Title: An Introduction to Quantum Groupoids and Their Duality

Speaker: Frank Taipe

Time: 9.2 (Tuesday), 14:30-18:00

 9.9 (Tuesday), 14:30-18:00

 9.16 (Tuesday), 14:30-18:00

Venue: Gewu Building 315

Abstract ：Operator-algebraic quantum groupoids generalise the concept of quantum groups within the framework of operator algebras by incorporating structures that accommodate nontrivial base algebras and partial symmetries. These entities—encompassing, C*-algebraic quantum groupoids and measured quantum groupoids—arise naturally in the analysis of depth-two inclusions of von Neumann algebras and in the study of noncommutative dynamical systems. In contrast to locally compact quantum groups, quantum groupoids possess a more intricate algebraic and analytical structure, allowing for the modelling of symmetries in contexts where global group symmetries are inadequate. This introductory mini-course outlines the foundational ideas and motivations underpinning operator-algebraic quantum groupoids, with particular emphasis on their connections to subfactor theory, their categorical interpretation, and their role in extending the notion of symmetry beyond the classical group-theoretic framework.