Martin's Blog

Trip to London

Posted by Martin Orr on Sunday, 08 November 2009 at 17:54

I took a trip to London on Wednesday. It takes 4 hours to get from where I live in Bures-sur-Yvette to St Pancras by Eurostar (and under 6 hours to Cambridge, where I went for a weekend in October). It is surprisingly cheap - £27.50 if you book far enough in advance (about 4 weeks in advance to travel mid-week). In London I went to see Ed, who did Part III and is now doing a PhD in Imperial, and went to the London Number Theory seminar. This seminar reminded me that the stuff I have been doing recently is much more "geometry" than "number theory" - I am generally happiest doing something in the middle.

I only planned to go to London for the day, but my time there was nearly doubled because I was confused about the time of the train home. I discovered this as I was going to check in, bang on 30 minutes in advance as requested, which was in fact the time the train was due to depart. So I heard it leaving. This was the last train to Paris so I had to wait until the next morning. When I explained to the lady at the ticket office what had happened, she looked like she thought I was completely stupid (which I was). But she said she would class me as having missed the train (I am not sure why this was being generous; maybe it is meant for people who had delayed connections), and so I could change the ticket without paying anything. But only to the next train, at 5.25 in the morning. Fortunately there is a youth hostel only a couple of minutes from St Pancras where I could stay.

no comments Tags london, paris, train

Functor of points of non-affine schemes

Posted by Martin Orr on Saturday, 07 November 2009 at 16:59

This post was inspired by Monday's algebraic geometry exercise class, although in fact it fits neatly into my series on functors of points (except that it requires you to know what a scheme is, while previously I have considered only affine schemes). I shall prove the following theorem:

Theorem. There is a canonical bijection between morphisms X \to Y of k-schemes and natural transformations of the corresponding functors of points.

3 comments Tags alg-geom, maths, points-func