The integral geometric Satake equivalence in mixed characteristic Abstract: The geometric Satake equivalence establishes a link between two monoidal categories: the category of perverse sheaves on the local Hecke stack and the category of finitely generated representations of the Langlands dual group. It has many important applications in the study of the geometric Langlands program and number theory. In this talk, I will discuss the integral coefficient geometric Satake equivalence in the mixed characteristic setting. It generalizes the previous results of Lusztig, Ginzburg, Mirkovic-Vilonen, and Zhu. Time permitting, I will discuss an application of this result in constructing a Jacquet-Langlands transfer.