Dr Xiao Han

Research

Hopf Algebras, Hopf algebroids (Groupoids and their Quantization), Noncommutative Geometry, Noncommutative principal bundles (Hopf Galois extensions)

Interests

My working area mainly focuses on non-commutative geometry, non-commutative principal bundle, Quantum groups (groupoids), and mathematical Physics. My work has been on the interface of geometry, algebra, and category theory. Specifically, noncommutative geometry including Hopf algebras (quantum groups) and non-commutative principal bundle with quantum group fibre (Hopf Galois extensions), and more recently on Hopf algebroids and Hopf 2-algebras. Noncommutative or `quantum' geometry is about working with coordinate algebras as of on a manifold but where the algebra could be noncommutative, with the most well-known approach being that of Connes using cyclic cohomology and the notion of `spectral triple' or abstract Dirac operator.