John Loftin
Rutgers-Newark
Title
The Geometry of Limits of Cubic Differentials
Abstract
Consider a closed Riemann surface $\Sigma$ of genus at least 2 equipped with a holomorphic cubic differential $U$. Such a pair induces a rich set of geometric structures of a convex real projective structure on the surface and an equivariant minimal embedding of its universal cover into the symmetric space $X=SL(3,R)/SO(3)$. These results heavily depend on nonconstructive analytic techniques (from affine differential geometry and Higgs bundles). I will discuss recent joint work with Andrea Tamburelli and Mike Wolf, in which the limiting structure for $tU$ as $t$ increases to infinity induces a minimal embedding into the asymptotic cone of $X$ which is explicitly determined by the geometry of $U$.