Linear Groups | Prof. Amber Habib | Part 1

Invited Speaker: Prof. Amber Habib (Professor and Head, Department of Mathematics, Shiv Nadar University, School of Natural Sciences, UP).

Title: Linear Groups

Abstract: Undergraduate courses on group theory tend to base their examples mainly on permutations and modular arithmetic (For obvious reasons: this makes it easier to have a self-contained course). On the other hand, much of the importance of group theory in other parts of mathematics or even physics, is due to groups whose elements are linear transformations. In this introduction, we shall see how these 'Linear Groups' feature an interplay of algebra, linear algebra, geometry and metric spaces, and also provide the motivating examples for the more general topic of Lie groups.

#Amber_Habib #mtts #CurryLeafTalks

Time Stamp

00:00:00 Welcome by Jyoti
00:01:32 Words from Session Chair: Prof A Satyanarayana Reddy
00:04:09 Introductory words from Amber Habib
00:11:05 Starting with Matrices
00:18:30 Operator Norm
00:21:40 Basic Properties of Operator Norm
00:27:24 Determinant and Consequences
00:29:38 Remarks about SL(2,R), SL(2,C) & Connection with Harish Chandra
00:32:00 Matrix group with examples
00:39:40 Linear groups with examples
00:43:40 Homomorphisms of Matrix groups
00:53:37 Tangent Spaces
01:05:45 A concrete example of Tangent Space
01:08:37 Another concrete example of Tangent Space
01:13:23 Exponential of a matrix
01:26:23 Plan for next Lecture : Part 2
01:27:42 Q&A

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Credits:
Thumbnail by: Jaskaran Singh
Session Chair: Prof. A Satyanarayana Reddy, Shiv Nadar University
Hosts: Jyoti, Priya Kaveri
Timestamps by: Tamoghna Kar
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