MSI Weekly Bulletin - Week starting Monday 21 November, 2005

In this talk I will explain the concept of T-duality, as it arises in String Theory. I will argue that in order to build a consistent mathematical framework for String Theory, T-duality implies that we should be considering generalisations of our conventional notions of the geometry of spacetime, including noncommutative geometry, generalised geometry (in the sense of Hitchin) and T-folds (a la Hull).

Kobayashi-hyperbolic manifolds can be viewed as a natural generalisation of bounded domains in complex space and are a standard class of manifolds considered in complex geometry. In a series of talks we will give the details of our recent results on the classification problem for such manifolds.