An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://www.nptel.iitm.ac.in/syllabus/111106044/

Goals of the Lecture:

– To see how the real plane can be equipped with two different Riemann Surface structures

– To see how the real 2-dimensional sphere can be equipped with a Riemann surface structure

Keywords for Lecture 2:

Complex coordinate chart, compatible charts, transition function, complex atlas, Riemann surface, holomorphic function, unit disc, complex plane, Uniformisation theorem, simply connected, Riemann sphere, Riemann mapping theorem