Abstract: The original Sato-Tate conjecture was posed around 1960 by Mikio Sato and John Tate (independently) and is a statistical conjecture regarding the distribution of the normalized traces of Frobenius on an elliptic curve. In 2012, the conjecture was generalized to higher genus curves by Serre. 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 dimension. In this talk, I will describe work in progress to determine Sato-Tate groups for two families of nondegenerate Jacobian varieties. This talk is aimed at graduate students and should be understandable to those that have had Abstract Algebra.
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