Martin's Blog

Michaelmas 2008

Posted by Martin Orr on Thursday, 16 October 2008 at 22:11

We've had almost a week of lectures now. I have fairly definitely committed to Algebraic Number Theory. It's getting a bit hard to describe the courses I'm doing now, so here's just a list with a few comments:

  • Local Fields (central to number theory)
  • Arithmetic of Abelian Varieties (algebraic number theory; this is a graduate course, so goes pretty fast)
  • Algebraic Geometry (these ideas underlie a lot of algebraic number theory)
  • Commutative Algebra (the algebraic techniques needed for all the above)
  • Differential Geometry
  • Finite-dimensional Lie Algebras and their Representations

The last two are less directly important for number theory, and are just for fun. Six courses is too much work, so I need to drop one of those two, but I don't know which. These courses are all significantly harder than last year.

The Cambridge Lindy Exchange starts tomorrow evening, so I'll be pretty busy with that all weekend. I'm also trying to get together some organised accounts for the Lindy Hoppers.

no comments Tags lindy, partiii

Active and passive groups

Posted by Martin Orr on Thursday, 02 October 2008 at 19:13

I have been studying category theory recently, and revising my idea of what a group is. There are two ways of thinking about groups, which I shall call active and passive. I have tended to almost exclusively think about groups passively, but I have realised that treating groups as active is useful too.

3 comments Tags groups, maths