Mengxue Yang

Last Update 2024/05/13
I am a differential / complex geometer. Classical opers defined by Beilinson and Drinfeld arose in the study of geometric Langlands. On a compact Riemann surface of genus g > 1, opers are a special kind of flat connections on vector bundles that satisfy transversality and nondegeneracy conditions with respect to a full flag of subbundles. I studied the space of generalized opers on vector bundles with an additional symplectic or orthogonal structure, which have a weakened transversality condition that also allows for certain partial flags of subbundles. Moreover, there is a biholomorphic correspondence between opers and Higgs bundles given by an hbar conformal limit. Opers also appear to be related to higher Teichmueller theory through Higgs bundles. Recently I have been thinking more about real symplectic Higgs bundles in the context of higher Teichmueller theory.
Back to Member List.