Description
We will discuss the geometry of strongly parabolic Hitchin systems for classical groups over smooth curves. We begin by relating the singularities of generic spectral curves to Kazhdan--Lusztig maps, and then explain how the generic Hitchin fibers can be identified with natural abelian varieties. If time permits, we will also discuss the structure of the Hitchin base for even special orthogonal groups. This talk is based on joint works with Xiaoyu Su, Xueqing Wen and Yaoxiong Wen.