Seminar | Institute of Mathematical Sciences
Time：15:00-16:00, Nov 1, Thursday
Location：Room 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.