Some recent developments in Kähler geometry and exceptional holonomy – Simon Donaldson – ICM2018

Plenary Lecture 1
Some recent developments in Kähler geometry and exceptional holonomy
Simon Donaldson

Abstract: This article is a broad-brush survey of two areas in differential geometry. While these two areas are not usually put side-by-side in this way, there are several reasons for discussing them together. First, they both fit into a very general pattern, where one asks about the existence of various differential-geometric structures on a manifold. In one case we consider a complex Kähler manifold and seek a distinguished metric, for example a Kähler–Einstein metric. In the other we seek a metric of exceptional holonomy on a manifold of dimension 7 or 8. Second, as we shall see in more detail below, there are numerous points of contact between these areas at a technical level. Third, there is a pleasant contrast between the state of development in the fields. These questions in Kähler geometry have been studied for more than half a century: there is a huge literature with many deep and far-ranging results. By contrast, the theory of manifolds of exceptional holonomy is a wide-open field: very little is known in the way of general results and the developments so far have focused on examples. In many cases these examples depend on advances in Kähler geometry.

ICM 2018 – International Congress of Mathematicians ©
www.icm2018.org

Видео Some recent developments in Kähler geometry and exceptional holonomy – Simon Donaldson – ICM2018 канала Rio ICM2018