Student seminar

Representation Theory Student Seminar 2021 Semester 2 and 2022 Semester 1&2

Organisers: Ting Xue, Yaping Yang, Gufang Zhao

Student organiser (2022S2): Davood Nejaty

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 11-12

Location: Peter Hall 107 and Zoom (please contact the organisers for zoom link)

Exercises

Schedule (2022S2)

Time: Wednesdays 11-12

Oct 19/26 Kevin Fergusson The unitary and symmetric groups

Oct 12 Ali Khalili The complexification of a compact group

Oct 4 Cancelled

Sep 21 Amit Ben Harim Induced representations, continued

Sep 14 Amit Ben Harim Induced representations

Sep 7 Haris Rao The Peter-Weyl theorem, continued

Aug 31 Yuhan Gai Functions on $\mathbb{R}^n$ and $S^{n-1}$

Aug 24 Cancelled

Aug 17 Haris Rao The Peter-Weyl theorem

Schedule (2022S1)

Time: Mondays 11-12

Location: Peter Hall 107 and Zoom (please contact the organisers for zoom link)

Student organisers (2022S1): Weiying Guo and Davood Nejaty

May 30 Beaudon Anasson Maximal compact subgroups

May 23 Zhongtian Chen Compact groups and integration, continued

May 16 Zhongtian Chen Compact groups and integration

May 9 Kevin Fergusson Fourier series and Representation theory

May 2 Davood Nejaty Review, continued

Grace Yuan Bruhat decomposition Notes

Apr 11 Organisational meeting and review of previous topics

Schedule (2021S2)

Time: Wednesdays 3:15-4:15pm

Location: Zoom (please contact the organisers for link)

Dec 1 Linfeng Wei Lie’s theorems, continued. Notes

Nov 24 Linfeng Wei Lie’s theorems

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

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, 2021	Examples	[S] 1	Benjamin Gerraty
Aug 11/18, 2021	$SU_2,SO_3,SL_2\mathbb{R}$	[S] 2	Eskander Salloum
Aug 25/Sep 1, 2021	Homogeneous spaces	[S] 3	Yifan Guo
Sep 8, 2021	Polar decomposition, Graham-Schmidt, Bruhat decomposition	[S] 4	Grace Yuan
Sep 22/29, 2021	Diagonalisation and maximal tori	[S] 4	Abraham Zhang
Oct 6/20/27, 2021	Smooth manifolds, tangent space, one parameter subgroups and the exponential map	[S] 5	Adam Monteleone
Nov 24/Dec1, 2021	Lie’s theorems	[S] 5	Linfeng Wei
May 9/2022	Fourier series and Representation theory	[S] 6	Kevin Fergusson
May 16, 23/2022	Compact groups and integration	[S] 7	Zhongtian Chen
May 30/2022	Maximal compact subgroups	[S] 8	Beaudon Anasson
Aug 17, Sep 7, 2022	The Peter-Weyl theorem	[S] 9	Haris Rao
Aug 31, 2022	Functions on $\mathbb{R}^n$ and $S^{n-1}$	[S] 10	Yuhan Gai
Sep 14/21, 2022	Induced representations	[S] 11	Amit Ben Harim
Oct 12, 2022	The complexification of a compact group	[S] 12	Ali Khalili
Oct 19/26, 2022	The unitary groups and the symmetric groups	[S] 13	Kevin Fergusson
	The Borel-Weil theorem	[S] 14	Ali Khalili
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

Special lectures by Arun Ram summer 2021/22

Student seminar 2020S2 and 2021S1