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It is believed that certain physical duality underlies various versions of Langlands duality in its geometric incarnation. By setting up a mathematical model for relevant physical theories, we suggest a program that enriches mathematical subjects such as geometric Langlands theory and symplectic duality. This talk is based on several works, main parts of which are joint with Chris Elliott and with Justin Hilburn.
17B37 ; 22E57 ; 11R39 ; 53DXX
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