Community

A major objective that this award enables is building a community of researchers working with asymptotic methods in relativity. This is a relatively small community of geographically distributed but thematically focused researchers.

During the years that I was out of active research, I worked as a coordinator of a similarly distributed research network in mathematical sciences on kinetic theory called KI-Net. With this award, I will employ skills that I acquired during that time to build a community in my own field of research.

This is a joint effort with David Hilditch, Rodrigo Panosso Macedo, and Alex Vaño-Viñuales.

Website

The community uses the aptly named website hyperboloid.al. All our events and activities are managed through this website. The website uses the Wowchemy research group theme; its source code is available through my GitHub page.

Workshops

The inaugural event of the community was the workshop Infinity on a Gridshell, held in July 2023 at the Niels Bohr Institute in Copenhagen. The speakers covered a wide variety of topics including black-hole perturbation theory, mathematical analysis of wave equations, and nonlinear Einstein equations. The workshop was a great success and we are planning to hold another one in 2024.

Topical Collection

We are planning to publish a topical collection in the journal General Relativity and Gravitation on the topic titled Hyperboloidal foliations in the era of gravitational-wave astronomy: from mathematical relativity to astrophysics. The guest editors for the collection are David Hilditch, Rodrigo Panosso Macedo, Alex Vañó Viñuales, and me. The collection will be open to all researchers working with hyperboloidal foliations. Submissions are accepted starting August 31, 2023.

For more information, please see the collection website.

Virtual Infinity Seminars

We run a monthly series of virtual seminars that started in October 2023. More information, along with links to slides and recordings of the seminars,is on our website.

YouTube Channel

Our YouTube channel hosts recordings of the infinity seminars. In the future, we plan to publish recordings of workshop seminars and introductory tutorials covering basics of hyperboloidal compactification and numerical methods.

We have a newsletter called Hyperbolic Times where we share monthly developments in our research area, including publications. We also announce the monthly seminars through this newsletter.

Code repository

To make it easier for students entering the field, we will have publicly available codes that demonstrate the basics of hyperboloidal compactification for solving wave equations. The repository will contain codes for solving wave equations using various methods including frequency domain, time domain, pseudo-spectral, finite difference, and finite element, among others.