Topological Mirror Symmetry of Parabolic Hitchin Systems

In this talk, we will first talk about generic fibers of parabolic Hitchin maps. In particular, we show that they are torsors over dual Abelian varieties when the structure groups are SLn/PGLn. Then we will follow Groechenig-Wyss-Ziegler's strategy to prove the topological mirror symmetry between parabolic SLn/PGLn Hitchin systems via p-adic integration. This is joint work with Xueqing Wen and Xiaoyu Su.