1pm - 2pm: Lunch
2pm - 3pm: Mahir Hadžić (University College London)
Title: Examples of naked singularities for the Einstein-Euler system
Abstract: In 1990, based on numerical and formal asymptotic analysis, Ori and Piran predicted the existence of self-similar spacetimes, called relativistic Larson-Penston solutions, that can be suitably flattened to obtain examples of spacetimes that dynamically form naked singularities from smooth initial data, and solve the radially symmetric Einstein-Euler system with sufficiently small sound speed. I will explain a rigorous mathematical construction of such spacetimes. Joint work with Yan Guo and Juhi Jang.
3pm - 4pm: Georgios Mavrogiannis (University of Cambridge)
Title: Linear and quasilinear waves on de Sitter black holes
Abstract: We discuss recent developments in the analysis of linear and non-linear wave equations on de Sitter black hole backgrounds, namely black hole backgrounds with positive cosmological constant. Specifically, in Schwarzschild de Sitter we use a physical space commutation, as opposed to the previous spectral approach, and give a new proof of exponential decay for the solutions of the linear wave equation and a new proof for the stability of the solutions of the quasilinear wave equation. We generalize our commutation to Kerr de Sitter, and prove the same decay and stability results.
4pm - 4.30pm: Tea break
4.30pm - 5.30pm: Alden Waters (University of Groningen)
Title: The relative trace formula in electromagnetic scattering
Abstract: Perfectly conducting obstacles in space change the scattering of electromagnetic fields. This talk establishes a relative trace formula for electromagnetic fields, effectively comparing the two scenarios using boundary layer theory. The trace formula is difficult to obtain due to the divergence free condition in Maxwell's equations in the absence of charge. I also discuss some of the necessary spaces for the Lipschitz case. This important formula relates the xi function to the scattering matrices for 1 forms.
7pm: Dinner
James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD
Lunch and the tea break take place in the common room.
Talks take place in room 5328.
Registration for attending the talks only is not required, but if you are attending the lunch and dinner as well, please send an email to Jan.Sbierski/AT/ed.ac.uk by 16th June.
Funding is provided by the University of Edinburgh.