AAG Seminar: An Exploration of Sato-Tate Groups of Curves

Abstract: The focus of this talk is on families of curves and their associated Sato-Tate groups -- compact groups predicted to determine the limiting distributions of coefficients of the normalized L-polynomials of the curves. Complete classifications of Sato-Tate groups for abelian varieties in low dimension have been given in recent years, but there are obstacles to providing classifications in higher dimension. In this talk I will give an overview of the techniques we can use for some nice families of curves and discuss the ways in which these techniques fall apart when there are degeneracies in the algebraic structure of the associated Jacobian varieties. I will include examples throughout the talk in order to make the results more concrete to those new to this area of research.

Host: Wanlin Li