Explore the mathematical and numerical foundations of general relativity through this comprehensive workshop featuring leading experts in gravitational physics and mathematical analysis. Delve into cutting-edge research on black hole stability, cosmic censorship conjectures, gravitational wave detection, and spacetime singularities as presented by renowned physicists and mathematicians from around the world. Examine the profound mathematical developments that have shaped our understanding of Einstein's theory since 1915, from Hilbert's variational formulation to recent breakthroughs in numerical simulations of binary black hole mergers. Investigate the formation and stability of black holes, the nature of Big Bang singularities, and the mysterious properties of anti-de Sitter spacetimes through both rigorous mathematical analysis and advanced numerical methods. Discover how mathematical insights and computational techniques work together to generate gravitational wave templates for LIGO and VIRGO detectors, while exploring new concepts like Christodoulou memory that may influence next-generation gravitational wave astronomy. Learn about inverse problems in cosmology, alternative theories of gravity, and the ongoing quest to resolve Penrose's weak and strong cosmic censorship conjectures that probe the fundamental limits of general relativity. Gain insights into multi-oscillating boson stars, the Penrose inequality for perturbed black holes, and the challenges of simulating fundamental fields in strong gravitational environments, all presented through detailed lectures by experts actively advancing these fields.

Syllabus

Dr. Andrea M. Ghez - From the Possibility to the Certainty of a Supermassive Black Hole - IPAM UCLA
Mihalis Dafermos - Strong Cosmic Censorship versus Λ - IPAM at UCLA
Georgios Moschidis - Instability of Anti-de Sitter spacetime for the Einstein-scalar field system
Robert Wald - The Memory Effect and Infrared Divergences - IPAM at UCLA
Grigorios Fournodavlos - The mysterious nature of the Big Bang singularity - IPAM at UCLA
Jonathan Luk - A tale of two tails - IPAM at UCLA
András Vasy - The black hole stability problem - IPAM at UCLA
Yakov Shlapentokh-Rothman - On Naked Singularities for the Einstein Vacuum Equations - IPAM at UCLA
Frans Pretorius - Testing General Relativity with Black Hole Mergers - IPAM at UCLA
Cécile Huneau - Global existence for a system of wave equations on a product space - IPAM at UCLA
Matthew Choptuik - Multi-oscillating Boson Stars - IPAM at UCLA
Zvi Bern - A new approach to the binary inspiral problem - IPAM at UCLA
David Hilditch - Dual-Frame Generalized Harmonic Gauge on Hyperboloidal Slices - IPAM at UCLA
Lydia Bieri - New Structures in Gravitational Radiation - IPAM at UCLA
Pengyu Le - Null hypersurfaces and the Penrose inequality for a perturbed Schwarzschild black hole
Katy Clough - Simulating fundamental fields in strong gravity environments - IPAM at UCLA
Yiran Wang - Some inverse problems in cosmology - IPAM at UCLA
Matti Lassas - Inverse problems for Einstein’s equations and other non-linear hyperbolic equations
Pau Figueras - Binary black hole mergers in cubic Horndeski theory - IPAM at UCLA
Anna Sakovich - Positivity of mass for asymptotically hyperbolic initial data sets - IPAM at UCLA
Martin Taylor - The nonlinear stability of the Schwarzschild family of black holes - IPAM at UCLA
Gunther Uhlmann - Seeing Through Space-Time - IPAM at UCLA
Anne Franzen - Flat FLRW and Kasner big bang singularities - analyzed on the level of scalar waves