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Jarod Alper will speak on  Tannaka duality for algebraic stacks

After reviewing various Tannaka duality statements in algebraic geometry and representation theory, we will establish a Tannaka duality theorem for algebraic stacks.  Namely, we will prove that a morphism of noetherian algebraic stacks with affine diagonal can be recovered by the pullback tensor functor on the tensor categories of coherent sheaves.  We will show a few applications of Tannaka duality.