Parabolic Hitchin System and Mirror Symmetry
报告人：Xiaoyu Su (Tsinghua University)
Abstract: A very important class of hyperkaehler mirror partners are moduli spaces of SL_r and PGL_r-Higgs bundles. Hausel and Thaddeus proved that the moduli spaces of SL_r and PGL_r-Higgs bundles on a smooth projective curve are mirror partners in the sense of Strominger-Yau-Zaslow ([SYZ96]) (i.e. generic fibers are dual abelian varieties). Inspired by the SYZ philosophy, Hausel-Thaddeus in [HT01, HT03] conjectured that the moduli spaces of SL_r and PGL_r-Higgs bundles over both smooth and parabolic curves are topological mirror partners (i.e. have equal stringy Hodge numbers) and proved this for r=2,3. On the other hand, a very recent paper by Groechenig-Wyss-Ziegler [GWZ20 Mirror symmetry for moduli spaces of higgs bundles via p-adic integration invent. math] uses p-adic integration to prove Hausel and Thaddeus' topological mirror symmetry conjecture holds over a smooth projective curve.
In this talk we will talk about our recent work on the topological mirror symmetry conjecture for moduli of Higgs bundles over parabolic curves. We will first review the concept of mirror symmetry and in particular in the since of Strominger-Yau-Zaslow and Hausel-Thaddeus. Then we will talk about our way to check the SYZ and topological mirror symmetry partners property for moduli of Higgs bundles over a parabolic curve. This is a joint work with Xueqing Wen and Bin Wang.