Thursday, 23 October 2008

First Galois Group lecture of the semester - Categorification

Professor Nige Ray, a name known to all, especially to first year undergraduate students at The University of Manchester (UoM), kindly agreed to give the first Galois Group lecture of the year. The Galois Group is an undergraduate Mathematics society* at the UoM, who aim to organise regular general audience lectures throughout the year, given by staff and undergraduate students.

The lecture was titled Categorification, a word which spell check refuses to correct, and one which I had trouble pronouncing myself when introducing Professor Ray! What's categorification? you ask. Well perhaps Professor Ray's abstract (below) might give you a brief idea, but this does not mean that I do not remember his lecture (although it was on Wednesday 13th October 2008 - some time ago, I hope you will agree!).

"Thousands of years ago, when people were learning to count their sheep (amongst other things!) the process of decategorification was seen as a stroke of genius, that allowed the development of number. During the last 30 years, it has dawned on mathematicians and theoretical physicists that the time has come to reverse this process, and work through ideas that had never been properly developed beforehand, but which are just as fundamental to mathematics as counting. In its own language, categorification involves replacing sets with categories, functions with functors, and equations with natural isomorphisms. I shall try to make some sense of this for a general mathematical audience."

In the build up to the lecture you could say that I had been surprisingly optimistic, namely due to the large room that I had booked in the Alan Turing building for the lecture. I wasn't to be disappointed (surprisingly!) as a record number of 89 people - ranging from undergraduate students, staff and some guests - attended a fantastic and interactive lecture. The one thing that stands out from these lectures is the atmosphere throughout the event. It was electric. I left the building for a second and observed the audience, which reminded me of why I enjoy organising these events. Everyone seemed to be in a different world altogether - that of categorification and counting sheep!

There exists a group of students (half of our audience!) who want to attend such lectures, and now they have the opportunity to do so. This year I have been trying to advertise the lectures in other universities around Manchester, and at the refreshments after the lecture (during which only one Jaffa Cake survived!) I was pleasantly surprised to find a retired IMA member there, who asked to be added to the mailing list for future lectures. The refreshments are as important as the lectures in my opinion, for they give students the chance to interact with staff and other mathematicians too, and you can always interrogate the speaker on something you didn't understand!

Such lectures are also a brilliant way of giving someone a snippet of a certain topic in maths. Now categorification is a blessed topic which has something for everyone (well there was mention of finite sets, abelian groups, vector spaces, knots etc), but if after the lecture you don't find it appetising then that's perfectly okay. The lectures are windows into areas of mathematics that one might not have the luxury of studying.

Whoops I digress! (I'm afraid you'll have to get used to this!). Overall the first lecture of the semester was a success, and I would like to thank all those who attended and I look forward to seeing you all at the next student lectures (which will be advertised in due course).

*Note: more than one society exists. We cater for the mathematical community whereas mathsoc caters for the "social aspects" of University life.

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