I am familiar with the geometry & topology of 4-manifolds and the arithmetic & number theory.
In smooth 4-manifolds, my interest lies in the classification problem with regard to exotic smooth structures as well as the reducibility of the moduli of algebraic surfaces under the deformation types versus the diffeomorphism types.
In arithmetic of moduli spaces, my interest lies in the philosophy of considering the moduli of fibrations and producing its arithmetic invariants with the aspiration of finding relevant applications to number theory under the global fields analogy.
I am currently visiting the Department of Mathematics at the Brown University hosted by Thomas Goodwillie.
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