Title: The Hitchin map and the spectral base

Abstract: We review the recent progress on Chen-Ngo's conjecture on the image of Hitchin map of moduli stack of Higgs bundles over higher dimensional projective manifolds. During the lectures, the following topics will be discussed: the classical case for curves, the non-abelian Hodge theory and the rigidity of representations of fundamental groups. Based on joint works with Siqi He and Ngaiming Mok.