Geometry Seminar: A. Ohanyan (Vienna)
Geometry Seminar (Geometric Analysis)
Speaker: Argam Ohanyan
Title: Non-smooth approaches to spacetime geometry
Abstract: Non-smooth spacetime geometry is a subject that has garnered a lot of interest in recent years. This is unsurprising, as even basic and physically well-motivated phenomena within smooth spacetime geometry lead to non-smooth scenarios. Another motivation is the success of non-smooth Riemannian geometry, where a study of metric length spaces and curvature bounds via triangle comparison has led to an incredibly fruitful theory which has delivered many new results even in the smooth context. In 2018, Lorentzian length spaces were put forth by Kunzinger and Sämann as the suitable synthetic setting for spacetime geometry. Since then, a lot of results from the classical theory of spacetimes have been rediscovered in this framework. In this talk, we first give the motivations for and discuss the basics of Lorentzian length spaces. We then continue with various recent developments related to curvature, Gromov-Hausdorff convergence and differential calculus in the synthetic setting.