Talks

Pulsar timing arrays (PTAs) consist of a set of regularly monitored millisecond pulsars with extremely stable rotational periods. The arrival time of pulses can be altered by the passage of gravitational waves (GWs) between them and the Earth, thus serving as a galaxy-wide GW detector. Evidence for the first detection of low-frequency (~nHz) gravitational waves has recently been reported across multiple PTA collaborations, opening a new observational window into the Universe. Although the origin of the GW signal is yet to be determined, the dominant sources are expected to be inpiralling supermassive black holes (SMBHs). I will discuss a recent work in which we compare the GW detections by PTAs with the expected signal implied by existing electromagnetic observations in a simple but robust manner. This study suggests that the currently measured GW amplitude is larger than expected by a significant amount. I will then show that additional information regarding the typical number of sources contributing to the background can already be inferred from current PTA data.

Many physical phenomena may be modeled by first order symmetric hyperbolic equations with degenerate dissipative or diffusive terms. This is the case in gas dynamics, where the mass is conserved during the evolution, but the momentum balance includes a diffusion (viscosity) or damping (relaxation) term.
Such so-called partially dissipative or diffusive systems have been extensively studied by S .Kawashima in his PhD thesis from 1984. For a rather general class of systems he pointed out a simple necessary condition for the global existence of solutions in the vicinity of constant solutions.
This condition that is nowadays named (SK) condition has been revisited in a number of research works. In particular, K. Beauchard and E. Zuazua proposed in 2010 an explicit method for constructing a Lyapunov functional allowing to refine Kawashima’s results and to establish global existence results in some situations that were not covered before. Very recently, advances have been made by T. Crin-B...

The lectures will introduce perturbations of Euler's equation by highly irregular paths where the perturbations are such that the solution preserves a range of physically relevant quantities. Using formal computations, we shall see that, when d=2, a purely Lagrangian formulation of the equation seems to be within reach.

However, special care is needed to give rigorous meaning to the noisy terms of the equation and in these lectures, we will consider the framework of rough paths. We will see how the so-called 'Sewing Lemma' can be used to define integrals as Riemann sums w.r.t paths of low regularity and how to use this result to construct rough path integrals. Then we will derive very precise a priori estimates for differential equations driven by rough paths and these estimates will be used to prove well-posedness of equations where the drift term satisfies an Osgood regularity. Moreover, we will study flows generated by the differential equations and see that the flows are volume ...

With upcoming LIGO runs and new projects like LSST and ULTRASAT, black hole (BH)-powered multi-messenger events will be at the forefront of astrophysics. A major challenge in studying BH-powered explosions is the vast dynamical range between the BH and the emission site, which has hindered theoretical models from capturing the underlying physics from observations. Using 3D neutrino-general relativistic magnetohydrodynamic simulations, I will present the first such models, introducing an innovative model that now enables us to link GRB classes in mergers to their central engines and binary merger origins. For collapsing stars, I will demonstrate how our simulations open new frontiers in astrophysics, including a novel idea of how nascent BHs acquire their strong magnetic fields, heavy element nucleosynthesis in supernovae, the evolution of relativistic jets, new types of transients, and predictions of new vigorous, coherent, non-inspiral gravitational wave sources that may already be detectable by LIGO. These insights will be crucial for extracting the physics of transients from future gravitational wave and electromagnetic detections.

We will discuss the functor of geometric Whittaker coefficients in the context of quantum geometric Langlands. We will prove that tempered twisted D-modules on the stack of G-bundles on a smooth projective curve have non-vanishing Whittaker coefficients. Roughly, this means that a certain natural subcategory of twisted D-modules on the stack of G-bundles can be controlled by the category of twisted D-modules on the Beilinson-Drinfeld affine Grassmannian. The proof will combine generalizations of representation-theoretic and microlocal methods from the preceding works of Faergeman-Raskin and Nadler-Taylor respectively.