Just a short message to inform everyone that tonight's discussion group will run normally but will be a free for all: whether you've recently found some tidbit of interesting maths which you want to tell us about or just want listen to a few varied "mini-DGs", this is a great opportunity to do so. The fun starts in MS.05 at 7:30 PM and once it's finished we'll head on to the pub as usual.

Modern mathematics is often seen to be built from the ground up from a foundation of set theory axioms, and we are all used to seeing maths done in terms of sets; however, category theory, designed primarily as a tool for algebraic topology, can be also be used as a foundation for mathematics.

Come and hear Ben Simpson explain how one can think of sets in terms categories, and how this makes several areas of maths that little bit shinier.

After which, we naturally transform ourselves towards the pub.

Update: Unfortunatley, it looks like Ben won't be able to present his talk this evening but we will nevertheless hold a "free-for-all" DG instead (same time and place, of course).

Tonight will be Christian Richard telling us about the Poincaré conjecture, the first (and only, so far) Clay Math problem to have been solved.

Join us in MS.05 at 7:30pm for an historical overview of the developments in algebraic topology, leading on from Poincaré's revolutionary ideas, and an explanation of their relevance to the Poincaré conjecture.

After which we go to the pub.

(Sorry about the late notice, was waiting on Christian to provide a description which he did not do.)

Ever seen a fractal on a poster? Would you buy one if you could?

Next Wednesday during Maths Café the WMS will be selling posters.

Posters currently available are here
http://warwickmaths.org/forum/banter/posters

Prices are
A0 £12
A1 £7
A2 £3.50
A3 £1 (Photo quality)

You will only be able to order them on Wednesday. We will send them to print that day, and they will be ready before next Wednesday when they can be collected or delivered.

Few theorems can be said to have opened up entire new areas of mathematical research - but this is what the Riemann Roch theorem managed.

Initially considered by Riemann as a helpful way of approximating the dimension of the space of certain meromorphic functions on a Riemann surface; this was then refined by his student Roch to give a precise formula for the dimension.

The applications of this single formula are numerous; but this formula also lead to many deep generalisations, starting with Hirzebruch's interpretation of the theorem in terms of vector bundles (and his use of algebraic topology, in particular the theory of characteristic classes, to express this). A few years later followed Grothendieck's interpretation of the theorem, changing the absolute viewpoint to a relative one, something new for the time, and introducing ideas that were going to lead to K-Theory.

Meet us in MS.05 at 7:30pm for an introduction to Riemann surfaces and the Riemann-Roch Theorem (not the generalizations!). Then we invert some line bundles and appear in the pub.