Tonight's DG will take the form of two half-DGs, both tackling very interesting but also very different topics:

• Up first is Rajiv Shah, who will tell us all about the axiom of choice, one of the most interesting and possibly also most controversial axioms of set theory. In its most simple form, the axiom meerly states that if one has any given collection of sets, one can find a function from this collection which simply picks an element from each set. While this seems intuitively obvious and is clearly useful in many different settings, a few mathematicians have argued almost ever since its introduction in 1904 by Zermelo, that the axiom of choice is not a desirable axiom because of certain very unintuitive consequences, especially with regard to non-measurable sets (the most spectacular example of this is perhaps the theorem known as the Banach-Tarski paradox, which states that given a ball in , one can, using only isometries, split it into no more than 6 pieces and rearange those pieces into two balls identical to the first).

• Next up will be Sam Derbyshire with a short talk about the Gauss-Bonnet Theorem, a result in differential geometry which unexpectedly relates two very important properties of a surface: its curvature and its Euler characteristic. As one of the nicest and most important theorems in the field, it has attracted quite a bit of attention and motivated many modern developments of the subject. Despite this, it remains very accessible and can provide a great introduction to understanding the geometry and topology of surfaces.

As usual, the talks will start at 7:30 PM in MS.04 and will be followed by our usual Monday evening pub social.