A research visit

Corridor

The picture on the left could be a corridor in any newish university building anywhere in the world. But when you look through the window at the end of the corridor, you see that it could only be in Australia. This is the corridor of the IT building at Monash University’s Clayton campus in Melbourne, where I have just spent three weeks visiting Graham Farr, Kerri Morgan, and Daniel Delbourgo to work on algebraic properties of chromatic roots. My office was on the right a few doors down.

For the sake of non-mathematical readers, I will save the description of the main work we did on chromatic roots and its context until a following post. A week of my visit was taken up with the 35th ACCMCC, which I described earlier. Here are a few notes about the rest of the visit.

The trip began on an unfortunate note since I travelled out with an injured shoulder after my fall in South London. Moreover, perhaps as a result of the cramped conditions on the plane (in the very back row of an A380, row 88), my foot played up, and on Thursday night I was almost unable to walk. But time, and emu oil, helped clear up both these afflictions, the foot almost instantly: in a day I went from thinking I would have to see a doctor urgently to being unaware that there had been a problem.

Wilson's Promontory

I managed several outings. The best was probably a trip to Wilson’s Promontory, nearly three hours’ drive from Melbourne, with Petr Vojtěchovský, Tony Evans, and Ian Wanless. Many of the trails were still closed as a result of damage from the floods last March (and the bush bore the scars of earlier bushfires), but we still managed some beautiful walks, to Tongue Point and Squeaky Beach and to the end of the beach at Tidal River. The sea was an astonishing blue, and the beaches were almost deserted on a beautiful sunny Sunday only two weeks before Christmas! We didn’t see any wombats or koalas, but met kangaroos, wallabies and emus, as well as blue fairy-wrens, wattlebirds, crimson rosellas, kookaburras, a king parrot, lizards, and of course many gulls. I also heard (for the first time on this trip) the lovely song of the butcherbird.

The day before, I had gone into Melbourne and had a very happy afternoon in the beautiful Botanic Gardens, where the air was resonant with the lovely sound of many bell miners, while swamphens stalked the banks of the lake. There were fine specimens of the three common araucarias (Bunya, Norfolk Island and hoop pines) as well as one I didn’t know (Captain Cook’s pine). I saw an an unfenced water child who was clearly unaccompanied: a companion would have told her to put a T-shirt on if she was sitting out in the sun all day! On the way in to the botanic gardens, I passed the old Melbourne Observatory. Unfenced water child

My host Graham Farr moonlights as a guide at the Observatory, and took me on one of the tours he was giving. It was a cloudy night, so there wasn’t much to see in the sky: we did see Jupiter and the four Galilean moons through the telescope installed for the transit of Venus in 1874, but when we got to the larger reflecting telescope used on the international sky survey, the clouds had closed in and all we could look at was the illuminated sign on the ANZ building in the City, a couple of kilometres away. Nevertheless, the history was fascinating: the observatory played an important part in timekeeping, meteorology, and the social life of the colony (the Governor used to entertain guests there) as well as astronomy. Outside, at the start of the tour, fruit bats flew off on their nightly errands, and magpies carolled.

The penultimate day of my visit being Sunday, I managed to find my way to the Dandenong forest by public transport. I spent a very happy few hours under the enormously tall mountain ash trees (unlike the British version, these are eucalyptus), and even succeeded in seeing a lyrebird, along with the statutory cockatoos, rosellas, and kookaburras. However, my visit didn’t mesh well with the schedule of Puffing Billy, the local steam train. He was out when I arrived; I heard him hooting as he set off on another journey as I walked down the road from the forest, but all that was left when I reached the level crossing was the smell of coal smoke and parties from the previous trip getting into their cars.

Apart from my conference talk, which was mostly about synchronization, I gave two talks to the Discrete Mathematics research group, on combinatorial representations and on hot and cold matrices. I had to produce slides in a hurry, since my shoulder was not quite recovered enough to risk a whiteboard talk. The slides of my conference talk are here, and the slides of the other two talks will hopefully appear at some point on the research group pages at Monash.

In addition, I did some work with Ian Wanless on subsquares of Latin squares, which I briefly mentioned in my report on 35ACCMCC, and with Bridget Webb and others on infinite perfect Steiner triple systems. Ian and I got significantly further; we were able to extend the bound on subsquares of order 4 (and the characterisation of squares meeting the bound) to all orders which are powers of 2. We also found a simple result which converts big O results into big Θ results in many cases. A paper should appear at some point.

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About Peter Cameron

I count all the things that need to be counted.
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2 Responses to A research visit

  1. The slides are now on the Discrete Mathematics Research Group web page, at http://www.csse.monash.edu.au/~gfarr/research/res-gp-mtgs.html

  2. The paper with Bridget Webb is in the current issue of the Australasian Journal of Combinatorics (vol. 54, pp. 273-278).

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