例外几何介绍
The classification of Riemannian manifolds with special holonomy contains two “exceptional” cases: G2 and Spin(7). Manifolds with holonomy contained in G2 or Spin(7) are called G2-manifolds or Spin(7)-manifolds, respectively. In this course, I will introduce various topics of G2 and Spin(7) geometry, mainly focusing on the G2 case. We start from the linear algebra in G2 geometry. Then we study topics such as the structure of a G2-manifold and calibrated geometry/ gauge theory/mirror symmetry on a G2-manifold.
讲师
日期
2022年09月16日 至 12月09日
网站
修课要求
Linear algebra, basics of Riemmanian geometry
参考资料
1. D. D. Joyce, Compact manifolds with special holonomy. Oxford Mathematical Monographs. Oxford University Press, Oxford, 2000. xii+436 pp. ISBN: 0-19-850601-5
2. D. D. Joyce, Riemannian holonomy groups and calibrated geometry. Oxford Graduate Texts in Mathematics, 12. Oxford University Press, Oxford, 2007. x+303 pp. ISBN: 978-0-19-921559-1
3. S. Karigiannis, Deformations of G2 and Spin(7) structures. Canad. J. Math. 57 (2005), no. 5, 1012--1055.
2. D. D. Joyce, Riemannian holonomy groups and calibrated geometry. Oxford Graduate Texts in Mathematics, 12. Oxford University Press, Oxford, 2007. x+303 pp. ISBN: 978-0-19-921559-1
3. S. Karigiannis, Deformations of G2 and Spin(7) structures. Canad. J. Math. 57 (2005), no. 5, 1012--1055.
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Kotaro Kawai于日本东京大学取得学士和硕士学位，并于2013年在日本东北大学博士毕业。此前他以助理教授身份就职于日本学习院大学，学习院大学是日本皇家高等学府，著名教授小平邦彦也在此就职。他于2022年加入BIMSA任副研究员。Kawai主要研究方向是的主要研究方向是微分几何，具体为有例外和乐的流形。