Principal bundles and the Langlands Program

The Langlands Program is a series of far-reaching conjectures, which first emerged in number theory but then extended to many areas such as algebraic geometry, representation theory, and mathematical physics. The geometric Langlands program is a statement about equivalence of certain categories of moduli spaces of principal bundles on algebraic curves. The research of Fedorov is about the Langlands duality for Hitchin systems, the Langlands program with ramifications, and motivic classes of moduli spaces occurring in Langlands program. Fedorov is also interested in applying the philosophy of Langlands program to classical questions of algebraic geometry such as studying principal bundles over local rings.

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