compared to Bob Dylan, so after a while I went back to Highway 61. Just three tracks in, we were interrupted by an announcement that we were 35 minutes from Calgary, the ordeal almost over.

Coming down into Calgary, we went through some quite bad turbulence; they were having a storm. (The runways were wet when we landed.) A passenger a few rows in front of me was airsick, and the disagreeable smell spread through the cabin. But finally we were down, just 35 minutes late. Customs and immigration took only ten minutes.

I had a shock when I looked at the limo receipt; I had mistakenly booked for 2:30 instead of 4:30. But the girl had adjusted the bookings and told me everything was fine, I should come back to the desk five minutes before departure, and I should go to the loo since it is a two-hour journey.

There were five of us on the minibus, all going to the Banff Centre. A family of father, mother and six-year-old boy from Los Angeles, the parents doing some art thing at the Banff festival; a girl frm Philadelphia who plays the trumpet and is teaching some classes there; and me. The little boy reads a series of comic books called "Captain Underpants", which the American girl had heard of. We chatted for a while and then fell to sleeping or watching the scenery.

Calgary is not a pleasant town. Set in saucer-like basins separated by ridges, it sprawls a long way, the suburbs consisting of patches of identical houses separated by wide expanses of mown grass which seems not to be used for anything. The whole place has a raw look, with no mature trees. But from the tops of the ridges we could get a glimpse of jagged mountains in the distance. The only thing of note was a large bird of prey in the far distance.

Eventually we turned west on the highway and Calgary fell behind. At first the ground was fairly flat with some cultivation. Then it became more undulating, and very green, and cattle replaced crops. The undulations became full-scale hills, with more trees (pine, and some with broad shiny leaves), and steep gullies ran down. By th roadside were increasing numbers of wildflowers, including some striking blue ones. All the time the mountains were drawing nearer, until after an hour we reached them.

They were as rugged as they had looked from a distance, with craggy cliffs riven by crevices, dangerous-looking scree slopes, and clear strata at vetiginous angles or violently twisted. But we didn't have to climb them; the road ran through a valley with a fast-flowing river and an industrial town. The panorama of mountains changed as we proceeded; one view of a mountain standing alone made us all catch our breath.

After another half hour we reached the entrance to the Banff National Park, which has a lower speed limit on the highway. Signs warned of wildlife on the highway, though we didn't see any. (Before the park, they had warned of pedestrians on the highway.) Before long we turned off, drove through Banff town (it has a "Swiss village") and round the back streets to the Banff Centre, where the driver let us off.

I read my instructions, which hinted that I should be somewhere different from the main reception. But I went in to reception anyway, and it was the right place. I got my key, my room card, a map, and rather complicated directions for getting to the building where I am staying (there is a large building site between). Chipmunks (maybe) scampered away across a lawn as I passed.

I dumped my bags in my room, found my way to the common room where my badge and computer account details were. But the notice said that the entry code to the room had been emailed to me. Fortuately I had printed out this email, so on my second try I got the badge and account.


Then I went over to dinner. They swipe your card at the door (it knows who you are) and then you are in and take what you like. I took a bowl of soup and found my way to the BIRS tables, and many old friends having dinner. At the first table I reached, Persi Diaconis invited me to sit down in a place which had just been vacated. Opposite him was Ben Steinberg, whom I met now for the first time, despite having exchanged many emails.

I ate and had a long conversation, first with Persi, then with Ben and Peter Neumann, who came by. I am told it stays light very late here at this time of year, but thought I should try to sleep at some point before my body thinks it is morning and time to get up. (The time difference was, indeed, seven hours).

Coming out of the dining room, we saw a small elk with a fine set of antlers eating the flowers in a flower pot outside the building.

Back in my room I tried the computer and found it worked; but I can't connect the white toy, and can't find a USB port on the SUN terminal.

20 July 2009

I woke several times in the night, but had no trouble getting back to sleep. Twice I heard trains rumbling past somewhere in the distance, whistling a minor chord rather than the FAB chord (major third and tone) of the Québec trains.

Eventually I realised I was wide awake so I got up and read my email. I am in an apartment with two rooms sharing a bathroom; I don't know who is in the other one, but whoever it is made quite a lot of clattering round locking and unlocking doors last night, and at one point there was a terrific crash. A notice in my room says that the thermostat is in the neighbouring bedroom, so presumably this is intended as a family apartment. Anyway, I showered quite early to avoid conflict over the bathroom.

I went early to breakfast. The Banff Centre caters for a lot of arty things (some of which the people on the bus yesterday were going to), with mathematics as just the small change; and the huge new building will dwarf the rest of the site. But it made for some interesting photographs of the mountains and trees through the building work.

At breakfast, I found Persi, John van Bon, and Richard Weiss. Later Katrin Tent and Martin Ziegler came, then Bob Guralnick and his wife who have just driven from Princeton. Other friends all around on other tables. Very nice breakfast, though I was somewhat restrained.


After that, it was almost time for the opening of the conference. Brenda, the BIRS person, told us a few things, including the fact that there is a computer manual in our desk drawer. She also said that this is the first week of good weather in Banff all year.

Gary Seitz gave the first talk, announcing his result with Martin Liebeck (long coming) about classes and centralisers of unipotent elements in algebraic groups. Then John Shareshian and Michael Aschbacher talked about finding a lattice which is not an interval in a subgroup lattice of any finite group. The classical candidate is the n-point line; Michael concentrated on this (and has reduced it to two problems about almost simple groups) while John seemed to prefer taking a slightly more complicated type of lattice.

At coffee time I discussed with Brenda the possibility of a walk around Sulphur Mountain on the Sundance trail for the free afternoon. I do not want to spend half the time in a car going to Lake Louise, which seems to be the popular alternative.

At lunch I fell into a discussion with Persi and Ben, which after a while came round to the order of the arguments in a wreath product, and hence to actions on the left or the right. On the way to lunch, we had discussed the little animals on the grass; Ben, the only Canadian resident present, was not sure what they are: too big for chipmunks, and the wrong sort of tail for squirrels. (Later it was suggested to me that they were marmots.)

After lunch they had put on a campus tour but I decided to go for a walk instead. I decided to see how far up the Tunnel Mountain trail I could get if I were to get back in time for the conference photo at 2.

View from Tunnel Mountain 1 View from Tunnel Mountain 2 Conference photo

The distant views were stunning, and there were quite a lot of wildflowers too: harebells, purple and orange daisies, stonecrop, and a grey-leafed shrub with yellow flowers, were the most common. I reached the ridge, which gives astonishing views of the next bit of the river valley and the other side of Mt Rundle. I had to turn back just before the summit, having had the best part, I'm sure.

Before the photo, Brenda appeared with a map and some bad news: the Sundance Trail is closed from April to October. I will have to find something else to do: I am sure I want to do a serious walk!

The photo was taken by the IT person and was very quick and painless, and then we had a lovely talk by Persi about his encounters with Gelfand pairs with an appropriate story from probability or statistics to illustrate each one, including a story from Piaget about how children learn the idea of randomness.

After tea we reassembled for the last three talks. Just before the first, Bill Kantor gave me the news that Bob Liebler has just died, on a hike, it seems. He didn't feel too good, and told his companion to go on ahead, and was not seen alive after that.

The last three talks were a mixed bag; the one most interesting to me, because of the project with Robert, was Ákos Seress' talk about distinguishing number. Having done primitive groups completely, he is now doing what he calls "two-step imprimitive groups", but it is far from complete. I think Robert and I are absolved from the burden of trying to cover this in the survey of bases that we are writing. (Distinguishing number is relevant to calculating the base size of a wreath product in the product action.)

When the talks ended, I went back to my room to dump my things, and discovered who my mystery neighbour is; it is Tim Burness. At dinner I ate with Bill and Phyllis Kantor. Phyllis had walked to the Hoodoos (a group of standing rocks down the river a little way) and thoroughly recommended it.

After dinner I went back to my room. I tried to look up Sundance Pass on Google but could find no information. I downloaded the conference photo, and also transferred my day's photos from the camera onto the white toy and wrote up my diary. The computer manual tells me where the USB port is - in a very inaccessible place where you need tiny fingers to get it in and out and run the risk of dislodging the keyboard and mouse leads. So I uploaded yesterday's diary and emailed it to Ro. There is a paper from Tatiana which I have to read, and the conference photo is on the web.

Then I went out to sit on the porch. I wanted to think about my talk and about a theorem of Ken Johnson that Persi quoted in his talk (that the permutation group generated by the left and right multiplications in a quasigroup is multiplicity-free), but soon Peter Neumann came by, and gradually quite a large crowd accumulated and a couple of bottles of wine appeared. We sat there until the mosquitoes drove us in. The others went to the common room to continue, but I decided it was my bedtime.

21 July 2009

I slept better, though still woke a few times. I had been having evening coffee to keep me awake until bedtime – meals are very early here, dinner 5:30-7:30 – but I think it is time to stop now.

Last night I read through the computer manual and found that there is free wi-fi here. I tried it out and it worked fine, no login required. But this morning it is not working.

I made my way to breakfast. It is quite chilly here in the morning, before the sun gets over the mountains. People told me the food used to be quite bad here, but it is excellent now. For breakfast, they have several sorts of cereal, a range of milk including soy milk and yoghurt, chopped fruit (melon, pineapple, etc.); cooked breakfast of bacon, sausage, ham, egg, diced fried potato (with a discreet amount of spring onion in it), waffles and tiny pancakes; muffins, bagels, a range of tea (Persi asked for Earl Grey yesterday and an individual pot appeared) and coffee, and they encourage you to take a piece of fruit when you leave. You can even have an omelette cooked to order!

After breakfast, I realised that I had made the reverse mistake with my booking for the airport bus: coming out, I booked the bus two hours too early; returning, two hours too late, so I would have missed my plane. The wireless wasn't working so I logged on to the SunRay to change the booking, which all went very smoothly and I got an acknowledgment almost immediately. Then I spent half an hour on Tatiana's paper, and got it almost ready (but another email from her says she is still not happy). This was very intense and concentrated work, and at the end I was exhausted.

We had three lovely morning talks: Martin Liebeck on triangle presentations of simple groups of Lie type; Tom de Medts on a beautiful construction for a locally finite tree with a vertex-transitive automorphism group in which the stabiliser acts as any prescribed group on the neighbourhood of a vertex; then Alex Lubotzky on short presentations of simple groups. He told the story beautifully, leading the audience down all the blind alleys that he and his collaborators had been trapped in. But it is a beautiful theorem!

In the interval, Cheryl gave everyone the news about Bob Liebler, as far as it is known.

Jan had arranged a hike to the Hoodoos after lunch, and expected me to be the leader. On the white toy, in the lecture room, with the Wi-Fi now working, I was able to find a webpage which gave the distance as 5.1km with a climb of 60 metres (one way), and a beautiful picture, which might have persuaded some of the doubtful. After lunch, leaving was a terribly slow business, as people kept disappearing, but fourteen of us finally set off. One disappeared early on; I am not even sure who it was.

We took a nice path through the woods and down to the river. The scenery here was very fine indeed, with the sheer cliff edge of Tunnel Mountain on our left and Mt Rundle towering over us on our right across the rapidly-flowing river with islands and backwaters.

Bow River

When we came to the first uphill, Richard Lyons slowed down. I went back to see how he was; he said he was turning back because he didn't feel too good, but would sit and watch the river for a while. After the news about Bob Liebler, you can imagine what a shock this gave me. But lightning doesn't strike twice, I told myself, and went on.

The trail climbed a bit, then levelled off through a nice bit of forest at the foot of the Tunnel Mountain cliffs (the ones I had stood above yesterday). Then it reached the road, and a map showed there was only a little over a kilometre to go. When we got there, it was a bit of a disappointment; the viewing platform was high above the rocks, and there seemed to be no way down (not that we had time to go further anyway). We turned for home.


On the way back, all walked at different speeds; I took a bit of trouble ensuring that nobody was lost, but basically felt that they could look after themselves now, so went on with Ákos Seress. When we got back to the Banff Centre, I was relieved to see Richard sitting on a seat in the shade looking completely relaxed. He had had a bit of a cramp, and, knowing that he was not very fit, had decided to play it safe. I had time for a relaxing cool shower before the afternoon talks.

These were more intense and long-winded than before, and a lot of the audience was not in good shape for them, especially when Yoav Segev insisted on going substantially over time. Finally we finished and it was dinnertime.

I ate with Bill and Phyllis, but Bill was soon hijacked by Ákos to talk about mathematics. So I went back to Corbett Hall. A party was going off to look at wildlife; they asked me but I declined, wanting to prepare my talk. Then Jan came with a map, thinking about a walk for the free afternoon. He hadn't noticed that, according to his map, the starting point is inaccessible to cars (but there is a gondola to take you there). It looks an attractive spot; I might be tempted to go with them (especially since there are several ways to extend the walk with extra bits).

After that, I went and got a beer, a dark Bigrock ale from Calgary, and sat on the porch drinking it. I wrote up my diary, transferred my photos, and read my email. Then I went back to my room, and printed out the revised Airporter booking. The schedule has been rearranged so that we finish at coffee time on Friday morning. I wouldn't have been able to catch an earlier plane, but I have all day to wait, so a chance to get a bit more hiking.

22 July 2009

I slept much more soundly, and was a bit late for breakfast (partly because I read my email and then found a very amusing account of Mayor's Question Time on London Reconnections). Parts of my talk were running in my head over breakfast. As usual I have too much material, but the bits that will probably be cut are actually some of the most interesting, showing the power of this approach.

I did take a little time to start writing an account, possibly destined for Strider. There is a story to tell, given yesterday's business.

But then the drawback of having two rooms sharing a bathroom became clear; my apartment-mate went in for a long session. I had to take a long walk to the lecture building to clean my teeth!

My talk went very well. I had 45 minutes, so I had to prune ruthlessly; but I managed to tell a story, make propaganda for both monoids and graphs, and I even got a cheer from Persi when I said that we have to solve some problems even if they are NP-hard. Afterwards there were a couple of interesting suggestions from various people including Peter Neumann, who made the conjecture that any primitive group and any non-uniform map generate a synchronizing monoid, and also suggested a possible source of affine examples.

Then Rob Wilson talked about his construction of the large Ree groups. Lovely stuff, and he makes it all look so easy. At the end, several members of the audience came out as secret Ree-group constructors. After the break, Pham Tiep talked about the problem of classifying representations which remain irreducible on restriction to a proper subgroup.

Jan announced that the walk would involve driving to the bottom of the road up to Sunshine Village and catching the bus up the hill, at a cost of 25 dollars per person. I said I would come but reserved the right not to go on the bus. Ruth was good enough to make me a copy of the map. I tried gently to persuade someone to come with me, but failed (maybe just as well – I ended up walking 21km in less than four hours, with 700m difference between the highest and lowest point).

We were divided up among the available cars (Peter and Sylvia Neumann took Simon Blackburn and me) and drove down the highway a bit and then off a side road up a little valley to the huge car park and gondola station. (Sunshine Village exists for skiing; it claims to have snow for nine months of the year.) On the way we passed a big herd of wild goats. They were still there when we returned home; I noticed that some of them were licking the road surface in a small lay-by; presumably they salt the roads in winter and some of the salt stays there.

At the car park, where the bus (a retired school bus, rather battered) was waiting, I went into the little shop in search of information, and picked up a leaflet about the wildflowers. There was also a notice on a board about "grizzly activity" reported in Healy and Simpson passes. This was not to scare people off, rather the reverse; you were encouraged to join an expedition to see the grizzlies. In the event, I saw no sign of any bears, but on the way down the dusty road I did meet two people with bells on their boots to scare the bears away.

The others got into the bus and set off; I found the trail and headed off along it. At first we went in almost the same direction, the trail just below the dusty gravel road - the bus driver told the party that sooner or later I would have to scramble up to the road. But the path along Healy Creek soon turned off while the road switchbacked up the hill.

Healy Pass trail

It was a lovely forest path with a huge cliff rising on the other side of the valley. Wildflowers grew beside the path, most of which I was able to identify from the leaflet, but a very common one with four curved and pointed petals was not listed - later I looked it up and found it to be bunchberry. The path climbed and crossed a lovely clear stream. A young hiker was sitting by the stream and explained to me that he had got ahead of his party. Sure enough, I soon found a large group of kids, and told the adult that I had seen one of his group.

Healy creek
The top

After a while the path levelled off in an alpine meadow with a discreet camping site and a food cache (both clearly signposted). I had decided to take a slightly less direct route to the start of the Simpson Pass trail; it turned out to involve a much stiffer climb. (The contour lines on maps of the Rockies are at 50 metre intervals, so the maps can be a bit misleading at first glance.) Nearing the top, I heard the noise of a helicopter echoing from the surrounding mountains; just as I stepped out from the trees, it was flying away.

I was now in competely different country, a flatter area with boggy lakes and stunning views of the mountains and a different selection of wildflowers. Soon I came to a couple of young people by a stream; they turned out to be park workers putting in stepping stones. It is possible that the helicopter was dropping them off for their afternoon's work. Then I met a hiker who stopped to talk. Just as he complained about the heat, a cooling breeze sprang up.

Lake 1 Lake 2

A very steep descent brought me to an open valley and the start of the Simpson Pass trail. After a short climb, the trail came to the bottom of a huge crumbling cliff, which had spilt a huge pile of stones and rubble along its base, stretching out nearly to the trail in places. From the map I saw that the Alberta–BC border runs along the top of the cliff; presumably, like the Queensland–NSW border, the surveyors were told to follow the top of the ridge.

At the end of the ridge, the path climbed gently to a pass, and I thought I was over, but not so. It crossed a valley and climbed the other side, with the steepest climb of the whole walk. Just before the real summit, it went round a cwm in which snow was lying in full sunlight (but on the shady side, so presumably only in sun for a few hours a day.) The top brought a view of a chain of huge bare mountains rising to almost 3000m. As I walked down the other side, a cloud shadow crossed one of the mountain flanks like a giant butterfly. The wildflowers here were the best yet.

View from Simpson Pass

The path led down a ski run to Sunshine Village, with one barn-like accommodation block and the top of the gondola and the bottoms of a couple of chairlifts. I headed down the dusty road with spectacular views of mountains all around. Several cars came by kicking up the dust, then a water truck spraying the road (and me). It made more dust than any of the others, but afterwards things were not so bad. The road went on down; I could see the trail I had taken earlier; and on the dot of 5:45, the scheduled meeting time, I walked into the car park. The bar was closed, but I had a bottle of water left, so I drank that, while checking the wildflowers. Among other things I had seen lots of Indian paintbrush, purple fleabane (the orange and purple daisies), glacier lily (well past its best), alpine forget-me-not, white dryad, white globe flower, heart-leaf arnica, yellow fleabane, heather, common stonecrop, and wild strawberry (no fruit yet, sadly).

There had been relatively few birds. Apart from some unidentified small ones, I had only seen a raven with something in its beak. But there were birds in the trees, making a lovely melodious whistling, in some places.

Soon the bus arrived, and we got into cars for the trip back.

Most of the others went to have showers, but I decided to eat first, since we were on that side of the campus. After dinner, I soaked for a while; I am remarkably un-stiff after quite a demanding walk. Then I took a beer and went and sat on the porch. After a while Peter joined me, and then Ben, and the talk fell to synchronization. On the walk I had checked Peter's affine construction and found an even better variant (which he must really have known about); and I trumped his conjecture about non-uniform maps always synchronizing a primitive group with an even stronger conjecture that the only maps that don't synchronize are maps onto the core of some G-invariant graph.

While we were sitting there, an elk came and sat down under a tree, allowing all the passers-by to inspect it. Jan, Ruth and Sylvia decided to jump into a car and drive off to Lake Minnewanka where a moose had been seen yesterday. (They didn't see it, but they saw a very fine sunset.)

Once the mosquitoes started biting, we went in to the common room, and tried (ineffectively) to prove one or other of these conjectures. By 10:30 we were all tired and went to bed to sleep on them instead.

23 July 2009

At breakfast time, there were ripples of cloud in the sky behind Mt Rundle. (The weather forecasts are divided about whether it will rain in the next couple of days or not.) On the way back, I saw a dark grey mouse-like creature with a short tail trying to pluck up courage to cross the path.

There were three morning talks: a lovely but fiercely technical talk by Richard Weiss on constructing affine buildings; Gunter Malle on a variant of the k(GV) problem; and Kay Magaard on maximal subgroups of rank 3 groups whose permutation characters don't contain the rank 3 character. I was a bit distracted in Kay's talk by trying to guess how long the chalk would hover over the board before making a mark (and also by his talking about the stabiliser of a non-singular point in the natural module for symplectic groups).

Jan asked me to lead the walk up Tunnel Mountain, but forgot to announce it. I said I would show up at 1 and take anyone who turned up at that time. Meanwhile Peter tried to refute my conjecture, but it turned out he hadn't quite got what the conjecture says.

By lunchtime, the sky was quite hazy; there are forest fires west of us, in BC, and just enough wind to blow the smoke over. Also clouds building up; a storm not impossible.

Only one person showed up for the walk, namely Ben (though Andrea Lucchini had walked up on his own; we met him coming down). The views were much less impressive than on Monday, because of the increasing haze in the air. Ben talked on about synchronization all the way up, but coming down the conversation turned to more general properties, and finally to producing a public draft of the paper. Ben thinks it should be re-written to give graphs a more prominent role (so my lecture was successful in one respect at least).

We missed a turn on the way back and had to climb back up the road for some distance, but were still back in plenty of time for tea. But it was so humid that I needed a cool shower first.

The afternoon talks were all rather heavy on detail, though all very different, and despite good intentions I found myself drifting off a couple of times.

By dinnertime, the sky was clouding over. Tatiana wants me to do another job on the paper, rewrite the introduction; I have been putting it off but it has to be done sometime. So after dinner I sat down and got on with it. As usual in such a situation, I found that there was little to do on the introduction, but there were other errors throughout the paper which needed fixing. By 9 I had done it all, sent it off, and earned myself a drink.

By now, clouds were rolling over, and thunder was echoing around the mountains, but no rain and little wind, and it was very hot and humid. Even the heat generated by the white toy had become oppressive. By the time I had finished my beer, it hadn't changed much, but I made an embarrassing discovery. When I had opened the window (with some difficulty), I failed to see that it was a double window; so I hadn't actually let any fresh air in after all. But even with the window open, it was still very stuffy. I had an early night: tomorrow morning will be packing and check-in.

The storm was a squib – by the time I went to bed, there was a lovely pink sunset light on the clouds in the west.


24 July 2009

I woke up and did the first job (checking in) before breakfast. It was simple enough: find Air Canada with Google, go to "check-in", type in my booking number, tick a few boxes, hit "print". Then I had to get dressed to go next door to the reading room to pick up the boarding pass from the printer.

I heard a rather worrying story from Katrin Tent at breakfast, concerning the LMS. She has had three papers recently mutilated by copy-editors. In one case, they had added her husband's name as an author on the paper; and they had preceded a list of conditions by the phrase "The following conditions are equivalent:". Yesterday, walking up Tunnel Mountain, Ben had told me a similar (but not quite so drastic) tale. Should I write to Kenneth Falconer about it?

At breakfast, I realised that I would be back in Britain in 24 hours if nothing went wrong. There were light clouds in the sky. Coming back, I met Cheryl, who wants to talk about the paper this afternoon – there goes my chance for a last walk.

I finished my packing and went over to the lecture room. The conference finished with two absolutely splendid talks by Ben Steinberg and Peter Neumann, and then Persi thanked the organisers. He said that he had heard many people saying this was one of the best conferences ever. As far as I am concerned, it had a very high proportion of excellent talks, and a very high proportion of things I am interested in. And having people like Persi to talk to is an added bonus.

There was supposed to be transport for our bags, but I sat down and fell into conversation with various people including Persi and Ben and missed my chance. At 11:30 Cheryl finished her work with Simon Guest, and we agreed to have lunch and work afterwards.

After lunch I went to the reception to check out and leave my bag. I had thought that we were meeting there, so waited for a while. While there, I was entertained by an extraordinary crow. It sat in a pine tree and uttered repeated calls in a recognisably musical monotone on the note of G. Then it flew to a neighbouring tree, which seemed to extend its repertoire, to a more crow-like caw and also a throaty rattle.

When Cheryl didn't show up, I remembered that she had suggested meeting in the lounge in Corbett Hall, when we had planned to do it before lunch. So I went back there and couldn't find her. I found Chris Parker, who hadn't seen her, so I went back to reception. A little while later Chris showed up, saying that Cheryl was now in Corbett Hall. So I went back, and we finally met up.

We sat in the lounge and talked about what to do with our paper. She also told me about a problem posed to her by a number theorist. Given a transitive group G, the problem is to minimize the sum of subdegrees for which the corresponding double cosets generate G. (This isn't quite how she stated it, but I think a further formulation is helpful: find the minimum valency of a G-invariant connected digraph.)

She had been going to walk with Peter and Sylvia, but they had now gone, so she agreed to come with me; we would walk as far up Mt Rundle as we could do in the time available. While I waited at the door for her, two chambermaids came in. I told them how much I had enjoyed my stay. One of them asked me where I was from; I said "London, England." She asked what language they spoke there, and was dumbfounded when I said "English"; she thought that English came from America. . .

We walked down the hill beside the river, with views of the Bow Falls, and a really scary sign telling you not to walk on a trail at the top of the cliffs (so you can't get a really good view of the falls). So we walked down the road, finding a river path after a while, crossed over the only bridge, walked back on the other side (with better, lower-level views of the falls), across a bridge over Spray River, and after walking along the road by the golf course for a while we found the start of the trail.

Bow falls
White camas

It soon started climbing, going almost straight up the sloping face of the mountain. There were nice woods, with Indian paintbrush and some waxy-looking flower that turned out to be white camas, as well as various fungi and a sponge-like moss. We hoped to get above the treeline but the clock beat us; we had to turn back at about 1800 metres. We talked about many things, including the struggles of the mathematicians in Australia with the bureaucrats running the research assessment there.

On the way back, we saw people paddling in the beautiful clear water of the Bow River. I was so tempted to take off my boots and go in, but time didn't permit. We went on, and back up the hill, where I retrieved my bag from the reception desk and had only a short wait for the bus.

I was the only passenger boarding at the Banff Centre, or indeed in Banff; there was one more passenger booked from Canmore, so the very good-natured driver phoned her up to say he was running a bit ahead of time, was that OK with her?

The bus rolled on down the valley between the mountains. Clouds were beginning to spill over the range on our right, and mysterious shafts of light penetrated the gloom; on the other side there was blue sky with only some high cirrus cloud. Then back through the hills and blue wildflower meadows, the cattle country, the cultivation, and finally the outskirts of Calgary.

It is not much of an exaggeration to say that half the trip is the journey from Banff to Calgary, and the other half is a trek through suburban Calgary; but finally we were at the airport, a quarter of an hour early. I went to the bathroom, where I changed my underwear and socks, shaved and brushed my teeth one last time; then I asked about the flight at the check-in desk (no queue!) and got a gate number.

Going through security I had a bad moment. "Any liquids?" "No". "Any large electronics?" "Yes, a netbook." "Put it in the bin." It turned out that he meant the tray that goes through the X-ray machine, not the trash can where excess liquid goes. . . Maybe it is Canada where they don't speak English.

I had actually gone into Zone A, because the security check at Zone B was closed. There were places to eat in that part of the airport, but after a long trek through a narrow winding corridor to Zone B, there were only a couple of tiny snack bars, all closed. It will be quite a while before I get to eat!

We started boarding a few minutes early, pushed back right on time, and taxied out to the runway under an extraordinary orange sky, with a thin crescent moon sinking into the murk. The woman who was seated beside me had gone to a spare seat somewhere else in the plane, giving me two seats to spread out my things on.

Dinner came promptly and the entertainment system didn't work, so there was nothing for it but to go to sleep.