Abstract: 

Let X be a compact arithmetic hyperbolic 3-manifold. Let f be a Hecke-Maass form on X, which is a joint eigenfunction of the Laplacian and Hecke operators. In this talk, I will talk about the L^2 restriction norm problems of f with high frequency. I will present a power-saving bound over the local bound by Burq, Gérard, and Tzvetkov for the L^2 norm of f restricted to a totally geodesic surface. I will also present a power-saving L^2 bound of f restricted to geodesic tubes. Both results are based on the amplification method developed by Iwaniec and Sarnak.

Speaker: 侯家齐，美国威斯康辛大学，博士生。