Differential geomtery of manifold with special holonomy and their calibrated submanifolds

我的研究方向是微分几何，这是一个纯数学领域，研究高维空间中某些几何形状的存在和性质。目前用于极小距离和大能量的物理理论(超弦理论和超引力)需要描述一些7维和8维的几何形状，这些几何形状具有与曲率相关的特殊性质。这些天体也一直具有独立的数学兴趣，因为它们与代数中出现的一些奇怪的例外密切相关。目标是研究可能存在的具有这些特殊曲率属性的几何形状类型。这将有助于更好地理解物理理论和描述它们所需的美丽数学。

My research program is in differential geometry, an area of pure mathematics which studies the existence and properties of certain kinds of geometric shapes in high dimensions. Current theories of physics for very small distances and large energies (superstring theory and supergravity) require for their description some geometric shapes of dimensions 7 and 8, possessing special properties related to their curvature. These objects have also been of independent mathematical interest, because they are closely related to some strange exceptions that arise in algebra. The goal is to study the possible types of geometric shapes that can exist with these special curvature properties. This will contribute to a better understanding of the physical theories and the beautiful mathematics which is needed to describe them.