Georgios Kydonakis (UIUC Math) Opers and nonabelian Hodge theory Abstract: We will describe two different families of flat $G$connections over a compact Riemann surface for a complex, simple, simply connected Lie group $G$. The first is the family of $G$opers, which for $G=\text{SL(2}\text{,}\mathbb{C}\text{)}$ can be thought of as global versions of the locally defined second order Schrödinger operators. The second comes from a particular subfamily of solutions to the socalled $G$Hitchin equations. The physicist Davide Gaiotto conjectured that for $G=\text{SL(}n\text{,}\mathbb{C}\text{)}$ the second family in a scaling limit converges to a limiting connection which has the structure of an oper. We will describe a proof of this conjecture. This is joint work with Olivia Dumitrescu, Laura Fredrickson, Rafe Mazzeo, Motohico Mulase and Andrew Neitzke. 
