Exact Mobility Edges for Almost-Periodic CMV Matrices via Gauge Symmetries

：Darren C. Ong（厦门大学马来西亚分校）
：2026-03-05 15:00
：海韵园实验楼S102

报告人：Darren C. Ong（厦门大学马来西亚分校）

时  间：2026年3月5日15:00

地  点：海韵园实验楼S102

内容摘要:

We investigate the symmetries of the so-called generalized extended Cantero–Moral–Velázquez (CMV) matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant fashion by passing to the class of generalized extended CMV matrices via explicit diagonal unitaries in the spirit of Cantero–Grünbaum–Moral–Velázquez. As an application of these ideas, we construct an explicit family of almost-periodic CMV matrices, which we call the mosaic unitary almost-Mathieu operator, and prove the occurrence of exact mobility edges. That is, we show the existence of energies that separate spectral regions with absolutely continuous and pure point spectrum and exactly calculate them.

个人简介：

Darren C. Ong (王忠理) is a Professor of Mathematics at Xiamen University Malaysia. He received his PhD from Rice University in the USA. His research focus is on spectral theory and mathematical physics. He has published several research papers in leading international journals, including International Mathematics Research Notices, Communications in Mathematical Physics, Transactions of the American Mathematical Society, among others.

 

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