Microlocal Analysis and Curved Spacetimes

Microlocal analysis has long provided a natural and powerful tool for studying partial differential equations from quantum physics. Recently, groundbreaking new perspectives have made it possible to extend these methods to relativistic theories set on curved spacetimes. This has created an unprecedented opportunity to answer longstanding questions in mathematical General Relativity and Quantum Field Theory, in particular in settings describing black holes or a Big Bang singularity. Remarkably, methods developed independently in different classical and quantum settings are connected in meaningful ways, for instance through spacetime compactifications, propagation estimates, and resonance expansions. Furthermore, uncovering local-to-global phenomena on curved spacetimes based on unique continuation theorems and related inverse problems has fueled dynamic developments in classical and quantum theories alike.

There is indeed an outstanding synergy between these interconnected techniques and problems, involving scattering theory, spectral theory, and propagation phenomena in close relationship with the underlying spacetime geometry. The meeting will carry this momentum forward and bring together specialists from different communities to advance fundamental problems in Mathematical General Relativity and Quantum Field Theory and foster new exchanges between classical and quantum perspectives through techniques of microlocal analysis.