Sunday, 26 June 2011
Alcalá alight
Friday, 24 June 2011
New paper!
A few days ago I uploaded a new paper onto the arXiv. It was written with Attila Pór, Pavel Valtr and David Wood. In it we consider the connectivity of visibility graphs, which are graphs drawn on point sets in the plane where two points are joined by an edge if they 'see' each other - i.e. there is no point on the line between them.
One of my favourite results in the paper is a lemma which says that if you have two properly coloured plane graphs drawn with straight edges which are separated by a line, you can add an edge between them which is also properly coloured. This is not true if they aren't separated by a line. It's one of those things which seemed like it had to be true, but was quite tricky to prove. In the end Attila found a tricky proof. Perhaps there is a short proof using something like Borsuk Ulam (wild guess) but we couldn't find it.
One of my favourite results in the paper is a lemma which says that if you have two properly coloured plane graphs drawn with straight edges which are separated by a line, you can add an edge between them which is also properly coloured. This is not true if they aren't separated by a line. It's one of those things which seemed like it had to be true, but was quite tricky to prove. In the end Attila found a tricky proof. Perhaps there is a short proof using something like Borsuk Ulam (wild guess) but we couldn't find it.
Tuesday, 21 June 2011
Berlin visits, past and future
After my month in Lausanne last year I headed to Berlin again for about three weeks. That trip was self funded, but around that time I got the news that my supervisor and I had been successful in our application for some travel funding for a small cooperative project in Berlin and Melbourne. This will also allow me to visit again next year.
So now I am back in Berlin. I took the old MEL-DRW-SIN-FRA route with Jetstar on the first two legs, then Qantas. This was not so bad actually, especially since I got all the connections (I was on standby tickets) even though it was busy. Anyway, it's nice to be here again. My stay will last until mid August, with next week being spent in Spain at Los Encuentros de Geometría Computacional. I also hope to make a weekend trip to Belgium to see the 24hrs of Spa Francorchamps.
It was somewhat emotional last time seeing this city which I enjoy so much again after I had decided to move my studies back to Melbourne. Now I feel more relaxed because I know it will always be here, and I'll be back.
One of the first things I realised after getting here was that Melbourne maybe does have the edge food-wise (sorry Berliners!). About a week ago I had eaten at my favourite Indian restaurant in Melbourne, and when I arrived I went straight to one of my favourites here. I'm afraid it didn't compare well. At least eating out here is a lot cheaper than in Melbourne, especially with our high dollar.
So now I am back in Berlin. I took the old MEL-DRW-SIN-FRA route with Jetstar on the first two legs, then Qantas. This was not so bad actually, especially since I got all the connections (I was on standby tickets) even though it was busy. Anyway, it's nice to be here again. My stay will last until mid August, with next week being spent in Spain at Los Encuentros de Geometría Computacional. I also hope to make a weekend trip to Belgium to see the 24hrs of Spa Francorchamps.
It was somewhat emotional last time seeing this city which I enjoy so much again after I had decided to move my studies back to Melbourne. Now I feel more relaxed because I know it will always be here, and I'll be back.
One of the first things I realised after getting here was that Melbourne maybe does have the edge food-wise (sorry Berliners!). About a week ago I had eaten at my favourite Indian restaurant in Melbourne, and when I arrived I went straight to one of my favourites here. I'm afraid it didn't compare well. At least eating out here is a lot cheaper than in Melbourne, especially with our high dollar.
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