Curvature and Moduli -- Some Intimations and Propaganda

Speaker: Kyle Broder
Affiliation: University of Queensland

Abstract

The last few decades have seen several developments which begin to foreshadow an emerging picture of the relationship between the deformations and moduli of complex manifolds and the curvature of the parameter and total space of the deformation.  In this talk, we will describe this rich and vibrant picture together with a discussion of open problems and prospective applications, including the Hopf problem concerning the existence of a metric of positive sectional curvature on the product of two spheres.