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Geometry and Topology Short Course
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دورهٔ کوتاهمدت درسی هندسه و توپولوژی
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TITLE
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Topics in Geometric Analysis
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SPEAKER
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TIME
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Thursday, February 6, 2020,
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12:30 - 14:00
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Thursday, February 13, 2020,
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12:30 - 14:00
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Thursday, February 20, 2020,
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12:30 - 14:00
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Thursday, February 27, 2020,
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12:30 - 14:00
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Thursday, March 5, 2020,
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12:30 - 14:00
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VENUE |
Lecture Hall 2, Niavaran Bldg.
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SUMMARY |
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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)
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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 |
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