AbstractIn this talk, we will discuss spectral variety and related moduli spaces of Higgs pairs on surfaces. We will first introduce the geometry of moduli of Higgs pairs and the spectral varieties. Indeed, we will talk about the Noether-Lefschetz type problems and the Picard schemes of the spectral varieties. If time permits, the Picard group of generic (very general) spectral varieties and it...
Abstract:Spectral analysis of signals is a core component of modern information techniques. The rapid developments of radar detection and wireless communications have advanced its research from fast Fourier transform (FFT) in the 1960s to subspace methods emerging in the 1970s, and then to sparse and compressed sensing methods of this century. In this talk, we revisit the Carathéodory-Fejér Th...