Problems in the Langlands Program

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The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations of affine Kac-Moody algebras at the critical level.