Geometric Langlands for hypergeometric sheaves

Generalised hypergeometric sheaves are rigid local systems on the punctured projective line with remarkable properties. Their study originated in the seminal work of Riemann on the Euler--Gauss hypergeometric function and has blossomed into an active field with connections to many areas of mathematics. I will report on a joint work with Lingfei Yi, where we construct the Hecke eigensheaves whose eigenvalues are the irreducible hypergeometric local systems. This confirms a central conjecture of the geometric Langlands program for hypergeometrics. The key tool we use is the notion of rigid automorphic data due to Zhiwei Yun. This talk is based on the preprint arXiv:2006.10870.