Summer 2003: Bled (Slovenia) and Tehran (Iran)

Bled, 21-28 June 2003


It's years since I kept a travel diary. Why am I starting now? Maybe the email from Nikhil and Nidhi Singhi mentioning that they had read some of my diaries.

Up at 5:30, out of the house with only a banana and a glass of milk for breakfast. To the tube station in time to see a train pulling out, then a 15 minute wait for the next. I'm not in a hurry, unlike four American girls whose plane is an hour earlier than mine; they were getting quite nervous.

The first check-in desks I came to were Austrian Airlines, and the queues not too long, so I was able to take myself to Wetherspoons for a more substantial breakfast before going to the gate. The bookshops had huge piles of the new Harry Potter book, and didn't seem to be shifting many. I did buy myself three books for a fiver each: I will have a long wait at Vienna airport on the way home.

The plane left on time, taking off to the east and flying over Richmond and Wimbledon, then past central London with fine views, and down the Thames estuary: I could see many places I've walked, including the horrible Mucking Marshes, and Canvey Island. After that, there were just enough clouds that visibility wasn't good for a while, so I did most of the Times crossword. Over Austria, large fields divided into multicoloured strips, and the lake and marshes south of the airport.

Through another security check in Vienna airport, then to a pair of gates downstairs from which you go by bus to the plane. A big crowd of people going through gate 18 to Prague, but only a handful of us for Ljubljana.

The check-in girl in London had thought that 12D was an aisle seat, but on the small Adria (Slovene airlines) plane, it was actually the window seat in the last row. Too cloudy for much of even what view wasn't blocked by the wing until approaching Ljubljana, in a valley that seemed too narrow and steep-sided for an airport, with a very winding river.

I had expected immigration formalities something like those in Budapest or Prague, but there was no form to fill in and no delay. With the flight ten minutes early, there was no one waiting for me (just someone from a completely different conference), so a changed some pounds into tolars at the automatic change machine and waited patiently.

After fifteen minutes or so, a woman from the agency turned up for me. She apologised for her lateness and blamed the traffic. (I saw later that there was roadbuilding and single-lane traffic.) I got into the car and off we went. She seemed a bit surprised that I had been in Bled thirty-some years ago.

We were driving round a roundabout when her phone rang. After a brief conversation she said "Are you Polish?", which I denied; she continued round the roundabout and headed back to the airport. It seemed that three Poles at a medical conference organised by a different group but sharing facilities had shown up needing transport. It is a bit hard to get used to the fact that the academic organisers, the conference organisers, and the hotel management are separate and money and vouchers have to circulate. I have no vouchers . . .

A second time we were off, up a valley between the steep tumbled mountains, clouds, sun, warm air, dark green high corn in plots by the roadside. At one point, a small plane was taking off towing a glider - lots of good thermals today, I expect; a large bird of prey also using them (from a glimpse, it seemed black and white with wide wings curved in front).

Finally into Bled. A glimpse of the lake, with the old buildings on the clifftop that I remember, before we turned off to stop at the hotel. After checking in, a shower, followed by a beer (the one word of Slovenian I remember from last time is "pivo") and a packet of peanuts from the minibar, while I finished the crossword (not something I can usually do unaided!)

What else to do then but walk round the lake? A gorgeously beautiful path, full of views and surprises. The lake itself under wooded hills, steep cliffs rising behind to tops shrouded in the only clouds in the sky. The water green and full of light, with shoals of fish and mossy submerged posts. Yellow and white waterlilies in flower, the water so clear that their stems are clearly visible. Swimmers, boats, and ducks (some with ducklings) on the lake. Views constantly changing, from mouldering masonry, to deserted alpine meadows, to crowded tourist beaches with accents from all over Europe and beyond, to formal gardens in the town. The bells of the church on the island resound over the water while the castle sits sits smugly on its cliff behind.

Many walkers, cyclists, joggers, and rollerbladers on the path; the last group often with children (carrying them, playing tag with them, or pushing them in pushchairs).

The white tourist train went past, followed by the rumble of a real train out of sight somewhere.

After a while, bored with the path, I turned onto a forest trail up the hill. It went round the back of the castle, and then descended on a stepped switchback (made for the benefit of attackers, one presumes). The air in the woods was full of birdsong and large but slow-moving mosquitoes.

Back in town, I bought, wrote and posted postcards, then went back to the hotel (where a conference poster is now prominently displayed).

From the hotel guide:

"Values can be stored at the Reception, suits have their own safes."

They also provide "face clotches" free of charge!

When I rounded the corner of the hotel on my way out to look for dinner, I was met with a stunning sight. Right behind the castle was a cloud backlit by the sun, with evening rays spreading out in all directions.

I was so captivated by the sight that I sat in a roadside restaurant and ate watching the spectacle while the light faded. The colours turned peach and slate (this sounds contrived but isn't), while a duo played oldies on keyboard and guitar in the restaurant across the road while a couple of senior citizens danced with skill and obvious enjoyment, and huge ants scurried to and fro. When the colours had faded, I had finished a remarkably good meal, and went home to bed.


I was woken at 5:30 by the minibar fridge switching on: a very soft noise, but I wake convinced that it is the alarm and I have to get up and catch a plane. (Yesterday I woke up before the alarm, set for 5:30 but in a different time zone.) Memory of where I am returned and I turned over and slept again.

It was overcast when I got up, but the clouds were lifting. I sat at the sunny end of the terrace and had an excellent breakfast in the hotel, after which I sat on the lake shore for a while, listening to the bells from the town church. They ring very rhythmically, with simple, slowly-changing melodic patterns, almost like something by Philip Glass.

Scullers were rowing up and down a straight course, and a small convoy of boats returned from the island. Small birds skimmed low over the water catching insects, some hitting the surface; an occasional fish jumped.

The clouds drifted up and dispersed and the sun gained strength. I walked to the castle a different way (up through the old town, with fine old middle-European buildings, some in poor repair) and back behind the church. By the time I went running, the sun had burned the clouds back to yesterday's level, and it was quite hot. I ran round the lake in half an hour.

Back at the hotel, registration had started, and so I picked up my pack before going for a shower. I went out to lunch in the pizza restaurant in the shopping centre in quite a big group. The pizzas were so big that staying awake in the afternoon session was a struggle.

(Maybe there was more to it than that. With some difficulty I have been relaxing more in the last day, less inclined to leap up and be busy. After the last talk I was good for nothing but a nap.)

When I finally emerged at about 8:30 and went out of the hotel, I met another stunning view, The clouds had cleared completely, and the distant mountains were in clear view. The cone of Triglav stood aloof from a tumbled range with dramatic overhangs. They were bathed in light and casting long shadows in the haze, while the lake and the hills behind it were in shade. (A girl came by and tried to take a flash photo of the castle.) I had an ice-cream and watched the gold slowly replaced with blue-grey, and then went home.


I didn't sleep very well - perhaps I went to bed too early, or perhaps it's something else, since I ached all over. This morning the sun was shining, but breakfast was indoors, and the air-conditioning set quite cool.

The ache made concentrating on the lectures quite difficult: a pity since they included two of my co-authors. At coffee time I met another co-author for the first time, Dejan Delic, who is looking for countable groups with all subgroups homogeneous (there can't be too many of these, I think.)

The high peaks were in full sunlight and dramatically pale compared to the nearer wooded slopes. Clearly the white limestone was a perfect canvas for the setting sun to paint on yesterday.

I skipped lunch to lie down. Unfortunately my room hadn't been done so I read my email instead. Some trouble connecting: Putty stopped with an incorrect checksum, Netscape didn't seem to have Java installed. Fortunately Internet Explorer did the job. Lots of mail, most of which I brutally deleted. After that I was able to lie down for a little while at least.

As the day wore on, the ache subsided, and the clouds came over. After the talks, I ran round the lake with Richard Nowakowski. It was quite a bit cooler and very humid. Though I creaked a bit starting out, I soon fell into a good rhythm. Richard had to stop and walk several times, and by the end the pace was much below what I was capable of; yet the time was 33 minutes, quite respectable.

After showering, he and I both arrived at dinner dripping sweat. I ate with Cheryl and John; she will introduce me tomorrow. By the time dinner was over. it was raining. I worked for a while and went to bed.


The aches plagued me all night and kept me awake; it was very hard to get comfortable. A hot shower helped a bit.

The morning was sunny, the faces of the distant mountains bright white - no wonder they take the colours of sunset so beautifully. I couldn't settle to anything before my talk, but once the adrenaline got flowing I was fine. Someone in the audience suggested delta-matroids as the right concept for permutation group bases: I don't think so but I will check.

Bojan Mohar made an interesting suggestion. As well as minimal base size, he has considered the smallest cardinality of a set of points with the property that the meet of the orbit partitions of their stabilisers is trivial. Of course such a set is a base, so this number is not smaller than the minimal base size. He has examples (automorphism groups of Paley graphs of prime order) where the base size is 2 but his invariant is about log n.

During the morning talks I remembered that I have seen something like this before! Laci Babai bounded the order of a uniprimitive permutation group by bounding the base size, and if I am not mistaken he did this by bounding the "separation number" in Bojan's sense.

Also, the definitions of irredundant, minimal and (probably) greedy base extend to separating sets in this sense. Lots of interesting stuff to work on here!

I walked round the lake, stopping for a pizza at the beach near the outflow (and of course it was far too much). The breeze had got up; waterlilies and swans bounced up and down on the chop.

In the late afternoon, a cracker storm blew up. The power flickered, and the computers in the conference office lost their internet connections. From the back of the lecture room, the rain sounded really heavy. But by dinnertime, it had stopped, and the sun shone from under the cloud cover.

Dinner was traditional Slovenian food, by candlelight with zither music (those standards that you know well but can't put a name to). Of course this took longer, and the problem session was somewhat delayed. It was very delicious but again, of course, there was far more to eat than I needed; I should have skipped it.

I presented one problem at the session: finding the smallest maximal clique in the graph on the symmetric group, two permutations adjacent if they agree in fewer than s points. Most of the other problems had little appeal to me, apart from the characterisation of isometric subgraphs of Johnson graphs..

The aches seem to be easing a bit. Not before time!


A glorious morning; early cloud cleared quickly and the views are bright after the storm. After breakfast I took a small walk to the town, looking for the bus station, which I didn't find (I've been told it exists but it's not on any map).

Morning talks about geometric things: Branko Grunbaum trying to reverse 2500 years of history by giving a definition of a polyhedron; Victor Chepoi with some very complicated results on median graphs and generalisations; and the regular Cayley maps team of Tom Tucker and Marston Conder with lots of fine detail about finite abelian groups.

I didn't need a big lunch before the excursion, so just had peanuts and juice from the minibar.

The excursion was both exhilarating and frustrating. We went by bus, first along the highway towards the tunnel under the Karavanke mountains to Austria, then just past the city of Jesenice with its vast and mostly derelict ironworks rusting away. We turned off onto a smaller road, where Tomaz Pisanski told the story of the day Slovenia declared independence, which occurred during the conference 12 years ago, and whose anniversary today is.

Then we turned onto the road over the Vrsic pass. This road, built by Russian prisoners during the first world war, in an area where a vast battle with a million victims (later written about by Ernest Hemingway), boasts 24 hairpin bends on the way up, and 26 on the way down on the other side.

We stopped first for five minutes at the Russian chapel built by the prisoners. It was of course locked. By mutual consent, Richard and I set off for a short walk, counting on the fact that five minutes would be ten. We saw some very nice orchids, and were back just as the last stragglers were boarding the bus.

Climbing higher, there were lovely wildflowers by the roadside, and spectacular views of the limestone mountains, including one with a window and the face of a girl pointed out by the guide. No stop at the top, but down with lovely views of the Soca valley, then down the valley a little way to the museum.

Why did they have to take us to see mountains and rivers in a museum when the real ones are all around? Most of the picture show was wasted on me, but there was a nice video installation filmed under water and shown on eight slightly time-shifted screens. Of course they dragged us away long before it finished! Also we heard the legend of Zlatorog, the golden-horned mountain goat who features on the beer bottles.

After the museum tour, it came on to rain, and so we were spared seeing wildflowers in a museum (we actually got to see the real thing at another short stop on the way back). The final stop, scheduled for 40 minutes, was at an alpine hut for a drink. Richard and I agreed to have a quick drink and then a short walk. Of course, the drink was anything but quick, with so many people all being indecisive; we set off ten minutes before advertised departure time but once again gambled successfully on a considerable delay.

We got to the top of the hill and were faced with a hallucinogenic view of these huge masses of limestone. We walked along the ridge for a while drinking in the view (including a closer look at the girl's face) and then decided to take a trail leading to the base of the rock face. We didn't quite make it, and then had to run down, but how much better mountains look this way than through a bus window!

I forgot to say that we saw a large bird of prey going into a dive into a small clump of pine trees.

Another impression from the day: the faint blue colour of the water in the rivers, both Sava and Soca.

(The placenames are taken from a very small scale map - I hope they are right!)

On the way back, Pavol Hell gave me enough information to introduce him tomorrow morning.

Back at 8:20 (much later than advertised), and so to dinner and bed.


The aches having almost gone, I was able to sleep in comfort. No problems with the session I chaired; I was able to make a small connection between us (we both left our home countries in the same year to study on the other side of the world, though for different reasons). Nice talk too.

At coffee, Misha Klin told me about a student of his who has a list of vertex-transitive association schemes on up to 23 vertices; he will encourage him to make this information available.

I skipped lunch to go for a run. Round the lake, but I decided to include the castle hill. The first turning after the inflow just led down to the road again. The second would have done the same thing but I noticed I was on a familiar path and backtracked; a very steep pinch took me to the top, and I went back through the town. The hills stopped me a bit but otherwise it was very easy. The birdsong in the forest was nice.

In the afternoon coffee break, Anthony Bonato proposed me a problem which I was able to solve, not in the way he expected. The problem concerned a model for the Internet graph (trendy stuff now), and I showed that the infinite limit of his model is almost surely the countable random graph.

During the afternoon, it clouded over, and in the last session there was a cracker thunderstorm. Dejan Delic had just been introduced when the power went off, leaving only the emergency lights. He had to wait nearly ten minutes before he could start. It was still raining heavily when we assembled to wait for the bus to the dinner, so no outdoor conference photo.

For dinner they took us by bus to Radovljica to a fine old restaurant. We didn't seem to have climbed, so when we got out of the bus I was surprised to find myself in a high place above the Sava valley. The storm had cleared and the sun come out, but the valley was full of wisps of cloud backlit by the sun, making a very fine display as they wended through the pine forests on the hillsides.

The dinner began with a wine tasting; five bottles of wine between (in our case) half a dozen people, accompanied by very nice sausage en croute and cooked ham. Then we were shepherded upstairs for a dinner which involved two soups, three kinds of meat (beef, lamb, and venison which Tomo says is actually elk and was very delicious), and infinitely many desserts.

Bojan invited me to propose a toast to the conference, which I was delighted to do. Afterwards, during the meal, he and I discussed having a European conference along the lines of the national conferences - unlike the current Euroconferences, everyone would be welcome, and all would be allowed to talk. I hope this goes further.

At a certain point in the evening, Marston Conder proposed a game in which someone sings a song and then nominates another nationality to follow. This produced some extraordinary performances by the Korean and French teams. Inevitably I got called in to be the English representative; since Cheryl had already been the Australian, I thought it would have been unsporting to play that card. I sang a verse and chorus of "Yellow Submarine", which seemed to hit the spot OK.

And so home and to bed.


Mathematicians were unsurprisingly thin on the ground at breakfast. By 8am, apart from me there were only Ken-ichi Kawarabayashi (who swapped with Richard Nowakowski to give the first talk, as he is leaving early), Tomo and his wife. Richard arrived as I was leaving. I give full marks to the Slovene wine; no ill effects at all this morning, though I wasn't very hungry, for a different reason!

After breakfast, I went down to the tourist place and bought a 1:30000 map, with a view to a walk in the afternoon (weather permitting). But plans were changed by the announcement that there would be a small "survivors' party" - the conference would treat everyone to an ice-cream in the lakeside restaurant.

After the talks (both Richard and Bojan said things that made me prick up my ears), Tomo showed some conference pictures - now digital photography has changed all this; after the red eyes have been fixed they will all be put on the web! And then it was over.

Rather than lunch, I took a walk, determined to get at least some use out of my new map. I went up the road behind the hotel, round behind the hill with the ski lift, and back in front of the hill. A sizeable cliff; and two cyclamens in flower on the path. Wild strawberries far from fruiting.

Back at the hotel, we set off for the restaurant. It was now beginning to cloud up; by the time we sat down, the thunder had begun (I took the precaution of sitting under an umbrella), and soon the rain had started in earnest. We crowded in, and neither I nor my very fruity banana split got wet.

After two hours, some of us decided to brave it and go back to the hotel. Of course, that did the trick; by the time we got back, the rain had shopped, the sky was clearing, and rags of cloud were draped over the forested hills around the lake.

A shock awaited me when I got to my room. The chambermaid had left the window open, and there were floods of water on the desk and everything on it. The Best Western brochures, the Bled brochure, and the telephone notepad were a complete write-off. Anthony Bonato's two papers were soaked, but fortunately they had sheltered my tote bag; and in the bag, the notepads had sheltered the rally crucial items (tickets, passport and organiser). I told the front desk, and a woman came to mop it up while I spread papers out to dry.

While waiting, I went down to the terrace to try to prove what I told Bojan at the lake, that the line graph of a complete graph has separation number one more than its rigidity number. The waiter came so I had a beer; the sun came out so I looked at the shining clouds; and the English oldies came to have tea. They were playing watered-down versions of slushy sixties hits. Eventually, when I had sorted it out - it turns out that I am correct if the order is not divisible by 3, otherwise the two parameters are equal - I couldn't stand it any more, and went away.

Back in my room, the wet paper was drying out satisfactorily. I had a sudden panic when I couldn't find my keys. Most likely I left home without them. I typed up my musings to send to Bojan.

After dinner, Richard and I decided on one final walk around the lake. Once underway, we decided to vary it by climbing up to the castle, and then walked along a forest trail to the bathing place. The light in the forest was dim, the pine needles soft underfoot, and the birdsong loud in the twilight.

When we got down, the mountains behind the lake were several shades of pale blue under a soft lilac sky. The lights of Bled reflected in the water, and hear at hand, a boat was tied up. By way of contrast, about a dozen headbangers were in the car park, throwing themselves around frenziedly to loud thrash music.

At this point it began to rain, and we were quite damp by the time we got back to the hotel, though this light shower was nothing compared to this afternoon's effort.


A day with lots of waiting around. I had breakfasted and checked out an hour and a half before the airport transport came. Richard and I passed the time chatting. The conference moving in was of German investment consultants. They were mostly in suits or at least shirt and tie, except for one who was conspicuously dressed down in pressed jeans and immaculate T-shirt; Richard conjectured that he was the boss.

Our driver was the same one who had brought me from the airport a week ago. The journey was fast and smooth, with several interesting things to see: lots of blue chicory flowers by the roadside; a hawk fluttering and then going into a vertical dive onto its prey with barely a pause before hitting the ground; an old castle on a hilltop; a farm with a big herd of ostriches; a large bird hovering over the airport (awaiting clearance for landing?).

At the airport, check-in, security and passport control were finished in record time. Even the duty-free shop didn't detain us for long, though I did buy a bottle of merlot (hopefully similar to the one at the dinner).

So there was nothing for it but t have a coffee and talk the time away until Richard's flight to Munich was called. He goes on to Manchester (heading for Bangor); curiously, the very next plane was direct to Manchester (presumably a charter). We said goodbye for a little over 24 hours at the departure gate.

It seems that the only commercial flights from this airport are international (though many of the destinations would have been internal before Yugoslavia fell apart), and most of the airlines flying here belong to former Yugoslav republics. I wonder how the logistics of dividing this up were worked out.

At a booth in the departure lounge, you can charge your mobile phone free of charge. (The words are not the same in Slovenian.) It took me a long time, and a mental dissociation, to notice that the large H of the duty-free shop's logo concealed a smaller G.

The flight to Vienna was quick and uneventful. I was in the same seat as before, right at the back; this time on the side away from the mountains, so there was little to see but cloud formations and blue fading into blue. The wind must have changed; our approach to Vienna was quite different, over mixed urban and rural landscape, with plotted fields sandwiched among highrise estates and huge railway yards.

In the airport, the long wait began. Nowhere to sit in the gate area, so I had to resort to a seat in a transit corridor (opposite a mural saying "More convenience for our passengers") for the four-hour wait.

After an hour, I needed a walk, so explored the terminal. Not a long job; five minutes took me to every nook. In desperation I bought a Guardian from one of the four shops, for the sake of the crossword. Browsing it, I find a reader reporting seeing the first second-hand copy of the latest Harry Potter book. In an hour and a half, I did all but two clues of the prize crossword, and the organiser got the last two for me, one being triply clued.

Then I returned to the gate area, only slightly less frenzied (eight long-haul gates and only twenty seats!). Two very big flights, to Montreal and Toronto, were leaving at the same time as ours.

Suddenly a queue formed, and moved quite fast, and we went through security and immigration and into the gate lounge for another wait. Again suddenly another queue formed and we were on the plane.

Take-off retraced our path over the same landmarks. The cloud base was quite high, and we had good views of the Danube in its two channels, and a new road crossing high viaducts heading into the mountains, before the whiteness surrounded us. But soon we reached a long break in the cloud, and had fine views of the mixture of forest, farms, and villages of Austria and southern Germany.

After that the cloud gave only intermittent views. Once there were two planes below us: one near the ground, probably landing in Frankfurt; the other, crab-wise, crossing our path just below us.

My neighbour was an 18-year-old Sarajevo boy on his third trip to England (his favourite country) though his first solo. I gave him some help with his landing card, and was pleased when we had a splendid view of central London.

The immigration queue was short when we arrived, but lengthened alarmingly rapidly behind us. Less than half an hour from touchdown I was on the Piccadilly line.

Tehran, 8-21 August 2003


Quite a busy day. I saw both Robert and Abi, made a web page for the London Algebra Colloquium, and began the process of filling next semester's programme; at 4pm the DTRS external representation document beta release was frozen and I got a printout to take with me. Then home to change and collect my bag, and off to the airport.

Terminal 4 is one of my least favourite places. The travel agent's letter had said I should get there 2 hours and 30 minutes before departure. With my usual caution it was nearer 3 hours. I stood for an hour while other flights were given check-in areas but ours was simply told to "Please wait". Finally I asked one of the BA employees, who told me that check-in would be in zone A and I should join the queue.

I stood in the queue for 15 minutes - a frighteningly long queue, with no perceptible movement. Then another BA employee came by and asked the people in front of me where they were going. They said "Luanda". "You should not be in the queue; please wait." Then I told my destination, expecting the same response. Instead I was taken through a rope barrier to a much shorter queue, and ten minutes later I was checked in. Through security, I had time for a sandwich and a visit to the bathroom, and then with an hour to go we had a gate number (the long trek to gate 19) and I went and sat and waited.

Right on time we were called to board. But instead of boarding the aircraft on the stand, we were directed to the ground and taken on buses to a far corner of the airport to find our Airbus. All aboard, the captain announced a five minute delay while the final catering supplies were delivered. This lengthened to an hour before we were finally off.

Now somewhere over Europe with dark below and a nearly full moon keeping me company outside my window, I can't sleep until the dinner has come, so I can think about my first talk (three hours after touchdown) and write this. Why am I going to Iran? This is a country which has been in the news twice recently, once for the murder of someone for taking a photograph, and once because of a refugee who face execution for the "crime" of bigamy if he returns there. Moreover, I (in common with the other westerners at the conference) have received three emailed death threats. This is all on the basis of religion, supposedly. Do they really want me to believe that a religion which attributes to its God the properties of mercy and compassion demands such things?

The captain tells us that Tehran time is three and a half hours ahead of London - just to make setting my watch more difficult! The Psion confirms that, the clever little thing.


Dinner over, lights too bright to sleep. Flight half over. A bizarre movie which seems to be mainly about kids in orange overalls digging holes in the desert - it's hard to discern the plot without the sound. There was an altercation just now between my neighbour, who was sleeping with his seat right back, and the person behind him who was obviously having some difficulty eating his dinner.

Eventually the film ended, and they showed the flight data, according to which we were just crossing the Black Sea coast. I looked out and, sure enough, a large sprawl of lights ending abruptly in a pool of blackness. Later, we crossed the southern coast, with one much smaller town visible, and then little but the occasional town. I dozed for a while, and then the cabin crew came round with drinks. It was still dark out my window, but on the other side, dawn had broken, with a line of lighter above the darker earth (that must have been the Caspian Sea), and orange sky shading into blue.

Just before landing, the plane turned to the north and west and I had a view of the city and the spectacular mountains behind. Tehran is like no other city I have seen; like every big city it has a characteristic appearance, but the apartment blocks are cardboard coloured and the earth is sand-coloured, so I was inexorably reminded of toytown. We were on the ground, to the minute, at the time they had told us in London.

Getting through the airport was a bit slow - the customs officer dealing with the queue I was in had to keep going away with difficult customers - but eventually I was through, met the contact from IPM, and was on the way.

Iranian traffic is as chaotic as Indian, but much more homogeneous: instead of having pedestrians, bullock-carts, cars, buses and trucks sharing the road, it seemed to be almost entirely medium-sized white cars. The traffic was quite ferocious (it was the morning rush hour), but gradually we got past the worst of it and came to the IPM guesthouse in a pleasant suburb very near the mountains. I dumped my bag, had a very quick shower, changed my clothes, and just had time for a quick breakfast (including carrot jam) before we had to go to catch the bus.

This is perhaps the most friendly place I have ever been. And, a good sign, during the day I discovered that young people are not shy in coming up and asking me questions. Moreover, they look after us very well: lots of computers for the visitors in a special room where we can work, tea and coffee and Iranian Danish pastries (nicer than the Danish ones!); a "Daily News" which began with a feature on my mathematical ancestry and also included the recipe for the rice dish we had for lunch (Bagali polow).

My talk went well despite the tendency for my eyelids to droop. And later, both Sam Hedayat and Willem Haemers brilliantly set up stuff for me to talk about later.

The IPM itself is in beautiful grounds where the Queen used to live before the revolution. (I am told that Reza Khosrovshahi has her office!) Huge mature trees and rose gardens; a building up the hill for the postdocs with good facilities; what seems to be an extensive library. One of the most spectacular mathematics institutes I have been to.

After the day's events most people went back to the guesthouse for a rest, but I decided to keep going until bedtime. I read my email and then talked to the organisers until it was time for the reception.

Several times I have been reminded of Pasadena (both Charles Johnson and Rick Wilson have mentioned it too). The grounds, not unlike the Huntington; the bare mountains very close; trees full of noisy parrots. At the reception in the garden we had some very good fruit (melons, fig peaches, grapes and cherries) and desserts (ice cream and an Iranian speciality). And so home to bed.


I slept well and woke up just before breakfast, in time to start writing notes about orbits of PSL(2,q) on k-sets, which I had discussed with the young guys (Tayfeh-Rezaie, Maimani and Omidi). Then off to the IPM in a bit of a rush. Interesting talks which I won't report in detail. After lunch a few of us went to the park at Niyavaran (opposite the IPM) which used to be part of the Shah's private palace, before we went off on the tour to his complex of more public palaces (to one of which Sam Hedayat had been, to be presented with a University medal).

The main palace was grand but not overwhelmingly so, done in the French style but the French would have done it better. The two things to catch the eye were the huge and absolutely priceless carpets on the floors, and some paintings of hunting and war scenes in traditional style around the big skylight upstairs. The pictures tried to speak to me but I couldn't understand what they were saying. A hunter had just shot a lion in the process of devouring a deer. The lion and the deer were in the position of sexual intercourse, and while the lion looked disdainfully at the hunter, the deer looked at him with real fear.

The smaller palace boasted a mirrored room, all the tiny mirror segments having been set by hand and reflecting the light of the chandelier at odd angles. It reminded me a bit of the Jain temple in Calcutta.

A stop at a teashop, then back to the guesthouse for the customary rest.

The sense of oppression, which had lifted, came back with two stories I heard today. While wearing a T-shirt might be acceptable, shorts most definitely would not; a student was thrown out of university for going running in shorts. Richard Bean was hauled off by the police at dawn because a neighbour had reported that there was a foreigner living there. What absurd things are criminalised by this regime?

Gradually we have become aware that we are followed round by security men. Some people think they are watching us; I think it is more likely that the death threats were taken seriously and they are guarding us.

Working out Moebius functions of some groups for the k-orbit problem gave me one surprise. After finding a very nice argument for dihedral groups, I did the calculations for A4, S4 and A5; if I am not mistaken, the answer is the group order divided by 3, 2, 1 respectively. These numbers have an obvious resonance in connection with the Lie algebras E6, E7 and E8. Probably the explanation is well known to some people. But it can't be a general phenomenon for reflection groups since nothing analogous holds for the cyclic and dihedral groups.

In the evening, we went to the Jamshidieh park, a super place: on the slope of the mountain, the landscaping slowly moving up the slope. The bottom section had shone paths, lanes among the gardens and avenues of trees, stepping stones across ponds. Each higher level has a restaurant featuring some traditional Iranian cuisine - Turkmen, Azerbaijani, Kurdish, etc. We went to the Kurdish restaurant. Like the others, half of the walls were living rock, and it had many interconnecting rooms and terraces, some with tables, some with divans, and with appropriate decor (an old astrolabe in the Azerbaijani section).

Further up, the steps were cut out of the rock and not always very well defines. The sprinklers were on; apart from watering us several times, they made the rock quite slippery.

We sat on the front terrace above the restaurant. There was a splendid view over Tehran, and as the darkness fell, the smog became less evident, and the lights came on. A nearly full moon rose, and later Mars (a week from its closest approach to the earth, fiery red - surely the planet I saw from the plane) made its appearance.

A good meal - juice, seedy bread and salads, lamb cooked in several different ways, alcohol-free beer (with added vitamins) to drink. Lots of good talk too: I learned a lot about the recent history of Iran, and its relations with the USA.

Then back down to the car park to catch the bus. The wet rocks made even Willem remark that he was glad the beer had been alcohol-free!


I meant to be up early - Mandana had taken my millennium poem very seriously, and had asked to read some more, so I selected a few and put them on the web. But since I overslept, I only just had time to do this and have a rushed breakfast before time for the coach.

Mandana showed me a book of poetry by Hafiz which belongs to Kathy Wilson. I opened it at random and found on one page a poem urging us to live in the present, and on the facing page a poem in code. This is someone I must read!

At least one talk contained material familiar to me: Dean Crnkovic talked about symmetric (36,15,6), (40,13,4) and (45,12,3) designs admitting Sp(4,3). I couldn't restrain myself from telling him afterwards that much more is known.

After lunch, a remarkable talk by Afra Zomorodian, justifying why a computational topologist is at a combinatorics meeting. (He uses "persistence" and some computational tricks to detect Betti numbers from simplicial approximations.) Then Willem Haemers gave us a nice theorem (Bruck-Ryser-Chowla in the singular case, from which various new nonexistence results follow.

A little competition was run, open to students, to discover the middle names of the invited speakers. The winner adopted the simplest strategy - she asked us! The prize was having her picture taken with the six of us.

Apart from parrots, the only birds in evidence are grey crows with black heads and wings, who strike dignified poses.

In the evening, after only a short rest, we were off in the bus again, to Reza Khosrovshahi's apartment for a delightful party. Reza's wife is a painter, and a very good one - I had wondered about asking whether any of the paintings were for sale, and had decided it was impracticable, but Kathy Wilson went ahead and bought one. His son plays the daf (frame drum) very well, and gave us a short performance after Rick had played the flute (and Kathy sang) and before yours truly strummed a rather battered steel-string guitar. The meal was superb, and there was plenty to drink. Such a good party that we didn't get home until 1pm.

12/8 2003

I only just managed to get up, wash some clothes, and have a rushed breakfast before it was time to catch the bus.

Richard Brualdi gave us a packed but beautiful talk, generalising the RSK correspondence and Bruhat order from the set of permutations to the set of matrices with prescribed row and column sums.

I talked about the DTRS project and, I think, raised some interest, but there was no time for discussion; an extra talk (by Ebad Mahmoodian) had been slotted in before lunch (in the garden today) and then off to the carpet museum.

That has to be one of the great sights of Tehran. Among other things, they have a reproduction of the oldest known carpet (2500 years old, found frozen inside a block of ice by a Russian archaeologist), and we had a chance to watch the museum's resident carpet weaver (who made this reproduction) at work and ask him questions. There were many really beautiful traditional carpets, and also some oddities: a carpet featuring famous people (including Napoleon, Nelson and Washington), a carpet with the signs of the zodiac in two different systems and described in three languages, and a carpet with a beautifully rendered English fox-hunting scene (even to the highlights on the horses' flanks). The paisley pattern is typical Iranian, though there is dispute about what it symbolises (theories ranging from a foetus to a Zoroastrian flame).

Back to the guesthouse for a short rest, then on to the next part of the packed schedule: the concert. There was a delay in starting; the Director was stuck in a traffic jam and we had to wait for him. They group (two tars, two bass tars, two kamanches, nay, santur, percussion and singer) played a non-stop selection in two "systems", the first mahur dastgah (major) and the second nava dastgah (roughly dorian, but with the sixth somewhere between the flat and natural). The next to last piece was in 5 beats (2+3); I don't know if this is traditional Iranian rhythm.

Rick played one piece after that; the Iranian musicians came out to listen and applauded him when he finished. (This was the surprise we had been promised.)

Then it was the dinner, and very fine the food was, with fresh fruit (including figs and watermelons) to follow.


Today, at fairly short notice, I was asked to chair the problem session, which I was happy to do. A good number of people contributed problems. A couple had misunderstood the instructions, and thought that I just wanted the problem handed in. One problem about crossing number was solved during the session. Afterwards, Carsten Thomassen, Manouchehr Zaker and I reduced another problem (finding a colouring of a graph given an oracle for the chromatic number of induced subgraphs) to the problem of finding a colouring given the chromatic number, which we think is NP-hard (but will have to check).

Lunch was outdoors, a pleasant change to the usual routine.

In the evening we were invited to Shahriar's in-laws' house for a party. The lady of the house had put on a fantastic spread, almost all made by herself. My impression of Iranian food, the one preconception of the country I had before coming (as a result of a not very good Iranian restaurant in Los Angeles) has completely changed. It was a feast for the eye as well as the palate.

Again a guitar was produced (a better one this time) and I was asked to play (after the Wilsons had done a performance).

So once again it was nearly 1am when we got back to the guesthouse, Mandana was on the edge; she had learned that she must accompany Dan Crnkovic to the airport at 2am, and had said some intemperate words. I hope she hasn't compromised her job; she is a jewel who will not easily be replaced. At least it ended up that she didn't have to go. This was a glimpse of what might be happening behind the scene to ensure that we are so well looked after. The bus driver certainly has to keep very long hours; the man who among other things produces a plate of melon for anyone who pauses near the kitchen for more than a minute seems to be always on duty and always smiling and helpful.


At 7:30 I managed to wake up and read through my slides for my last talk. I found that the ones with the data on row parities and derangements in random Latin squares of order ten were missing. Fortunately there are computers in the guesthouse; I logged in to my computer and read the TeX file for the slides, copied it out, and wrote out replacements by hand. Then, of course, I had only a very short time to have a bite of breakfast before it was time to go.

Mandana was back on duty with a smile on her face.

The morning session was long, and included a presentation by two undergraduates on their work on a concept generalising chromatic index (it is also required that, if two vertices are at distance k or less, the sets of colours on edges at those vertices must be distinct. Not exactly my cup of tea, but they gave remarkably good performances - for both it was their first conference talk and their first talk in English, and yet everything was clear.

My talk went OK, and then Richard Brualdi (who had the grace to finish a few minutes early) gave a very good thanks to the organisers and we were done. It remained to have lunch, to say many good-byes and take many photographs, and return to the guesthouse. We were all so tired that after the obligatory melon we retired for a nap.

We assembled for tea at 6:30 and then at 7 it was back on the bus. In the garden of the Shah's private palace at Niyavaran there is a little craft fair. We walked around the stalls. Rick Wilson bought a ney (which he can't play, and probably will never learn, since several other kinds including shakuhachi are ahead of it in the queue, but as he said, he can hang it on the wall). It had some very delicate pokerwork done by the stallholder, though it was made by someone else. They had a beautiful tar with a flower picture on the front, but one string was missing and the others put on wrong. Mandana bought us all a drink of perfumed water, but many people didn't like it.

Afterwards, we decided to walk home. We walked down the edge of the park, and decided to do a circuit. At one point, we heard some music, and found a concert about to start in a tent; I would happily have gone, but the others wanted to get on. The park also had the music of running water and cicadas. At the bottom of the hill, the fountains and coloured lights in the big pools were on.

We phoned the guesthouse to order pizza. (Two types are available: minced lamb or vegetable.) Then Willem undertook to guide us home. After getting lost a couple of times down dark cul-de-sacs, it took longer than expected. At a bakery in a small side street, one of the guards (who has been very friendly) bought us a loaf of some kind of shortbread-like confection - I felt happy walking past lovely old houses, eating the bread, and listening to the stream which runs in a drain here carrying water and coolness from the mountains.

Mandana told me that although public life is very restricted in Iran, private life is completely free. I demurred, thinking of running, and she admitted that not being able to use a bicycle does bother her. Women can drive but not cycle: not very green!

The pizza arrived at the guesthouse at the same time as we did. We ate it, then those who leave straight after the tour said goodbye to Mandana and we went to bed.

15/8/2003: Tour of Esfahan

After a somewhat disturbed night (partly by Richard Brualdi teaching the kitchen man to play solitaire on the computer outside my room), I woke on the dot of 6:30, and managed to get ready in 20 minutes. Then I had time for a leisurely breakfast before the coach at 7:30.

The journey to the airport was much less fraught than my journey the other way on Saturday. We made a small detour to pick up Reza, and arrived there at about 8:15. So there were fourteen of us: four organisers, six invited speakers, Kathy, two guards, and the photographer.

On the way I saw two things new to me in Tehran: beggars, and men on bicycles.

No problems checking in: they did us in bulk and didn't even look at identification. Some delay at the gate, though; apparently the seats on the plane needed fixing!

I was over the wing and not by the window, so little to see except glimpses coming in to Esfahan. But they gave me one of the few English-language papers they had, so I read that. A mixture of kids' stuff ("What do you get if you cross a rabbit with a termite? Bugs bunny!") and news about whom the foreign minister had telephoned recently. Quite a lot had an anti-American slant: a report that the Americans had used napalm in Iraq taken from the Independent. Scary, too: an item about the Guardian Council explained how it had rejected two bills passed by Parliament. These implemented two UN resolutions, one forbidding discrimination against women (rejected because against Sharia law, which I infer enjoins such discrimination) and one forbidding the use of torture (rejected on the bizarre grounds that someone would have to pay to implement it - so a country which can afford to build the third tallest tower in the world cannot afford to implement a law forbidding torture). An article listing Saddam's crimes, which seem to consist almost entirely of actions against Shi'ites. Also an article about the group who gave the concert we passed last night: a world music group mixing traditional Iranian instruments with electric guitars.

Esfahan airport is in the middle of barren desert, but coming into town things became steadily greener: trees, herds of goats, then fields of wheat, and many flowers in the town. A minibus and guide met us at the airport. He refers to us as "the fourteen innocents".

The first stop of the tour was at a mausoleum (to, I think, the brother of the eighth Imam of Shi'a) opposite the Ali mosque, with a minaret 50 metres tall built a thousand years ago. The mausoleum had fine marble floors, carpets, and calligraphic tiles including 110 names of God. Some very fine tiles outside as well. The huge pictures of ayatollahs outside such places disturb me in some way: I thought Islam forbade the making of idols (which these clearly are!)

The next was a real surprise. The last thing I had expected was a cult of muscle building and martial arts. In a "gymnasium" or "power house" we watched a performance which (according to the guide) originated at the time of the Mongol invasion, when the Iranians toughened themselves to resist the Mongols with these exercises, including jumping and fast spinning, juggling heavy clubs (up to 30 kilograms each), and swinging vast metal bows over their shoulders. The walls were covered with pictures of men with bulging muscles (two of whom were in the audience, though now much older). The master of ceremonies had a huge drum and a microphone.

But it wasn't just physical. Among the audience were several poets who took turns to perform (and apparently at one point argued in verse, though it passed over my head). The whole performance was very ritualised. Someone about to perform would beg others to go first, and they would all refuse (especially if he was old and revered). At various points, health was wished to various people (including our group). It turns out that our guide is involved in this: he took a turn at one of the exercises with clubs, and greeted many of the performers.

Remarkably, given the many male buttocks under tight fabric, ladies were not forbidden, although none of the local ladies come.

The whole thing went on for an hour and a half; I was getting a bit numb on the hard seat. Then we went for lunch in the Shahrzad restaurant, the best in central Esfahan.

From an unprepossessing exterior, we ascended the stairs to a large and impressive room full of people. The windows were coloured glass, there were mirrors on the walls and ceiling, and there was a small glassed-in area with many green plants. We were provided with a plate of bread and a plate with half an onion and some mint leaves. First we had barley soup, then a selection of four dishes: chicken in a delicious sauce, rice cake with saffron, yoghurt and chicken, minced lamb kabab, and lamb shank. Extremely tasty. Mock beer or Fanta to drink. Tea, coffee or dessert to follow.

Then to the Hotel Kowsar (the name is one of the rivers of Paradise), for a complicated check-in with a very long form to fill in, and a nap before the next round of sightseeing (though I squandered the nap time on my notes, and wished I'd squandered it on walking).

First stop after lunch was the Masjid Jameh, which the books translate as "Friday mosque" but according to our guide means "congregational mosque". The guide, Reza, revealed himsef as a poet and an engineer as well as an athlete. On the way out he recited to us four lines of his 54-line poem about Esfahan, and in the mosque he discussed the engineering principles that have enabled a mud-brick structure to stand for so long. Some of it was a bit dodgy (e.g. mud bricks are "a semiconductor", and right angles allow light but not heat, but in the main he was sound. The huge area of mosaic was most impressive. For all that, the place was utterly deserted.

Next we went to the "shaking minarets", a tomb in a structure with two minarets built so that, when one is shaken, the other visibly moves as well. This has been going on for 700 years. A strong man shakes the minaret every hour. (We were told that until recently anyone could do the shaking.) It was built to attract the gullible with an apparent miracle.

Next to an isolated red hill topped with the remains of a vast Zoroastrian fire temple. Our guide had of course been involved in measuring it. The site was spoilt by a reinforced concrete reservoir just below the temple. It is no longer used but cannot be demolished for fear of damaging the temple -- but at least they are considering other methods of demolition (chemical or laser).

But no time to climb the hill; we must be off to our next stop. Back into town we took a narrow meandering road by the river. It seemed too narrow for the bus, and indeed we were stopped by the police and fined. Thousands of people were out picnicking by (or even in) the water. There were many irrigated rice fields, and some vegetables (most of which I couldn't recognise).

Our next stop was a working Zoroastrian fire temple. Because the priest wasn't there, the guide took it on himself to explain to us the basic tenets of Zoroastrianism. Founded by Zoroaster, who lived a hundred years before the Buddha, the religion has simple and attractive beliefs. The slogan is "good thoughts, good speech, good actions". They like light: they pray in the direction of the sun during the day, and the fire by night. They respect nature, which led them to air burials (which paradoxically have been banned by the Environment Department). Later the two Rezas disagreed about how many Zoroastrians there are in Iran: the guide said 40000 but our Reza claimed 120000.

Now it was time to eat, so we went to a fast food and tea house (which didn't serve tea). Most of us were content with a salad, though some went back several times.

We took our tea in the splendid Abbasi Hotel, converted from a caravanserai some time ago. We sat in the courtyard, with soft lights, fountains, quince and persimmon trees, and the floodlit dome of the Blue Mosque like an ornate moon rising just beyond the trees and rooftops. Afterwards, we looked around the public rooms and saw the ornate interior, far grander than any of the Shah's palaces we saw in Tehran.

A visit to the Imam Square, second largest in the world (behind Tienanmen Square and ahead of Red Square). We walked round the square with its two mosques and royal palace. The popular sport seems to be riding motorbikes with two or more people on board through the crowd at a faster than safe speed. Mars was high in the sky, a waning moon chasing after it.

Next the bus was supposed to take us to the old Pol-e Jubi bridge with a former aqueduct above. But there was a revolution led by Willem, and finally five of us with one guard set out to walk. Apart from a couple of scary road crossings, it was a very pleasant walk down tree-lined streets. The bridge was a fine structure in good shape, and the view of lights reflected in the river was really stunning. Across the bridge, it was just a short walk to the hotel: there were traffic lights, but they made little difference to the flow of traffic. And so to bed: more of this ordeal tomorrow.


On a wall this morning, the same size and style as the idolatrous pictures of ayatollahs and the anti-American slogans, was the Windows logo.

Further in general, Shahriar remarks that the people who suffer most from the regime are small children. What is done in many homes is illegal, though tolerated. (I opened the Koran at random this morning and found a verse forbidding one to enter another's house without knocking at the door and being given permission first.) So the children must learn not to talk outside about what happens in the home, or indeed to lie about it.

We went first to the palace with forty pillars, the Chehel Sotun. Actually there are twenty pillars; the number is made up with reflections in the vast pool. The pillars were wooden, and have been attacked by insects; so they have all been given steel cores.

Inside the palace we saw some extraordinary miniatures, including a picture with people committing homosexual and lesbian acts, to say nothing of the inevitable flasks of wine. Yet another thread to the contradictions of Iran. Several pictures showed musicians, mostly playing the instruments we heard in Tehran, but, curiously, one playing pan pipes. Queen Elizabeth slept in one of the rooms, and wrote to her hosts of her feelings; we were not told what she said.

A short walk through a garden with birds following the play of the sprinklers brought us to the Imam Square.

First, the Blue Mosque, or Imam Mosque. How can I describe the effect of such huge areas covered with finely-detailed tiles and mosaics? The highlight was probably the echo under the dome, consisting of many closely-spaced but entirely distinct echoes. Here the guide was not wholly convincing. He said that the sound is amplified because waves from the point on the floor under the dome are reflected horizontally on striking the dome, and then back to their origin on second reflection. This is a plausible explanation of the amplification (one could easily calculate the shape of a surface which would do this) but not of the clarity. His explanation of the multiple echoes, that different paths give different echoes, is clearly wrong.

There was a fine view of workmen repairing the dome from the ravages of time and weather. Many other amazing prospects - a minaret framed by an arch, two sides of the courtyard reflecting one another, the square through the gate arch - presented themselves as we went round.

Next, the Ali Qapu Palace. More wooden beams reinforced with steel. Most of the plasterwork quite badly deteriorated, but in the music room right at the top the cut-out shapes of arches, wine-bottles, instruments and so on (cast in gypsum plaster) were mostly intact. These were said to transform the sound of a single musician into that of many and increase pleasure - not for me!

Then across the square from the palace to the Ladies' Mosque (Sheikh Lotfollah Mosque), with the striking peacock ceiling. (The ceiling decorations formed the tail, a pulley hanging from a nail accidentally became the head and beak, and a reflection from a window over the entrance formed the neck of the peacock. Very striking.

We were assailed by beggars while waiting for the bus. I simply said "no" to them (I have no note smaller than 10000 rials), but Reza gave then a small note and then told them to go away or he would call the police. It was, of course, a woman with a baby, and also a young girl in tow.

Finally before lunch, we went to the decorated bridge, the Pol-e Khaju, and were given an explanation about how it also functions as a dam, and the arches are of different sizes to avoid having disturbances all of the same frequency when water is flooding through. Huge numbers of people were resting in the cool, well-ventilated shade.

Lunch was a traditional Esfahan dish (which even many of the Iranians hadn't eaten before), served at a restaurant which does nothing else. It consists of lamb, boiled, minced, and then grilled, served in a large thin folded bread, with pickle or yoghurt, and mint leaves and onions. I thought it very tasty, but some of the group were underwhelmed.

Instead of a nap, I wrote up my notes, and then walked up along the river to the 32-arch Si-o-Se Pol bridge and back on the other side. Many young men practiced the first few phrases of English conversation on me:

"How are you?"
"Fine, thank you. How are you?"
There were boys playing in the water, and one small boy with a polythene bag full of water containing small fish. Near the end of the walk, there were people paddling swan boats.

I got back with ten minutes to spare before we were off for the last leg, to the bazaar.

This was for me the most frustrating part of the trip. Shopping is not my favourite activity, and left to myself I would have done a quick scan through the bazaar and then homed in on something I might want. But no, that wasn't allowed, we had to keep together, and having people watching me buy things is very inhibiting! We were taken to a stall and shown printed tablecloths, then to another stall with miniatures on camel bone, another with jewellery, etc. Eventually I saw some bells and managed to buy one - expensive but with a nice resonance, similar to the one that the drummer in the gymnasium had. It will be good for chairing sessions at conferences!

I waited outside the bazaar, and a young man struck up a conversation. Soon his friends joined us. They were students, mostly engineers. Our Reza strolled over and joined in. After a while, one of the group said to me, "He has a real sense of humour!"

Carsten and Charlie both managed to buy carpets; Rick and Kathy bought lots of different things; and Willem, braver than I, spent the afternoon in his own company.

Two small incidents. Someone asked whether the price quoted to foreigners was higher than the "real" price, and was told, "This isn't Turkey!" Someone else was thinking of buying a carpet in Aladdin's Cave but didn't have the money, and was told that he could take the carpet and send a bank draft when he got home.

After tea in a remarkable tea-shop (more like a junk shop), I got away and, with Richard, went to buy some postcards from the shop near the palace. On the way back, we were (separately)waylaid by two men wanting to practise their English. Mine was a high school student whose uncle is a professor of genetics.

Eventually it was time to go; guide Reza left us, stepping off the bus into the busy traffic with nothing but a round of applause. We headed out through the rush-hour traffic. (I have changed my mind about Esfahan traffic being nothing to compare with Tehran; it is not as chaotic but grinds to a complete halt more often.) Gradually the traffic thinned away, and in a lovely twilight, the mountains stood clear and rugged from the flat plain, contoured with shadow.

A bit of a wait at the airport, since we hadn't been delayed on the way. Time for an ice-cream and a few pistachios, and to write the postcards. They are only photos with printing on the back, very hard to write on with a fountain pen. I hope the ink doesn't smudge too badly. There was only one stamp in the whole airport, so I posted one to Hester, and will try to send the others tomorrow sometime.

When we arrived at the airport the minibus wasn't there, but it turned up shortly afterwards. On the way back, the bus was sideswiped by a car (no damage done), and then we were held up because of a collision ahead.

Rick, Kathy, Richard and Charlie are all leaving tonight. I looked at Rick's and Kathy's pictures of Esfahan, and went to bed quite late.


Up just before 8. Today we are down to four. Carsten and Willem went into town in an IPM car, Carsten to the carpet museum, and Willem to the National Museum. Hadi and I walked in to the IPM, up a remarkable short cut involving a lot of sharp turns and back streets (but remarkably few cars).

Reza is away today: his wife's mother died on Friday (I think) and he must go to the funeral.

I finished typing up the problems, and then Hadi and I did some mathematics. He told me about a construction of his using generalized balanced weighing matrices, which produces a near-partition of the lines of PG(3,q) into symplectic quadrangles, the intersection of any two being a fixed spread. I proceeded to construct such an object, which is almost certainly the same as his, from the Klein quadric. Several interesting questions arise: association scheme properties; proving that the two are the same (which should help me to understand the role of the group in a GBW); and looking at his extension to higher dimensions, which only works in even characteristic and where the common part is bigger than a spread (but what is it?)

Carsten came back from the carpet museum just before lunch. So we switched to talking about Willem's problem. Hadi ordered us lunch which was served in Reza's office: it was excellent (chicken kabab, pickle, salad, rice, bread and yoghurt). By the time we had finished lunch we were convinced that we had a solution. The ad hoc argument seemed to work, but I checked it out with GAP and got the same result.

Then the guys working on PSL(2,q) came and I had a session with them. We finished working out orbit lengths for subgroups (except S4 and A5, which I left for them), and made a start on counting the subgroups and working out the Moebius functions. We are now not too far from some kind of answer: not a formula (that is too much to hope for) but at least a simple algorithm.

I rejoined the others and we got talking about whether we have settled the problem about finding colourings. We are convinced that it is hard; we tracked down a survey by Poljak in Discrete Mathematics 111 which might contain the answer, but couldn't print it out; it seems that the IPM's subscription doesn't cover that year. Further searches were frustrated by computer problems.

By this time Willem was back. We showed him our solution and convinced him that it worked. We decided to reward ourselves with ice cream. Offered the choices Iranian or soft, large or small, we went for the first in each case - and it was very filling!

When we got back, we wondered if our example for Willem's problem was really the smallest. I was able to find one with just eight points, based on a kind of swastika. By this stage we had run out of steam, so we walked home.

[Footnote: Later on, Donald Preece reduced the number of points to 7 by identifying opposite pendant vertices.]

Willem had arranged to go to dinner with Mandana, and I decided to come too: Hadi was visiting relatives and Carsten, who flies tomorrow early, wanted to eat in. We took a taxi most of the way up the hill to a restaurant Mandana knows. We sat in the garden; the temperature was perfect and lights hung from the trees. The food was of the burger and pizza type, but nicely served with salad and very tasty (even if they think that Greek salad has finely chopped meat, no cheese, and lots of pink dressing). We had a pleasant talk about language, literature, religion, and all those big things. Mandana has decided to take the job at IPM. She gave me a learned English book on Persian literature published in 1923. After a lovely time we walked together most of the way home before taking our separate paths.

Farhad replied to my email; we meet at 5pm tomorrow to walk on the mountain.


Mandana arrived at about 9:45 and set out with Willem and me for the bazaar. This involved two taxis (don't ask me why - maybe they are territorial). Like all shopping trips I didn't enjoy it much. Almost immediately we came to a souvenir shop. Feeling under pressure I bought two woven mats and two lacquer pencil cases. Then I was paralysed and couldn't buy anything else in the whole bazaar. Not that there was much, except for some nice antique jewellery which was probably far outside my range.

We had some curious drink - clear but full of tiny golden-brown bits swirling around, and with an odd taste I can't describe.

Then we all decided enough was enough, and at that moment a shared taxi pulled up. It took Mandana to near her house and Willem and I to the gates of the IPM (though the driver was convinced we wanted the palace).

Reza was in - his meeting was postponed - so he, Hadi, Willem and I had a nice talk until lunch. This was ordered in as yesterday, and was even more excessive - pizza as well as chicken kabab. We talked and worked through the afternoon until the gang came to see me and discuss the PSL(2,q) problem, with a couple more to be sociable. Then the others stayed on to talk generally about mathematics, which I was happy to do.

Just before 5, I thought I would have a serious assault on Charlie's problem, and managed to crack it. There is some subtlety in it! Then Farhad and two friends showed up, and we set off in a car.

We started off at a little square tucked in between two cliffs. The road followed the stream, and became a path with many steps. This part of the stream valley was chock-a-block with restaurants. It seemed as if huge numbers of people must come here sometimes.

Ascending further, we reached an old village, with an old mosque, a rooster crowing, and a pair of mules bringing a load of empty bottles down. (We were to see many of these, mainly mules but some donkeys, going up with full bottles and down with empties.) At the top of the village, what had been a stepped path turned into a steep trail over rock and gravel. The hills were bare rock, but the stream valley was full of fine trees.

After a while, we reached the top of a ridge and saw a spectacular waterfall ahead of us. Its name translates into something like "twin falls" and it must be an amazing sight in the snowmelt. We continued up and overtook a big party of schoolgirls (about 30 of them). Finally we reached a point not far from the top of the falls, but to continue would have meant tackling fixed ropes. Besides, we'd been walking for an hour and a half; I was quite tired (the young guys outstripped me, though not by very much) and any longer would have meant descending in darkness. So we turned back.

There was a glimpse of Tehran through the gorge (or rather, some buildings dimly visible in the smog). At the bottom of the slope by the waterfall was a pomegranate tree with some red fruit visible.

Of course, downhill was harder than uphill, with much greater possibility of slipping. We came to a hut with running water, and splashed some on our hands and faces. A man came out. He had drinks, so we took lemon beer. The others also induced me to try a yoghurt drink which had to be shaken up. Sour, and refreshing.

After a while, we caught up with four mules. Two crossed the bridge (the way we'd come) and the other two descended to the stream on the same side. We decided to follow them. The path was roughly level as the stream fell away, and we were rewarded with a lovely view of the restaurants with their coloured lights far below us.

Finally down a winding road brought us to just above where the car was parked.

I'd offered to invite the others for a meal, so we drove to a Macdonalds clone in a lovely curving street lined with trees. I ordered a pizza and a soft drink. The pizza was good, but the soft drink was much smaller than Macdonalds size, and I was parched by the end of it. We went next door for ice creams, which improved things very much. I had some purple berry, chocolate, and Iranian ice cream (bright yellow with pistachios, like yesterday). Then they drove me back to the guesthouse, where I drank lots of water, emailed Charlie, said goodbye to Willem, and confirmed the arrangement with Mandana.


A leisurely breakfast, and I'd finished writing out the solution to Charlie's problem before Mandana came.

We went back to the Sad-Abad palace complex. In one of the museums there is an exhibition of miniatures by a 20th century artist whose name I didn't record. Some lovely pictures in the classical style, some much more challenging and disturbing, like his illustration of Omar Khayyam's ruba'i where the dust is full of human faces and limbs.

Then we walked in the park discussing literature, ending up in a tea-house. Mandana asked if she could translate my poems into Farsi, adding "There is no copyright in Iran, of course!" She also said something which nobody ever said to me before: "There is no `you' in your poems." She wrote out two of her English poems for me, both very striking and effective. I pointed out that although they both have "you" in them, they are both first-person poems.

Then it was suddenly time to leave for IPM. We found a taxi quickly but the traffic was bad. We went out to lunch to the place where the chicken kababs came from, and had, guess what, chicken kababs... as usual, very tasty.

When I mentioned that I have six months' leave next year, Reza immediately invited me to come to Tehran in April. Something to think about, but I told him that Lyon have first claim.

In the afternoon I worked with the PSL(2,q) gang again. They had diligently found in the literature a general formula for mu(1,G) if G is soluble or if G is PSL(2,q). This is enough to count the regular orbits, but we need more detail (all values of mu(H,G)) to find all orbit lengths.

Home with Hadi at 6pm. Mandana came at 7 and we went to the Turkoman restaurant in Jamshidieh park. Unusually we had to wait a long time for a taxi; we'd just given up and started to walk when one came. It took us up to the top of the road. We walked along to the next road leading up to the park. There were many people waiting and no sign of a taxi, so we walked up the hill to the park, and then up to the restaurant.

In the park, Mandana was greeted by a man who had been a servant at the university where she was a student four years ago.

We sat at a table on a terrace at the restaurant with the lights of Tehran coming on in the falling darkness. We had a plate of walnuts, cheese and herbs, and some Turkoman dishes: beef and rice (a bit ordinary) and eggplant and garlic (delicious). The herbs etc went very nicely in a folded piece of bread; Mandana says this is a common Iranian breakfast.

Moths played around a nearby light, brilliant fluorescent white and appearing as trails of shiny beads when they flew fast. Inevitably the flew into the light and died.

After the meal we looked inside the restaurant, shaped and built like a Turkoman house. An alcove covered in rich carpets, a central fireplace (this would be nice in the winter), models of a man playing a tar and a woman weaving.

Then we walked down through the park. There were taxis at the gate but we decided to walk all the way, taking a bit over an hour altogether. Mandana came to the guesthouse and took a taxi home from there.


Breakfast with Hadi, who told me about his former classmate who, following serious heart trouble, a stroke, and many operations, can no longer walk or talk (but can say his prayers in Arabic), and wants only to see his daughters married and settled - a difficult position for the daughters, I think, especially one who is a mathematics professor at the university and doesn't want to get married! Tomorrow morning there will be nobody here for breakfast.

After breakfast I found the references for the write-up of Charlie Johnson's problem on MathSciNet, and finished that off, and also made some notes on Hadi's construction (including workpoints for myself).

Mandana came, and I talked her into going to the Niyavaran park instead of Sad-Abad (so we would not need a taxi). We were walking up the road when a car came past; it was the lady from IPM with her mother and sister. They gave us a lift to the park, and offered us peaches and sour cherries.

I suggested going to the art museum, but the ticket seller persuaded us that the main palace was much more worth seeing, so we went there instead. Indeed, it was interesting: both huge ornate public rooms with mirrored walls and ceilings and lavish carpets and furniture, and the more intimate rooms such as the bathroom with monogrammed bathrobes and towels, and the private dentist's surgery. A remarkable collection of autographed photos of world leaders: I recognised a few, including Eisenhower, Nixon, Queen Elizabeth.

Then we sat on a wall in a back garden near where the gardeners were watering and had a talk, and later went down to the public park in search of tea (which we found after some difficulty) and talked some more. Time passed, and I was a bit late for the IPM, but when I arrived they had only just sent out for the chicken kababs. Reza, Hadi and I had a very enjoyable lunch and talk ranging over many things, mathematics, mathematicians, and far beyond.

Mandana showed up a bit before 6. She wanted to talk to Reza about the job (which I think she is definitely going to take) but he had left early. So we set off for the restaurant where we ate with Willem not so long ago, in search of a cup of tea. After walking a fair distance up the hill, we decided on ice cream instead.

Over coffee, Mandana translated one of her Farsi poems into English, I making a few comments on idiom and synonyms along the way. She got to the last line, "lightning strikes", and said that she didn't know what it meant. Suddenly it all became clear to me. The poem is about play, and her form of play is dancing. One day she will be dancing this poem, and lightning will strike, and she will know what it is that she is looking for, she will realise that the "I" and the "You" are one and the same. Moreover, she must know this at some level, in order to write the poem.

After we had recovered from this shock, we walked back, and she left me at the guesthouse.


I set my alarm for 4:30. I slept very soundly until 2:45 and then dozed; I dragged myself out of bed five minutes before the alarm went off.

While taking a shower I realised that, since all Mandana's poems are full of play, she must have known that life is a game that we play as well as we can - this was a casual remark I made to her which she took to heart, but my remark must have been only a reminder.

I checked my email one last time before leaving. A puzzle: there is a message from saying that a virus has been found in an attachment I sent. Since it is a Microsoft virus, and since I haven't sent any attachments since I have been in Iran, I am at a loss to understand.

The driver arrived punctually, and at that time of day the journey to the airport took only twenty minutes. The airport was ghastly. I had to stand in the queue for three-quarters of an hour to get through the first security gate. Then I queued for twenty minutes at the check-in desk, to be told that my name wasn't on the list and the flight was full; I should come back at eight o'clock. By 7:20 the queues had eased a bit, and so I went back. This time several people seemed to be expecting me, and I was checked in double quick. Upstairs through passport control, I came to the duty-free shop, and made a final despairing attempt to buy something, getting a couple of mats and a picture-book. The display screens were displaying last night's flights and a Microsoft error message; I got to a lounge with two gates only, both of them calling long overdue flights.

Compared to all this, our boarding was remarkably orderly, and we were away only half an hour late, expecting to be early in London. After take-off the women removed their scarves and we settled down for the tedious journey.

A six-hour flight, pretty much unrelieved tedium. It ended with our being stacked for a quarter of an hour and then having to wait ten minutes while they found us some buses. But the immigration queue was mercifully short.