# Abstract Jarod Alper - Lecture 1

**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.