Lectures on Higgs bundles and related topics
10:00am-12:00pm
Xiaoyu Su (Tsinghua University)
Lecture 3: Simpson correspondence
We give an introduction to the non-abelian Hodge theory for curves. We will start form the case of line bundles and then introduce the de Rham, Dolbeault and Betti moduli spaces, which parametrizing the flat connections, Higgs bundles and representation of fundamental groups. Then we will introduce the C^\infty view of point for such objects and sketch the proof of the Simpson correspondence.
Lecture 4: Gauge construction of the moduli spaces of vector bundles and Higgs bundles
We start this lecture from an introduction to the symplectic quotients, and then apply its infinity dimensional version to construct the moduli space of vector bundles and Higgs bundles. We will finish this lecture by a computation of the dimension of the moduli spaces.
Lecture 5: The moduli spaces of Higgs bundles and SYZ-mirror symmetry
In this lecture, we will give a short introduction to the Mirror Symmetry conjecture and introduce the Strominger-Yau-Zaslow Mirror Symmetry. Then we show that the pair of parabolic SL-PSL Hitchin systems are mirror partner in the sense of SYZ.