Abstract: This talk aims to advertise a pattern/phenomenon that has emerged in many different mathematical areas during the past decades but is not currently well-understood. I will begin with a broad overview of the Kahler packages (Poincare duality, Hard Lefschetz, and Hodge-Riemann relations) that appear in geometry, algebra, and combinatorics, from the classics of Lefschetz to the recent wo...
Abstract:In this talk, I will discuss in detail the convergence result of the Gaussian mixture particle filters, in which each particle in the estimation system is regarded as a Gaussian distributed random variable, rather than a simple particle as in the classical particle filters. The convergence rate of the particle system will be given. The relationship between the Gaussian mixture particl...