|Friday 10 April 2020|
|Events for day: Thursday 27 February 2020|
| 12:30 - 14:00 Geometry and Topology Short Course|
Topics in Geometric Analysis
The main goal of this short course is to present a proof of Calabi_Yau theorem. It was first conjectured by Calabi that any volume form on a compact Kahler manifold can be realized as the volume form associated to a Kahler metric. In a seminal work, Yau proved Calabi's conjecture. A very important consequence of Calabi-Yau theorem is the existence of Kahler-Ricci flat metrics on compact Kahler manifolds with trivial canonical bundle.
Outline of the course:
1) background material on complex manifolds, Hermitian and Kahler metrics, Ricci form
2) Some background on elliptic PDE such as Schauder estimates
3) Yau's ...
8:30 - 12:00 Mini-course
Statistical Properties of Piece-wise Expanding Maps
In this mini-course, we will illustrate some functional analytic approaches to the study of the statistical properties of dynamical systems.
We will present Lasota-Yorke technique for existence of absolutely continuous invariant measures for some classes of dynamical systems. We will then study the spectral properties of Frobenius-Perron operator in order to obtain more information about such invariant measures. If time permits, we will continue to talk about the speed of convergence of the iterates of the transfer operator and the central limit theorems.
A. Boyarsky, P. Gora, Laws of chaos ...