Báo cáo khoa học 演講訊息

We study Hitchin's equations and Higgs bundles over a non-orientable manifold whose oriented cover is compact K\"ahler. Using the involution induced by the deck transformation, we show that the moduli space of Higgs bundles is Langrangian/complex with respect to the hyper-K\"ahler structure on Hitchin's moduli space associated to the oriented cover.We then establish a Donaldson-Corlette type correspondence and relate Hitchin's moduli space to representation varieties. This is a joint work with N.-K.~Ho and G.~Wilkin.