Workshop on Group Representations and Related Mathematical Problems

Conference Summary: Workshop on Group Representations and Related Mathematical Problems

Date: June 29 to July 5, 2025
Location: Kunming Tianyuan Mathematical Research Center (TYMRC), China

The "Workshop on Group Representations and Related Mathematical Problems" was successfully held at the Kunming Tianyuan Mathematical Research Center (TYMRC) from June 29 to July 5, 2025. Jointly organized by Academician Zhang Jiping of Peking University and Professor Liao Jun of Hubei University, the workshop brought together over fifty experts and scholars from universities and research institutions across China and abroad.

Aims:
The workshop aimed to:

1. Explore cutting-edge topics in finite groups and representation theory.

2. Report on the latest research trends in related mathematical problems.

3. Foster interdisciplinary collaboration within representation theory and related fields.

4. Offer specialized short courses taught by leading authorities.

Participants:
The workshop attracted more than 50 participants from France, Hong Kong (China), and Mainland China. Attendees included experts, postdoctoral researchers, and PhD students from institutions such as:

· Aix-Marseille University (Olivier Dudas)

· University of Hong Kong

· Academy of Mathematics and Systems Science, Chinese Academy of Sciences

· Peking University

· Tsinghua University

· Capital Normal University

· Shanghai Jiao Tong University

· Fudan University

· Southern University of Science and Technology

· Xiamen University

· Wuhan University

· Harbin Institute of Technology

· Shandong University

· Chongqing University

· Lanzhou University

· South China University of Technology

· Central China Normal University

· Southwest Jiaotong University

· Xidian University

· Yunnan University

· Shanghai University

· Hunan Normal University

· Shantou University

· Huaqiao University

· Jiangxi Normal University

· Hainan University

· Hubei University

Scope:
Conference presentations covered a wide range of research frontiers, including:

· Representations of Finite Reductive Groups

· McKay Correspondence

· Lie Groups and Algebraic Groups

· Spectral Sequences

· Deligne–Lusztig Theory

· Alperin Weight Conjecture,Broué's Abelian Defect Group Conjecture

· Group and graph
These sessions facilitated thorough discussions on the latest advances and future challenges in finite group representation theory.

Short Courses:
Four specialized short courses were offered:

1. Chen Yifei (Academy of Mathematics and Systems Science, CAS): An Introduction to McKay Correspondence

2. Olivier Dudas (Aix-Marseille University): Symmetries of Characters of Finite Reductive Groups

3. Yu Jun (Peking University): Finite Order Automorphisms of Lie Algebras and Algebraic Groups

4. Xu Xingzhong (Hubei University): Spectral Sequences

Academic Presentations:
A total of 30 high-level academic talks were delivered, spanning diverse areas such as:

· Representations of finite groups

· Algebraic representation theory

· Lie Algebras and Vertex Operator Algebras

· Groups and Graphs

Summary and Outlook:

Participants engaged in lively and in-depth academic discussions on the aforementioned topics, fostering collaboration and exchange between young scholars and established experts. The workshop achieved significant outcomes, with the excellent software/hardware facilities and open environment of the Tianyuan Center providing a high-quality platform for interaction. Several collaborative initiatives were initiated during the conference.