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:We first give an brief introduction on the topic of hyperplane arrangement. Then we give concrete formulas for these L^2 type invariants at degree 1 and study their connections with combinatorics. If time allows, some similar results for smooth complex quasi-projective variety will be discussed