|Date: Friday, April 06, 2018
Location: 3866 East Hall (3:00 PM to 4:00 PM)
Title: Applications of persistent homology in symplectic and Riemannian geometry
Abstract: Riemannian metrics are usually not easy to be compared in a quantitative way. In this talk, we will view this problem from symplectic geometry. The tools that will be introduced are persistent homology and symplectic homology. The former one with root in applied algebraic topology now has a fast development in various branches of geometry while the latter one is a standard tool (with origins of Floer theory) for study of nice domains of symplectic manifold. More concretely, we will introduce a quantitative measurement between two "normalized" metrics and our main result is that this measurement can be controlled by some combinatorics data, which implies some coarse geometry type result on the space of Riemannian metrics.
Speaker: Jun Zhang
Institution: Tel Aviv University
Event Organizer: Dan Burns