Introduction to Exceptional Geometry
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.
Lecturer
Date
16th September ~ 9th December, 2022
Website
Prerequisite
Linear algebra, basics of Riemmanian geometry
Reference
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.
Audience
Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Kotaro Kawai got a bachelor's degree and a master's degree from the university of Tokyo, and received his Ph.D from Tohoku university in 2013. He was an assistant professor at Gakushuin university in Japan, then he moved to BIMSA in 2022. His research interests are in differential geometry, focusing on manifolds with exceptional holonomy.