# An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves

IIT Madras, , Prof. T.E. Venkata Balaji

Updated On 02 Feb, 19

IIT Madras, , Prof. T.E. Venkata Balaji

Updated On 02 Feb, 19

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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 httpwww.nptel.iitm.ac.insyllabus111106044Goals of the Lecture- To look at the set of all possible Riemann surface structures on a cylinder and theneed for a method to distinguish between them- To explain the motivation for the use of the Theory of Covering Spaces to distinguishRiemann surface structures- To motivate the notion of a covering map by examples- To get introduced to the fact (called General Uniformisation) that any Riemann surfaceis the quotient (via a covering map) of a suitable simply connected Riemann surface- To understand the idea of the Fundamental group and where it fits into our discussionKeywords for Lecture 6Cylinder, punctured plane, punctured unit disc, annulus, Riemanns Theorem on removable singularities, covering map, covering space, pathwise connected, locally pathwise connected, admissible neighbourhood or admissible open set, universal covering space or simply connected covering space, fundamental group, uniformisation of a general Riemann surface

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.