Introduction

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 Spin(7) case. We start from the linear algebra in Spin(7) geometry. Then we study topics such as the torsion of a Spin(7)-structure, topological properties of compact Spin(7)-manifolds, the moduli theory, and calibrated geometry.

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.