Lecture Content：

We identify the quantized Hall conductance of Landau levels with a Fredholm index by using the theories of Helton-Howe-Carey-Pincus and Toeplitz operators on the classic Fock space and higher Fock spaces. The index computations reduce to the single elementary one for the lowest Landau level. This brings new insights to the extraordinarily accurate quantization of the Hall conductance as measured in quantum Hall experiments. This is joint work with Guo Chuan Thiang.

Speaker Introduction:

Xia Jingbo is an internationally renowned operator theorist, serving as a professor at the State University of New York at Buffalo and a distinguished professor at Jiaxing University. His main research interests include function spaces, operator theory, and operator algebras, where he has achieved a series of significant research outcomes. His related work has been published in top-tier international mathematical journals such as the American Journal of Mathematics, Advances in Mathematics, Transactions of the American Mathematical Society, Communications in Mathematical Physics, Indiana University Mathematics Journal, and Journal of Functional Analysis.