In this talk, I will establish a sharp bound on the growth of cuspidal Bianchi modular forms. By the Eichler-Shimura isomorphism, we actually give a sharp bound of the second cohomology of a hyperbolic three manifold (Bianchi manifold) with local system arising from the representation Symk⊗Symk¯ of SL2(C). I will explain how a p-adic algebraic method is used for deriving our result.

You can joint the Zoom meeting at https://ethz.zoom.us/j/68930894558

The password is the first Fourier coefficient of the modular j-function (as digits).