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 1112
Location: Peter Hall 107 and Zoom (please contact the organisers for zoom link)
Exercises
Schedule (2022S2)
Time: Wednesdays 1112
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 PeterWeyl theorem, continued
Aug 31 Yuhan Gai Functions on and
Aug 24 Cancelled
Aug 17 Haris Rao The PeterWeyl theorem
Schedule (2022S1)
Time: Mondays 1112
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 3:154:15pm
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, GrahamSchmidt
Sep 1 Yifan Guo Homogeneous spaces, continued. Notes
Aug 25 Yifan Guo Homogeneous spaces Notes
Aug 18 Eskander Salloum , continued. Notes
Aug 11 Eskander Salloum
Aug 4 Benjamin Gerraty Examples
Date  Topics  Reference  Speaker 
Aug 4, 2021  Examples  [S] 1  Benjamin Gerraty 
Aug 11/18, 2021  [S] 2  Eskander Salloum  
Aug 25/Sep 1, 2021  Homogeneous spaces  [S] 3  Yifan Guo 
Sep 8, 2021  Polar decomposition, GrahamSchmidt, 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 PeterWeyl theorem  [S] 9  Haris Rao 
Aug 31, 2022  Functions on and  [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 BorelWeil 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