# Sato-Tate Groups in Dimension Greater than 3

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The focus of this talk is on Sato-Tate groups of abelian varieties -- compact groups predicted to determine the limiting distributions of local zeta functions. In recent years, complete classifications of Sato-Tate groups in dimensions 1, 2, and 3 have been given, but there are obstacles to providing classifications in higher dimensions. In this talk, I will describe my recent work on families of higher dimensional Jacobian varieties. This work is partly joint with Melissa Emory.