Explore advanced mathematical physics through this comprehensive thematic programme examining the intersection of dispersive partial differential equations and mathematical relativity. Delve into cutting-edge research presentations covering scattering theory, nonlinear wave equations, general relativity, and spacetime dynamics through expert lectures from leading mathematicians and physicists. Study topics including Kerr spacetimes, Einstein field equations, soliton dynamics, wave scattering on curved backgrounds, and gravitational collapse scenarios. Examine specific applications such as the nonlinear stability of black holes, wave propagation in cosmological settings, critical phenomena in field theories, and the mathematical foundations of general relativity. Learn about modern analytical techniques for studying dispersive equations, including modified energy methods, scattering theory for nonlinear systems, and asymptotic analysis of wave solutions. Investigate connections between classical field theory and contemporary mathematical analysis through discussions of Yang-Mills fields, Einstein-Vlasov systems, and nonlinear Schrödinger equations. Gain insights into current research challenges and future directions in mathematical relativity and dispersive partial differential equations from presentations by internationally recognized experts in both fields.

Syllabus

Warren Li - Scattering towards the spacelike singularity in Kasner spacetimes
Jonathan Luk - High frequency spacetimes in general relativity
Andras Vasy - Waves on Kerr-de Sitter space
Volker Schlue - Scattering problems with homogeneous asymptotics
Benjamin Dodson - Global well-posedness and scattering for the conformal nonlinear wave equation
Jérémie Szeftel - The nonlinear stability of Kerr for small angular momentum
Alexander Wittenstein - Existence and stability of corotational wave maps into perturbed spheres
Ryan Martinez - The Modified Energy Method for a Nonlocal Quasilinear Wave Equation
Ambre Chabert - Weakly turbulent solution to the Schrödinger equation on the 2D torus with potential
Avy Soffer - Scattering Theory of Linear and Nonlinear Waves: A Unified New Paradigm
Claudio Munoz - Kink dynamics for the Yang-Mills field in an extremal Reissner-Nordström black hole
Piero D'Ancona - Dispersion estimates for Dirac equations with Aharonov–Bohm magnetic fields
Marko Sobak - Haunted Einstein-Yang-Mills wormholes
Michael McNulty - Stable blowup for the higher-dimensional Skyrme model
Philippe G. LeFloch - Optimal shielding for Einstein gravity
Hans Ringström - Formation of quiescent big bang singularities
Christoph Kehle - Extremal Critical Collapse
Hans Lindblad - Scattering for wave equations with sources and slowly decaying data
Sung-Jin Oh - Late time tail of waves on dynamic asymptotically flat spacetimes of odd space dim...
Kenji Nakanishi - Initial classification of global behavior around multi-solitons for the nonlin...
Michal Kowalczyk - Asymptotic stability of kinks in the odd energy space.
Liam Urban - On the past maximal development of near-FLRW data for the Einstein scalar-field Vla....
O.-N. Avadanei - Low regularity well-posedness for the generalized surface quasi-geostrophic front..
Matthias Ostermann - Stable self-similar blowup for nonlinear wave equations beyond light cones
Maximilian Ofner - Expansion thresholds for the stability of cosmological fluids
Raphaël Côte - Perturbation at blow up of self similar solution for mKdV
Herbert Koch - The Korteweg-de Vries hierarchy in rough function spaces
Mihaela Ifrim - Modified scattering for the three dimensional Maxwell-Dirac system
Didier Pilod - Finite point blowup for the critical generalized Korteweg-de Vries equation
Gong Chen - Dynamics of multi-soliton solutions to Klein-Gordon equations
Håkan Andréasson - Oppenheimer-Snyder type collapse for the Einstein-Vlasov system