Friday, March 24, 2006

I feel it would be somewhat dishonest of me to only write about the good aspects of both my academic and social life, so this week other than getting another paper online, I've had a bit of a damper put on my research status. Not too major I hope.

In January I put a paper online which was the first that was entirely my own work. There are some fun results and a couple of somewhat important results. The usual course if events is that you submit a paper to the Arxiv first (you only need to be affiliated with an institution to do this, and not be on the blacklist - an interesting story of the balance of academic freedom vs. the domination of crackpots!). After a little time of seeing what the reactions to the paper are, you submit it to a journal to be peer reviewed by an anonymous researcher in a field close to your own. They then say whether a)It should be accepted in it's current form b) It should be accepted with minor corrections c) it should be revised and then reconsidered or d) rejected completely.

I received my news a couple of days ago that (quite fairly) several of the sections to my paper were somewhat superfluous and clouded the more interesting result. It was also claimed that one of the sections was not concrete enough and therefore unclear. These are all perfectly reasonable statements and in fact I agree with them in terms of what is important for other researchers to read. Whether or not once I've made these pretty major structural changes to the paper it will be accepted was a little unclear but I've little choice but to rewrite, resubmit and hold my breath.

Anyway, it was a bit of a blow to my academic confidence which, despite the release of the new paper, is feeling a little low at the moment. My research career so far is around two and a half years old and I've spent almost all that time working in a single rather narrow area. Now that I try and branch out a bit, I realise how many areas in my knowledge have become extremely hazy with the long hiatus since I learnt them for the first time three years ago.

Anyway, I remain somewhat stoic on this and press ahead in an attempt to learn as much as I can as fast as I can. Unfortunately my academic personality is a rather fickle one as I flit from one book to another and skip through papers, probably without studying them in as much depth as I should. There's just SO MUCH OUT THERE TO LEARN that knowing what is vital and what can be left for another time is a tricky balancing act that I'm far from mastering.

Anyway, I'm not too worried and feel that an awareness of these problems, as I've mentioned before, sees to a good part of the battle.


In some maths news which will probably be on every science blog in the next few days is the announcement of the 2006 winner of the Abel prize for mathematics. Essentially the Nobel prize for maths (I'm not sure whether one would claim that this or the Fields medal is more important).

Sorry, this will be a little technical but probably brief.

This year it was awarded to Lennart Carleson, in large part for his work on harmonic analysis and his proof of convergence of Fourier series on the space of square integrable functions. This is something that as a physicist I had taken for granted when introduced to the concept as an undergraduate. Square integrable functions are particularly important in quantum mechanics and in particular in defining the Hilbert space of states. So this proof is an important one in many areas of physics.

Reading the official site for the Abel prize it looks like Carleson has been a major player in solving some of the most complicated problems in mathematics over the last few decades including proofs of the existence of strange attractors in certain systems.

Attractors come about in the study of dynamical systems, whereby a wide range of starting conditions for your system (which may be a complex set of pendulums for instance) end up in, or near, a small set of states after some time. Their states appear to be attracted to the subset. Attractors have very important applications in areas ranging from the stability of heartbeats to solutions in string theory. The state space of such systems can be plotted to indicate the points of attraction and probably the most famous of these is the Lorenz attractor which is found in chaotic dynamical systems.

In my brief meanderings to try and find out a little more about the subject of convergence I found that the concept 'almost everywhere' has a mathematically rigorous definition.

The definition is that if a property holds almost everywhere then the space in which it doesn't hold is the null set. Not being a mathematician, this definition seems pretty odd to me but apparently this concept is important in some areas of analysis.


Anyway, I'm clearly flitting again and have books that I should be reading and coroot lattices to digest (a healthy afternoon snack that I recommend to all). Another full weekend in view but first things first.

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