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課程名稱 |
複幾何分析
Topics on Complex Geometric Analysis |
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開課學期 |
107-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
張樹城 |
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課號 |
MATH5099 |
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課程識別碼 |
221 U8440 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期五8,9,10(15:30~18:20) |
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上課地點 |
天數201 |
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備註 |
總人數上限：10人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
(I). Lectures:
1. Kaehler manifolds
2. De Rham theorem and Dolbeault
3. vector bundles
4. Pic (X) and Div(X)
5. Hodge decomposition theorem and Hodge conjecture
6. currents
7. Poincare-Lelong formula
8. line bundles
9. Levi-Civita connections, Chern connection, Chern classes
10. Riemann-Roch theorem
11. L^2 estimates
(II). Topics on
1. Kaehler Ricci flow and Chern-Ricci flow.
2. Lagragian submanifolds and Legendrian submanifolds.
3. CscK metrics and K-stability.
4. Yau uniformization conjectures.
5. Cheeger-Colding Theory.
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課程目標 |
待補 |
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課程要求 |
1. Real and complex analysis
2. Riemannian Geometry |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
1. Kaehler Ricci flow and Chern-Ricci flow.
2. Lagragian submanifolds and Legendrian submanifolds.
3. CscK metrics and K-stability.
4. Yau uniformization conjectures.
5. Cheeger-Colding Theory.
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參考書目 |
1. J.-P. Demailly : L2 Estimates for the dbar-operator on Complex Manifolds.
2. J.-P. Demailly : L2 Vanishing Theorems for Positive Line Bundles and Adjunction Theory.
3. J.-P. Demailly : Complex Analytic and Differential Geometry.
4. Shanyu Ji, Topics on Complex Geometry and Analysis.
5. Fangyang Zheng, Complex Differential Geometry.
6. G. Szekelyhidi, An Introduction to Extremal Kaehler Metrics
7. S.-C. Chang, Lecture note on Kaehler Ricci flow
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
report related papers |
100% |
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