School of Mathematical Sciences Academic Report [2025] No. 021  

(High-Level University Construction Series Report No. 1044)  

Lecture Title: Non-Flat Braided Symmetric Algebras and Quantum G₂ Invariants

Speaker: Prof. Zhang Ruibin (University of Sydney)  

Date & Time: 3:00–4:00 PM, March 28, 2025  

Venue: Huiwen Building Room 1420, Shenzhen University  

Abstract: Quantum analogues of symmetric algebras over finite-dimensional modules for quantum groups are mostly "non-flat" in the sense that their homogeneous components have dimensions smaller than those of the corresponding symmetric algebras. Studies of quantum symmetric algebras have so far focused largely on the few flat cases arising in invariant theory, with very little known about non-flat cases. We present results on a class of non-flat quantum symmetric algebras, which is joint work with Hongmei Hu.  

Biography: Prof. Zhang Ruibin is a Professor in the School of Mathematics and Statistics at the University of Sydney, Australia, and serves as Vice President of the Australian Mathematical Society. He has received prestigious awards such as the ARC Queen Elizabeth II Fellow and ARC Australian Professorial Fellow. His research focuses on Lie theory and its applications in quantum physics, with significant international contributions to quantum (super)groups, Lie superalgebras, low-dimensional topology, noncommutative geometry, and quantum physics. He has published over 140 high-impact papers in leading mathematical journals, including Annals of Mathematics、J. Eur. Math. Soc.、Adv. Math、Comm. Math. Phys.、Proc. Lond. Math. Soc., which are widely cited by international peers.  

All faculty and students are welcome to attend!

Invited by: Xiao Wei

School of Mathematical Sciences  

March 27, 2025