AbstractThe early 20th century witnessed an explosion of activity, much of it centered at Harvard, on rigorizing the property of ergodicity first proposed by Boltzmann in his 1898 Ergodic Hypothesis for ideal gases. Earlier, in the 1880’s, Henri Poincaré and Felix Klein had also initiated a study of discrete groups of hyperbolic isometries. The geodesics in hyperbolic manifolds were discovered...
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...