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Lecture Series 2019

Table of Contents

LS1901: The Extension Problem & Cohomology of Groups #

Number of Talks: 2

  • Speaker: Balarka Sen (B. Math, 2021)
  • Abstract: One of the most natural ways to understand a group is to “break it down” to smaller groups which are easier to understand. The problem then translates to understanding how these smaller “stratum groups” interact, or glue together, in the original group. This is known as ‘the extension problem’. We will try to understand the geometry of the basic examples of group extensions we understand: semi-direct products, in which case this “gluing recipe” is relatively simple. We will try to understand precisely when a group can be written as a semidirect product of two smaller groups, and in the process introduce and motivate “cohomology theory”, an idea which seems to have left it’s trace on most corners of twentieth century mathematics.
  • Pre-requisites: Basic Group Theory.
  • Date and Time:
    • Saturday, 26th January 2019, 3:15 PM
    • Sunday, 27th January 2019, 3:15 PM
  • Venue: G-24 Classroom, Academic Building