# Representation theory of finite groups

**Lecturer:**Arthur Bik**Date:**Thursdays 7:30-9:00 and Fridays 9:15-10:45**Room:**SG 3-10**Keywords:**Representation theory, Group actions, Characters**Prerequisites:**Basic knowledge about groups and vector spaces**Remarks:**https://personal-homepages.mis.mpg.de/arbik/reptheory22.html

## Abstract

Representation theory is about understanding and exploiting symmetry using linear algebra. The central objects of study are linear actions of groups on vector spaces. This gives rise to a very structured and beautiful theory. The aim of this course dealing with finite groups and complex vector spaces is to introduce this theory. Representation theory plays a major role in mathematics and physics. For example, it provides a framework for understanding finite groups, special functions, and Lie groups and algebras. In number theory, Galois groups are studied via their representations; this is closely related to modular forms. In physics, representation theory is the mathematical basis for the theory of elementary particles. After introducing the concept of a representation of a group, we will study decompositions of representations into irreducible constituents. A finite group only has finitely many distinct irreducible representations; these are encoded in a matrix called the character table of the group. One of the goals of this course is to use representation theory to prove Burnside's theorem on solvability of groups whose order is divisible by at most two prime numbers. Another goal is to construct all irreducible representations of the symmetric group.To keep informed about changes to this lecture subscribe to lecture mailinglist

## Regular lectures: Summer semester 2022

**Representation theory of finite groups**- Arthur Bik
- Thursdays 7:30-9:00 and Fridays 9:15-10:45, SG 3-10
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**Bielefeld-Leipzig online seminar: Mathematics of Machine Learning**- Benjamin Gess
- Wednesdays 16:15-17:45, Videobroadcast

**Mathematical methods in biology and neurobiology**- Jürgen Jost
- Friday, 14.00, MPI MiS E1 05 (Leibniz)
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**Tropical Probability Theory**- Rostislav Matveev
- Wednesday, 11.00-12.30, MPI MiS A3 02
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**Non-backtracking operators of graphs**- Raffaella Mulas, Leo Torres
- Mondays at 3pm, starting May 2, MPI MiS A3 01
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**Recent developments in discrete Ricci curvature**- Florentin Münch
- Wednesday, 15.00, MPI MiS A3 01
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**First-order and online optimization methods**- Katerina Papagiannouli, André Uschmajew
- Lectures: Tuesdays 11:00-12:30, Exercises (biweekly): Tuesdays 14:00-15:00, MPI MiS G3 10
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**Spin Glasses**- Tobias Ried
- tba, Videobroadcast
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**IMPRS Ringvorlesung****Lecturers:**Bernd Rosenow, Felix Otto, Sayan Mukherjee**Date**: usually Thursdays, 9.15 - 10.45, see schedule for**divergent dates and times**and more info**Room:**MPI MiS, Leibniz-Hörsaal, also hybrid- To keep informed about changes to this lecture subscribe to lecture mailinglist