Mathematics Colloquia and Seminars

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I will describe a certain purely algebraic way of modifying the root data of a reductive group using a multiplicative quadratic form on its coweight lattice. Such quadratic forms can be geometrized as gerbes (the "higher" version of principal bundles) on the factorizable affine grassmannian, a collection of spaces appearing in the geometric Langlands program. I will also describe this correspondence and indicate how it can be invented by trying to prove the geometric Satake equivalence without knowing what that is.