Dr. Lingfei Yi, Minnesota – Physical rigidity of Frenkel-Gross connection

Mode: In-Person

Title: Physical rigidity of Frenkel-Gross connection

Abstract: A G-connection over a smooth complex curve is called physically rigid if it is determined by its local monodromies. We show that the Frenkel-Gross connection is physically rigid, thus confirming the de Rham version of a conjecture of Heinloth-Ng^o-Yun. The proof is based on the construction of the Hecke eigensheaf of a connection with only generic oper structure, using the localization of Weyl modules. We will review the notion of opers and give the sketch of the proof. Time permitting, we will describe a conjectural generalization of the result relating theta connections to Langlands parameters of Epipelagic representations.