This seminar is a “joint seminar with Spectral Geometry in the Clouds  https://spectralclouds.github.io/
 
Spectral Inequalities and Quantitative Unique Continuation for Schrödinger operators
Spectral inequalities quantify how strongly a linear combination of low-energy eigenfunctions can concentrate away from a prescribed observation set. In Fourier analysis ,the classical counterpart is the Logvinenko-Sereda theorem, where thickness of the observation set is a natural geometric condition. I will discuss spectral inequalities for confining one-dimensional Schrödinger operators with rough potentials, and some analytic tools behind them. I will also highlight open problems, including sharpness of the geometric hypothesis and extensions to high-dimensional. The talk is based on a joint work with Jiuyi Zhu.