Independence of ell of Monodromy Groups -- CheeWhye Chin

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Lafforgue's theorem of the Langlands Correspondence for GL(r)
over function fields can be used to establish certain
long-standing conjectures of "independence of ell" in the
theory of ell-adic representations.  I will focus on the
question of independence of ell of monodromy groups.  I will
explain the motivating origin of this conjecture, what is now
known about it, and some recent progress on the case when the
monodromy groups are not connected.