Abstract. In joint work with Valentin Blomer and Djordje Milićević, we proved non-trivial bounds for the sup-norm of non-spherical Hecke-Maass forms on SL(2,Z[i])\SL(2,C). The term "non-spherical" refers to the fact that the form to be bounded is not invariant under the right action of SU(2,C), and "non-trivial" means that we achieve a power saving in the dimension of the SU(2,C)-representation generated by the form. On the way, we developed analytic theory of independent interest, including uniform strong localization estimates for generalized spherical functions on SL(2,C) and a Paley-Wiener theorem for the corresponding spherical transform acting on the space of rapidly decreasing functions. We plan 4 talks in the series. This talk will be given by Gergely Harcos using Zoom.

For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).