Current seminars

Abstract: I will discuss the difficulties associated with the definition of the energy in the radiating regime for linear theories on a de Sitter or anti de Sitter background.

Abstract: There are a number of reasons due to which it is advantageous to have a phase space based, or microlocal, approach available for analyzing wave propagation. In this talk I will explain a microlocal framework for wave propagation on asymptotically flat spacetimes of arbitrary dimension which in particular includes operator corresponding to Lorentzian metrics arising from solutions of Einstein’s equations in the 4 spacetime dimensional setting. On the compactification of Minkowski space that underlies this, which is a manifold with corners (with the usual null infinity, scri, being a boundary hypersurface), the operators lie in a combination of Melrose’s totally characteristic (also called b), and Mazzeo’s edge pseudodifferential operator algebras. I will give an introduction via a simpler setting (which includes Minkowski space and a different class of perturbations), and then explain the reasons for, and complications with, moving to the present setting. This is joint work with Peter Hintz.

Abstract: Within geometrical optics, Rytov’s law states that the polarization vector is Fermi–Walker transported along light rays. A transport law of this kind was experimentally observed in optical fibers – a regime in which ray optics does not suffice, but wave optics is required. In this talk, I will present a perturbative solution to the full Maxwell equations in arbitrarily bent fibers, under the sole assumption that the fiber’s radius of curvature is much larger than its diameter. At leading order, this provides a rigorous derivation of Rytov's law. At next order, one obtains non-trivial dynamics of the electromagnetic phase and polarization. We discuss potential experiments signatures of of these corrections and compare with similar results on this subject. This is joint work with Marius Oancea. arXiv:2302.10540 [physics.optics]

Abstract:

Abstract: In this lecture, we aim to present some rigidity results for compact initial data sets, in both the boundary and no boundary cases. For example, under natural energy, boundary, and topological conditions, we obtain a global version of a well-known result of H. Bray, S. Brendle, and A. Neves. We also prove some extensions of results obtained, in a previous work, by M. Eichmair, G.J. Galloway, and the author. Finally, as time permits, we are going to present a number of examples in order to illustrate some of the results presented in this lecture. This is part of a joint work with G.J. Galloway.

Abstract: