|Saturday 26 September 2020|
|Events for day: Thursday 06 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
Group Actions, Ergodic Theory and Rigidity
Our aim in this course is to review some results and techniques in ergodic theory of action of Lie groups and their discrete subgroups and then to sketch the proof of a profound theorem of G. A. Margulis known as "superrigidity".
Margulis' superrigidity theorem says that under some conditions on Lie groups and their discrete subgroups, any isomorphism between discrete subgroups extends to isomorphism of the ambient groups, and roughly speaking these discrete subgroups determines the Lie groups completely.
To this end, we need to talk about some backgrounds from the structure theory of semisimple Lie groups and Algebraic gr ...