Linear Groups | Prof. Amber Habib | Part 2

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 Priya Kaveri
00:00:58 Words from Session Chair: Pradip Kumar
00:03:06 Introductory words from Amber Habib
00:04:18 Highlights from Part:1 by Priya Kaveri
00:08:45 Review of first lecture by Amber Habib
00:14:26 Exponential Map
00:36:44 Lie Algebra
01:08:28 Example: Tangent Space of SL(n,R)
01:11:16 Example: Tangent Space of O(n,R)
01:24:37 Lie Algebra Homomorphisms
01:29:10 References for further study
01:32:49 Q&A
01:43:43 Vote of thanks by Priya Kaveri

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Credits:
Thumbnail by: Jyoti
Session Chair: Dr. Pradip Kumar, Shiv Nadar University
Hosts: Jyoti, Priya Kaveri
Timestamps by: Tamoghna Kar
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