# IMS Annual General Meeting 2009

## 11th September 2009

The annual meeting of the Irish Mathematical Society will take place in Trinity College Dublin.

### Location

**Salmon Lecture Theatre**

Hamilton Building

Trinity College Dublin

Time: 2.00 pm

### Mathematical schedule

*Speaker:*
Dr. Brendan Guilfoyle (IT Tralee)

*Title:*
A proof of the Caratheodory Conjecture by mean curvature flow

**Abstract**: The Carathéodory Conjecture (c1924) states that a closed smooth
strictly convex surface in Euclidean 3-space contains at least 2 umbilic
points. In this talk we outline a proof of this Conjecture, obtained in
collaboration with Wilhelm Klingenberg, which uses parabolic PDE methods.

We give some of the background and history of the Conjecture, as well as an indication as to why it is such a difficult problem. Then we describe the proof, which brings together neutral Kaehler geometry, mean curvature flow and pseudo-holomorphic curves. While the talk will be aimed at non-specialists, we will indicate the major technical challenges involved and some of the implications for further research. Business schedule

There will be a short break following this lecture and then the IMS will hold its AGM in the same room starting at 3:30pm.