It's been a while

Oh dear. It has been a long time since I wrote anything in this blog. Perhaps that was because of the overly academic way in which I was writing before. These days, time is at a premium so writing a blog isn't top of the list. In any case. I'm starting with this PhD thing at the moment. Trying to learn goodness knows what, goodness knows how fast. Last week I managed to go to a conference in Paris. I think I've recovered my passion for mathematics which had begun to wane. It was one of those birthday bashes for great mathematicians who have reached the grand old age of 60. This mathematician was Michel Broue (with an accute). He seems like a pretty genial fellow, and pretty laid back too - I suppose you can afford to be when you're head of the mathematics department at the Ecole Normale Sup.! Well, it was an awful lot of fun to go and see these guys speak. By these guys, I mean the likes of Jaques Tits, Pierre Cartier and Jean-Pierre Serre. My favourite had to be Cartier, who gave an awesome talk on the differences and similarities between the Lie theory of symmetries of differential equations and the Galois theory of symmetries of roots of polynomials. He was really genuinely excited about the mathematics and exuded "great mathematician" without forcing it or being condescending. What a guy....*sigh*. Perhaps one day I'll end up like him. In the mean time, it's sheaf cohomology for me. It's crazy stuff, buried in a technical mire, but maybe that's because I don't understand it yet. Essentially a sheaf cohomology is just defined as a way of assigning a homology group to every pair (X,S), where X is, in the most general case, a topological space and S is a sheaf of K-modules for some principal ideal domain K. Essentially, you get a load of homology groups H*(X,S), one for each sheaf S over X. After that, they have to satisfy the Eilenberg-Steenrod axioms etc. It turns out that special cases of sheaf cohomologies are de Rham, Alexander-Spanier, Cech and various others. Seems pretty cool to me. Although right now, slow going. Perhaps I should go and see my supervisor soon. I definitely ought to get some work done before hand though. So Adieu.