6 November 2025
3:30pm CET
JACQUES SMULEVICI
(Sorbonne Université, France)
Title: Non-linear waves and time-periodicity
Abstract: I will give an overview talk concerning the possible existence and stability of solutions to non-linear wave equations which are periodic in time. Such solutions can arise in a variety of mathematical models, from fluid dynamics, elasticity, and general relativity, where in particular, there were investigated numerically by Maliborski and Rostworowski (2013) for the Einstein-scalar-field model in spherically symmetry near the Anti-de-Sitter spacetime.
I will start the presentation with some reminder concerning the linear wave equation on Anti-de-Sitter before presenting some results and methods for semi-linear wave equations. In a second part, I will describe a recent construction of special coordinates for 1+1 Lorentzian metric on ℝx𝕊1 with time-periodic coefficients, which is expected to be an essential step to extend the previous results to quasi-linear wave equations.
This is joint work with Athanasios Chatzikaleas (National and Kapodistrian University of Athens ).
4 December 2025
3:30pm CET
ANNACHIARA PIUBELLO
(University of Copenhagen, Denmark)
Title: A geometric choice of asymptotically Euclidean coordinates via STCMC-foliations
Abstract: Asymptotically Euclidean initial data sets (IDS) in General Relativity model instants in time for isolated systems. In this talk, we show that an IDS is asymptotically Euclidean if it admits a cover by closed hypersurfaces of constant spacetime mean curvature (STCMC), provided these hypersurfaces satisfy certain geometric estimates, some weak foliation properties, and each surface exhibits generalized stability. Building on the work of Cederbaum and Sakovich (2021), which established that every asymptotically Euclidean IDS has a unique STCMC foliation, we conclude that the existence of such a foliation characterizes asymptotically Euclidean IDS. Furthermore, we explore the connections to the center of mass and show why these coordinates seem well-adapted to describe this concept. This is joint work with O. Vičánek Martínez.