The Hyperboloidal Horizons 2026 workshop brings together researchers across mathematical relativity, geometric analysis, and gravitational wave physics to explore the theory and applications of hyperboloidal foliations. Spacelike surfaces that asymptotically approach null infinity offer a geometric framework for analyzing wave propagation, with implications for both analytical and numerical treatments of the Einstein field equations.

As a follow-up to our previous meeting in 2023, Infinity on a Gridshell, the workshop will highlight recent advances in black hole perturbation theory, gravitational self-force, and the nonlinear numerical evolution of asymptotically flat spacetimes. Particular attention will be given to the role of hyperboloidal methods in modeling gravitational radiation across the inspiral, merger, and ringdown phases of compact binary coalescence. We will also investigate new frontiers where hyperboloidal foliations may be applicable, such as electromagnetic scattering theory and quantum field theory.