Dinakar Muthiah

Last Update 2022/11/21
I am working in algebrogeometric and combinatorial aspects of representation theory.
One topic I have been investigating is the padic theory of KacMoody groups. A special case of this is a notion of a double loop group. This is very closely related to the geometry of double affine Schubert varieties. Conjecturally, these double affine Schubert varieties should also be closely related to instanton spaces as well as Coulomb branches for quiver gauge theories.
A closely related topic is the geometric Satake equivalence and MirkovićVilonen (MV) cycles. In this area I have been studying both the MV basis as well as MV polytopes and their affine generalizations. Finally, I have been recently thinking about ChernMather classes and characteristic cycles for Schubert varieties.
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