Titel 

Rigid automorphic data on $\mathbb{P}^1 \setminus \{0,1,\infty \}$ 

Abstract

Hypergeometric local systems are famous rigid local systems on $\mathbb{P}^1 \setminus \{0,1,\infty \}$, arising as solution sheaves of the hypergeometric equation. In work of Kamgarpour and Yi, the geometric Langlands correspondence is worked out for hypergeometric local systems, using Yun’s notion of automorphic data. A related construction was carried out earlier by Yun to obtain conjecturally rigid local systems of types $G_2, E_7, E_8$ and others, which he then used to prove existence of a motive with Galois group of type $E_8$. In this talk, I will explain similarities between these two constructions, and outline a project in progress with Masoud Kamgarpour, in which we aim to build a framework to construct rigid local systems on $\mathbb{P}^1 \setminus \{0,1,\infty \}$ that recovers these two classes of examples, and conjecturally leads to further classes of rigid local systems on $\mathbb{P}^1 \setminus \{0,1,\infty \}$.