数学科学研究所
Insitute of Mathematical Science

Seminar: Geometric structures, a nonlinear ODE and triangles on the sphere

Seminar | Institute of Mathematical Sciences


Time:15:00-16:00, Nov 1, Thursday

LocationRoom 302, Library


Speaker: Matthew Randall,IMS, ShanghaiTech University


Abstract: The mathematical study of geometric structures on manifolds or higher dimensional spaces inextricably involve the theory of connections. With a connection one can construct quantities such as curvature from which geometric invariants of the manifold can be obtained. One familiar example is that of the Levi-Civita connection on a Riemannian manifold, and its scalar curvature is such an invariant. On another type of geometric structure known as a (2, 3, 5)-distribution on a 5 dimensional manifold, ÉlieCartan has shown in 1910 how to build a connection on the manifold and was able to extract invariants from the curvature of the connection. For a class of (2, 3, 5)-distribution described by a single function of a single variable F(q), the curvature invariant is given by a 6th order nonlinear ODE. We discuss the solutions of this ODE, which turn out to involve triangles on the sphere. The talk includes cameos of mathematicians past and present.


地址:上海市浦东新区华夏中路393号
邮编:201210
上海市徐汇区岳阳路319号8号楼
200031(岳阳路校区)