NPTEL 黎曼曲面和代数曲线入门 一维复环面和椭圆曲线 (NPTEL, An Introduction to to Riemann Surfaces ...）
https://www.youtube.com/playlist?list=PLbMVogVj5nJSm4256vuITlsovUT1xVkUL
封面：https://www.instagram.com/p/BxjVzBuFqxR/
公开课目录：https://github.com/wenhan-wu/OpenCourseCatalog
讲师：T.E. Venkata Balaji
课程链接：https://www.youtube.com/playlist?list=PLbMVogVj5nJSm
视频选集
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01. The Idea of a Riemann Surface
57:13
02. Simple Examples of Riemann Surfaces
57:47
03. Maximal Atlases and Holomorphic Maps of Riemann Surfaces
50:58
04. A Riemann Surface Structure on a Cylinder
54:56
05. A Riemann Surface Structure on a Torus
48:27
06. Riemann Surface Structures on Cylinders and Tori via Covering Spaces
56:44
07. Moebius Transformations Make up Fundamental Groups of Riemann Surfaces
48:34
08. Homotopy and the First Fundamental Group
53:35
09. A First Classification of Riemann Surfaces
49:03
10. The Importance of the Path-lifting Property
57:49
11. Fundamental groups as Fibres of the Universal covering Space
56:52
12. The Monodromy Action
53:33
13. The Universal covering as a Hausdorff Topological Space
01:01:02
14. The Construction of the Universal Covering Map
55:26
15. Completion of the Construction of the Universal Covering- Universality of th
37:29
16. Completion of the Construction of the Universal Covering- The Fundamental Gr
43:47
17. The Riemann Surface Structure on the Topological Covering of a Riemann Surfa
59:12
18. Riemann Surfaces with Universal Covering the Plane or the Sphere
01:18:54
19. Mod-04 Lec-18 Classifying Complex Cylinders Riemann Surfaces
01:01:22
20. Characterizing Moebius Transformations with a Single Fixed Point
56:08
21. Characterizing Moebius Transformations with Two Fixed Points
01:01:38
22. Torsion-freeness of the Fundamental Group of a Riemann Surface
46:25
23. Characterizing Riemann Surface Structures on Quotients of the Upper Half-Pla
01:12:59
24. Classifying Annuli up to Holomorphic Isomorphism
45:18
25. Orbits of the Integral Unimodular Group in the Upper Half-Plane
01:15:20
26. Galois Coverings are precisely Quotients by Properly Discontinuous Free Acti
01:05:23
27. Mod-05 Lec-26 Local Actions at the Region of Discontinuity of a Kleinian Sub
01:11:25
28. Quotients by Kleinian Subgroups give rise to Riemann Surfaces
50:51
29. The Unimodular Group is Kleinian
01:06:11
30. The Necessity of Elliptic Functions for the Classification of Complex Tori
48:16
31. The Uniqueness Property of the Weierstrass Phe-function associated to a Latt
01:08:15
32. The First Order Degree Two Cubic Ordinary Differential Equation satisfied by
01:06:12
33. The Values of the Weierstrass Phe-function at the Zeros of its Derivative ar
49:25
34. The Construction of a Modular Form of Weight Two on the Upper Half-Plane
55:50
35. The Fundamental Functional Equations satisfied by the Modular Form of Weight
54:34
36. The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the
56:55
37. The Weight Two Modular Form Vanishes at Infinity
50:47
38. The Weight Two Modular Form Decays Exponentially in a Neighbourhood of Infin
43:36
39. A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Confo
50:24
40. The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic Curve
59:17
41. A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-Inva
51:28
42. The Fundamental Region in the Upper Half-Plane for the Unimodular Group
01:16:24
43. A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly Once
49:46
44. Moduli of Elliptic Curves
01:08:12
45. Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in C
01:00:33
46. The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Pla
01:09:14
47. Complex Projective 2-Space as a Compact Complex Manifold of Dimension Two
43:29
48. Complex Tori are the same as Elliptic Algebraic Projective Curves
36:19
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