Michal Wrochna: Feynman problems for the Klein-Gordon and wave equation

The Klein-Gordon or wave equation has rather unusual features if one imposes so-called Feynman asymptotic conditions. It enjoys a theory that in many ways resembles elliptic settings: think Fredholm operators, limiting absorption principle, standing waves, etc. In this talk I will give an overview of this theory and explain how it arises in applications at the interface of General Relativity, QFT and differential geometry. I will then present new results on asymptotically Minkowski spaces for Klein-Gordon equations with complex mass term that use new mixed classical-semiclassical estimates. The talk is based on joint works with Nguyen Viet Dang (Sorbonne Université), Christian Gérard (Paris-Saclay) and András Vasy (Stanford).