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
//eta.impa.br/dl/PL020.pdf
//arxiv.org/abs/1808.03995
本文分为Kahler几何与例外和乐群两部分。第一部分主要讨论Fano流形上Kahler-Einstein度量的存在性与各种稳定性的关系（特别给出了YTD猜想的四种不同证明）。第二部分讨论例外和乐群G_2和Spin(7)，尤其是具有这两个和乐群的流形上的规范理论(Donaldson-Thomas理论)和校准几何。
相关附件
1-PL020 Donaldson.pdf
