People

Mengxue Yang
Position
Project Researcher (from 2023/09/16 )
Research Field
Mathematics
E-Mail
<mengxue.yang _at_ ipmu.jp> 
PHOTO

Last Update 2023/10/24

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.


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