IPM

                                پژوهشگاه دانش‌های بنیادی
پژوهشکدهٔ ریاضیات


Geometry and Topology Short Course دورهٔ کوتاه‌مدت درسی هندسه و توپولوژی




TITLE  
Topics in Geometric Analysis


SPEAKER  
Reza Seyyedali  
IPM  
 


TIME  
Thursday, February 6, 2020,   12:30 - 14:00
Thursday, February 13, 2020,   12:30 - 14:00
Thursday, February 20, 2020,   12:30 - 14:00
Thursday, February 27, 2020,   12:30 - 14:00
Thursday, March 5, 2020,   12:30 - 14:00


VENUE   Lecture Hall 2, Niavaran Bldg.



SUMMARY

 

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 original proof on apriori $C^0$ estimate
4) Some advance approach to Calabi-Yau theorem
5) an overview on complex Monge-Ampere via Pluripotential theory (if time permitted)

 




تهران، ضلع‌ جنوبی ميدان شهيد باهنر (نياوران)، پژوهشگاه دانش‌های بنيادی، پژوهشکده رياضيات
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Niavaran Bldg., Niavaran Square, Tehran
ipmmath@ipm.ir   ♦   +98 21 22290928   ♦  math.ipm.ir