Abstract

In this talk, we will focus on Sp/SO Hitchin systems on marked curves with residues of Higgsfields lying in special nilpotent orbit closures which are related by the Springer correspondence. Wewill first show how to resolve singularities of generic spectral curves using Spaltenstein'sdescription of Kazhdan-Lusztig maps for classical groups via characteristic polynomials. Then wewill discuss generic fibers of Hitchin maps and show the mirror symmetry for parabolic Sp/S0Hitchin systems. This is a joint work with Xueging Wen and Yaoxiong Wen.