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Lecture Series 2021

Table of Contents

LS2102: Conjugacy Classes and Irreducible Representations of a Group #

Number of Talks: 2

  • Speaker: Shahbaz A. Khan (B. Math, 2022)
  • Talk 1: A Brief Introduction to the Representation Theory of Finite Groups
    Abstract: In this talk, we introduce some concepts from the representation theory of finite groups. Our goal ll be to have a foundation upon which we can build the proof of Burnside’s result about the conjugacy classes of a finite group in the next talk. We’ll briefly discuss unitary and irreducible representations, morphisms and some basics of character theory. Time permitting, we will also discuss the orthogonality relations.
    Slides: Available here.
    Date and Time: Saturday, 27th March 2021, 12:00 PM - 1:30 PM
  • Talk 2: Conjugacy Classes and Irreducible Representations of a Group
    Abstract: In this talk, we will develop the theory of characters further and work with real characters to find nstraints on the number of conjugacy classes of groups with odd order. Specifically, we will understand two theorems credited to Burnside which state that the number of real irreducible characters and real conjugacy classes of a group are equal, and that the number of conjugacy classes in the case of a group with odd order is congruent to the order modulo 16.
    Slides: Available here.
    Date and Time: Sunday, 28th March 2021, 12:00 PM - 1:30 PM
  • Venue: Online (Zoom)
  • References:
  • Pre-requisites: Familiarity with groups and linear maps.
  • Videos: Available here.

LS2101: Arborealism in Group Theory #

Number of Talks: 2

  • Speaker: Balarka Sen (B. Math, 2021)
  • Abstract: We study groups acting on trees following H. Bass and J. P. Serre. The main goal is to reach the arboreal dictionary through many motivating examples. On the way, if time permits, we talk in varying degrees of informality about Cayley graphs and how to recognize them, Stallings’ theorem on ends of groups, Property T, Bruhat-Tits trees, and expander graphs.
  • Reference:
    • Trees – Jean-Pierre Serre
  • Pre-requisites: Nothing specific. However, some familiarity with Groups and Trees would be helpful.
  • Date and Time:
    • Saturday, 20th March 2021, 2:00 PM - 3:30 PM
    • Sunday, 21st March 2021, 2:00 PM - 3:30 PM
  • Venue: Online (Zoom)
  • Videos: Available here.