Morse Theory analyses manifolds by looking at the behaviour of differentiable functions on that manifold. We can gain a lot of insight into the topology of a manifold by looking at the critical points of a differentiable function on that manifold: different matrices of second partial derivatives (the Hessian) gives different local behaviours, like saddles, maxima or minima. Looking at what happens between different critical points, we can try to patch up what happens near each critical point to reconstruct our manifold somehow.

To do this, our smooth functions need to be sufficiently nice; the so called Morse functions.

We can in fact strengthen the approach by taking more care at what happens around critical points; we will then find a particularly neat way of packaging that information and passing from that information to topological information. In particular, a theorem of John Jones (with Graeme Seagal and Ralph Cohen) will make its appearance!

So make sure to come to MS.05 at 7:30 to learn about what Morse Theory is all about and why it's so amazing! After which we flow to the pub!