Hyperboloidal Horizons 2026

Abstract

The Hyperboloidal Horizons 2026 conference 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, this conference 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.

Goals

• Advance Hyperboloidal Methods Discuss recent progress in the hyperboloidal approach to wave-like and dispersive PDEs, including its use in black hole perturbation theory and the computation of quasinormal modes.
• Foster Cross-Disciplinary Exchange Promote collaboration between researchers in applied mathematics, geometric analysis, numerical relativity, and gravitational wave astronomy.
• Bridge Linear and Nonlinear Regimes Present progress on the application of hyperboloidal methods to the full nonlinear Einstein equations, with the goal of enabling stable 3D numerical simulations without symmetry assumptions.
• Understand Asymptotics and Conserved Quantities Explore geometric analysis of asymptotically hyperbolic manifolds and its relation to conserved quantities and decay properties at null infinity.
• Support Emerging Researchers Provide a platform for early-career scientists and foster the growing community around hyperboloidal research and asymptotic methods in relativity.