ABSTRACT:

Quasi-periodic Schrödinger operators possess a rich background in quantum physics. From a mathematical perspective, they are deeply connected to diverse fields such as dynamical systems, fractal geometry, harmonic analysis, and number theory. In this talk, I will survey recent advancements in the study of the spectral properties of quasi-periodic Schrödinger operators, with a particular emphasis on methodologies rooted in dynamical systems. This work is primarily collaborative, undertaken with A. Avila, Y. Last, M. Shamis, and J. You.

BIO:  

Qi Zhou earned his PhD from Nanjing University in 2012. From 2012 to 2015, he held postdoctoral positions at Pierre and Marie Curie University (Sorbonne Université), Paris Diderot University (Université Paris Cité), and the University of California, Irvine. He subsequently served as a professor at Nanjing University from 2016 to 2019. Since 2019, he has been a professor at the Chern Institute of Mathematics, Nankai University. His research focuses on dynamical systems and mathematical physics. In 2024, he was an invited speaker at the International Congress of Mathematical Physics (ICMP).