Student seminar

Representation Theory Student Seminar 2021 Semester 2

 

Organisers: Ting Xue, Yaping YangGufang Zhao

Overview

This is a learning seminar on representation theory and related topics, aimed at 3rd year undergraduate students, MSc students, as well as PhD students in mathematics or related fields.

In the learning seminar, participants are expected to learn a topic based on the reference given, and present their work to the other participants. The audience are expected to ask questions and make comments during the presentation. Discussions tangential to the topics are welcome. The idea is for all participants to actively learn and discuss together.

This semester the topic will be Lie groups and their representations. We will follow the chapter on Lie groups by Graeme Segal in the reference below.

Reference: Carter, Roger; Segal, Graeme; Macdonald, Ian, Lectures on Lie groups and Lie algebras. With a foreword by Martin Taylor. London Mathematical Society Student Texts, 32. Cambridge University Press, Cambridge, 1995.

Time: Wednesdays 3:15-4:15pm

Location: Zoom (please contact the organisers for link)

Exercises

Schedule

Oct 27 Adam Monteleone Smooth manifolds, tangent space, one parameter subgroups and the exponential map, continued.

Oct 20 Adam Monteleone Smooth manifolds, tangent space, one parameter subgroups and the exponential map, continued.

Oct 6 Adam Monteleone Smooth manifolds, tangent space, one parameter subgroups and the exponential map

Sep 29 Abraham Zhang Diagonalisation and maximal tori, continued. Notes

Sep 22 Abraham Zhang Diagonalisation and maximal tori

Sep 8 Grace Yuan Polar decomposition, Graham-Schmidt

Sep 1 Yifan Guo Homogeneous spaces, continued. Notes

Aug 25 Yifan Guo Homogeneous spaces Notes

Aug 18 Eskander Salloum SU_2,SO_3,SL_2\mathbb{R}, continued. Notes

Aug 11 Eskander Salloum SU_2,SO_3,SL_2\mathbb{R}

Aug 4 Benjamin Gerraty Examples

 

Date Topics Reference Speaker
Aug 4 Examples [S] 1 Benjamin Gerraty
Aug 11/18 SU_2,SO_3,SL_2\mathbb{R} [S] 2 Eskander Salloum
Aug 25/Sep 1 Homogeneous spaces [S] 3 Yifan Guo
Sep 8 Polar decomposition, Graham-Schmidt, Bruhat decomposition [S] 4 Grace Yuan
Sep 22/29 Diagonalisation and maximal tori [S] 4 Abraham Zhang
Oct 6/20/27 Smooth manifolds, tangent space, one parameter subgroups and the exponential map [S] 5 Adam Monteleone
Nov 24 Lie’s theorems [S] 5 Linfeng Wei
Fourier series and Representation theory [S] 6 Joshua Culbert
Compact groups and integration [S] 7 Justin Tan
Maximal compact subgroups [S] 8 Beaudon Anasson
The Peter-Weyl theorem I [S] 9 Haris Rao
The Peter-Weyl theorem II [S] 9 Haris Rao
Functions on \mathbb{R}^n and S^{n-1} [S] 10
Induced representations [S] 11
The complexification of a compact group [S] 12
The unitary groups and the symmetric groups [S] 13 Weiying Guo
The Borel-Weil theorem [S] 14
References [S] Graeme Segal, Lie groups, in Carter, Roger; Segal, Graeme; Macdonald, Ian, Lectures on Lie groups and Lie algebras. With a foreword by Martin Taylor. London Mathematical Society Student Texts, 32. Cambridge University Press, Cambridge, 1995.

 

 

 

Past seminar

Student seminar 2020S2 and 2021S1