# Reading Seminar: Representation theory - The basics

**Lecturer:**Joscha Diehl**Date:**first lecture: Tuesday 16.10.2018 at 11:00h**Room:**Section F**Language:**English**Target audience:**MSc students, PhD students, Postdocs**Keywords:**representation theory; symmetric group; GL

## Abstract:

Groups are a fundamental construct to understand “symme- tries”. They are best understood by studying their action on linear vector spaces, that is via **linear representations **i.e. their concrete realization as matrices. This for example appears in

- harmonic analysis (think: the Fourier transform of periodic functions)
- tensor decomposition (a matrix (a 2-tensor) can be split into a symmetric part and an antisymmetric part; what about higher order tensors?)
- the study of certain Markov chains

This is a reading group of

*Fulton, William, and Joe Harris. Representation theory: a ﬁrst course. Vol. 129. Springer Science & Business Media, 2013. *

We will go through Chapter 1-15; at the speed required by the group. Starting essentially from scratch in Chapter 1, at the end we will have a solid understanding of representations of the symmetric group (permutations) and the general linear group (invertible matrices).

Each week one designated “leader” will guide the session, but all attendants are asked to read the relevant chapter before. We will work with examples (by hand and by code) as much as possible. We will meet for the ﬁrst time in the common area of Section F3, Tuesday 16.10.2018 at 11:00h.

## Regular Lectures (Winter 2018/2019)

**Condition: the geometry of numerical algorithms**- Paul Breiding
- Tuesday, 09:00 - 10:00, MPI MiS G3 10, till January 30

**Information, Physics and Computation**- Pau Vilimelis Aceituno
- Wednesday, 13:00 - 14:30, MPI MiS A3 02

**Introduction to Random Algebraic Geometry**- Antonio Lerario
- Tuesday, 09:00 - 10:00, MPI MiS G3 10, from February 6 to March 27

**Random dynamical systems and stochastic porous media equations with nonlinear noise**- Benjamin Gess
- Monday, 16:15 - 17:45, MPI MiS A3 01

**Artiﬁcial Neural Networks and Machine Learning: Theoretical Foundations**- Nihat Ay
- Thursday, 11:15 - 12:45, MPI MiS A3 01

**Geometric and topological methods for the analysis of data in biology, neurobiology and other fields**- Jürgen Jost
- Friday, 13:30 - 15:00, MPI MiS A3 01

**Singular stochastic PDEs**- Nicolas Perkowski
- Wednesday, 11:15 - 12:45, MPI MiS A3 01

**Seminar on inverse spectral theory**- Angkana Rüland
- Thursdays, 9:15 - 10:45, Leipzig University, SG 3-14

**Introduction into regularity structures**- Falix Otto
- Wednesday, 09:10 - 11:00, MPI MiS A3 01

**Toric Varieties**- Mateusz Michalek
- Friday, 11:00 - 12:30, MPI MiS G3 10

**Morse Theory and Closed Geodesics**- Hans-Bert Rademacher
- Wednesday, 13:15 - 14:45, Leipzig University, SG 3-10

**An introduction to Information Geometry and Mathematical Population Genetics**- Tat Dat Tran
- Friday, 15:15 - 16:45, MPI MiS A3 02

**Reading Seminar: Representation theory - The basics**- Joscha Diehl
- first meeting: Tuesday 16.10.2018 at 11:00h, F3 Section

**Reading Seminar: Geometric Measure Theory**- Renan Assimos Martins, Kostas Zemas
- Monday, 15:00 - 17:00

**Geometric and Algebraic Combinatorics**- Bernd Sturmfels
- October, 29 – November 2 and November 16

**IMPRS-Ringvorlesung**- Nihat Ay, Christiane Görgen, Guido Montúfar, André Uschmajew, Stefan Hollands
- Tuesday, 10:00 - 12:00 (tba), MPI MiS G3 10