Boundedness of spectral projectors on hyperbolic surfaces

In this talk I will discuss recent and upcoming results on the boundedness of spectral projectors. The seminal work of C. Sogge gives the optimal result on any Riemannian manifold with bounded geometry for spectral windows of size 1. However when the width is smaller, the bounds become sensitive to the global geometry of the underlying manifold. I will focus on the case of hyperbolic surfaces of infinite area, and present new estimates that hold universally in that setting. This is based on joint and upcoming work with Jean-Philippe Anker and Pierre Germain.