Posted by martin on
Sunday, 15 March 2009 at 22:28
Another term has just finished. This term I studied:
* Elliptic Curves (quite easy; major objects of study in algebraic number theory)
* Modular Forms (a bit harder; more central objects in algebraic number theory)
* Curves and Abelian Varieties (quite hard - only a handful of people did it; this is really algebraic geometry, but very relevant to number theory)
* Complex Manifolds (differential geometry, so not my main line but handy background; I didn't try to follow this one in detail)
I have also done some work on an essay (worth the same credit as a lecture course) on Complex Multiplication (which is about a special type of elliptic curves). I gave a seminar on this last Friday but beyond the content of that I don't know much about it yet - I shall have to work on it over the holiday.
Other big news is that I have a place at the Université Paris Sud in Orsay for the second year of a French masters next year (because getting funding to go straight to a PhD in Paris would be a problem), and this week I heard I have got the Rouse Ball Travelling Studentship in Mathematics from Trinity to pay for it.
Tags paris, partiii
Posted by martin on
Sunday, 07 December 2008 at 20:07
Term has just finished and it's been hard work so I have had no time to post all the way through. At the end of term, I gave a talk on Kummer theory (a bit of Galois theory - you can read the "abstract":http://www.srcf.ucam.org/cugms/node/787) as part of the Part III seminar series. My talk was fairly easy, intended to fill in some stuff that was assumed in the Part III Local Fields lectures but not included in Part II Galois Theory. None of the number theory talks provoked many questions afterwards.
Out of the seminars I attended (although these were only on one day out of 2.5) the number theory seminars had the largest audience, twenty-something; this included a significant proportion of PhD students and academic staff, while the others (category theory and differential geometry) were mostly attended by Part III students.
Tags partiii
Posted by martin 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.
Tags lindy, partiii
Posted by martin 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.
Tags groups, maths
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Posted by martin on
Tuesday, 30 September 2008 at 13:26
Another while with no post, reflecting the quiet nature of life in Belfast (although I do have a partially written mathematical post). I have produced a website for Grass Roots Conservation Group; and I’ve been studying Miranda’s Algebraic Curves and Riemann Surfaces (an unusual approach to the subject I think) and Mac Lane’s Categories for the Working Mathematician (which leaves me feeling that I know the formal stuff but not the reasons why).
I managed to find some swing in Belfast. It’s a pretty small scene, and the girls were quite happy to have a new lead. Muriel’s, where people gather on Thursday nights, has room for about three couples to dance, which is plenty. A teacher has recently started beginners classes (broader swing more than lindy) on Tuesdays in McHugh’s.
I spent the weekend at the Edinburgh Lindy Exchange, a much bigger dancing experience, and now feel like I’ve had plenty for a while. After that, I’m back in Cambridge and there is lots to be done now in preparing for the Cambridge Lindy Exchange for which we’ve had lots more bookings following ELX.
Tags lindy, travel, website