# Strong multiplicity one and $l$-adic Galois representations

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Stefan Patrikis, Princeton University
Fine Hall 314

The strong multiplicity one theorem and its refinements amount to a local-to-global principle in the theory of automorphic representations of $GL(N)$. I will discuss a Galois-theoretic analogue with a surprisingly elementary proof, along with some related questions about the images of $l$-adic Galois representations.