Seminar| Institute of Mathematical Sciences
Time: Thursday, October 24th, 2024 , 14:30-15:20
Speaker: Tao Ding, ShanghaiTech
Abstract: I will give a light review on how the analysis of boundary conditions in 2d gauge theories is connected to the study of (auto) equivalences of triangulated categories and, if time allows, how it comnect to other problems in pure mathematics, such as homological projective duality and the study of semiorthogonal decompositions.This talk is designed to be accessible to both mathematicians interested in geometry and statisticians focused on data science. The statistical analysis of covariance and correlation matrices presents unique challenges, as these matrices do not reside in a vector space with a standard additive structure. However, non-singular covariance and correlation matrices form Riemannian manifolds, providing a robust geometric framework that enables the adaptation of classical linear statistical methods for this non-linear context. In this talk, I will introduce a manifold-valued time series model that incorporates key Riemannian operations, including the Riemannian metric, exponential and logarithmic maps, parallel transport, orthonormal coordinate systems, and Fréchet sample means and variances. We will particularly highlight the mathematical formulation within the quotient space, specifically focusing on the newly developed Riemannian manifold of full-rank correlation matrices. Finally, I will present statistical modelling results within this manifold framework, with a specific application to EEG data from epilepsy.