Geometric Langlands with marked points

During the pandemic, I started a reading seminar at Hangzhou about Geometric Langlands program and mirror symmetry. During our study, it was clear that the entire program should extend to the Riemann surface with marked points. A necessary step is to understand the mirror symmetry of insertions we will put on marked points. The investigation of this problem leads to the discovery of a rather subtle phenomenon of the order of finite covers of nilpotent orbits and recent advance of Yaoxiong Wen and his collaborators on the proof of topological Geometric Langlands for $SP(2n)/SO(2n+1)$ pair.