A Geometric Jacquet-Langlands Transfer for Automorphic Forms of Higher Weights

Geometric approaches in constructing the Jacquet-Langlands transfers were pioneered by Ribet and Serre. Their works motivate many of the later progress in this direction. In this talk, I will discuss a geometric construction of the Jacquet-Langlands transfer for automorphic forms of higher weights. The essential ingredient of the construction is the integral coefficient geometric Satake equivalence in mixed characteristic obtained by the speaker and Scholze independently.