Speaker: Gunhee Cho (University of California, Santa Barbara)
Title: Introduction to a Hopf fibration and an anti-de Sitter space in sub-Riemannian geometry
Abstract: Sub-Riemannian geometry is a generalization of Riemannian geometry and we introduce Hopf fibration and anti-de Sitter space as natural objects in sub-Riemannian geometry that appears very naturally in various contexts of Physics and Mathematics. On the other hand, Theorem of Hurwitz says that every normed division finite-dimensional algebra has four types: real numbers, complex numbers C, quaternions Q, and octonions O; we introduce heat kernel analysis and its sub-Laplacian, and horizontal Brownian motion on Hopf-fibrations and anti-de Sitter spaces over C, Q, and O, and introduce recent progress including the octonionic setting. These works are the joint work with Fabrice Baudoin.