The central region of the Milky Way is a very complex region at very-high-energy (VHE, E>100 GeV) gamma rays. Among the VHE gamma-ray sources are the supermassive black hole Sagittarius A* lying at the the centre of the Galaxy, supernova remnants and pulsar wind nebulae. The detected diffuse emission at TeV energies revealed the detection of the first Galactic Pevatron - a cosmic-ray accelerator up to PeV energies. At the ten-to-hundred GeV energy range, the Galactic Center region harbors the base of the Fermi bubbles - giant bipolar structures extending on ten-degree spatial scale, possibly related to past activity of Sagittarius A*. Beyond the rich VHE astrophysics, the GC region is expected to be the brightest source of particle dark matter annihilations in VHE gamma rays. The H.E.S.S. observatory located in Namibia is composed of five imaging atmospheric Cherenkov telescopes. It is designed to detect gamma-rays in the ten GeV up to several ten TeV energy range. The observation of the Galactic Center region is one of a long-term key science observational program carried out by H.E.S.S. The four-telescope observations performed by H.E.S.S. led to the detection of the first Galactic Pevatron and provide the strongest constraints so far on the annihilation cross section of dark matter particles in the TeV mass range. The PhD work will be focused on the data analysis and interpretation of the H.E.S.S. observations of the inner Galaxy survey program with the full H.E.S.S. array. In the first part, the PhD student is expected to characterize the spatial and spectral properties of the Galactic Center TeV diffuse emission. Second, she/he will develop a novel analysis method to search for new diffuse emissions connected to the Galactic Center outflows, using a multi-component template-fitting technique. The third part of the work will be dedicated to the search for dark matter in the Galactic Center region and in the complementary dwarf galaxy satellites of the Milky Way. The PhD student will be involved in the data taking with the H.E.S.S. telescopes towards these objects and will participate to the detection prospects of dark matter with the next ground-based gamma-ray observatory CTA.

The Euclid satellite, to be launched in 2022, will observe the sky in the optical and infrared, and will be able to map large scale structures and weak lensing distortions out to high redshifts. Weak gravitational lensing is thought to be one of the most promising tools of cosmology to constrain models. Weak lensing probes the evolution of dark-matter structures and can help distinguish between dark energy and models of modified gravity. Thanks to the shear measurements, we will be able to reconstruct a dark matter mass map of 15000 square degrees. These shear measurements are derived from the galaxy shapes, which are blurred by the PSF (point-spread function) of the optical imaging system. One of the main problems to achieve the scientific goals is therefore the need to model the point spread function (PSF) of the instrument with a very high accuracy. The PSF field can be estimated from the stars contained in the acquired images. It has to take into account the spatial and spectral variation of the PSF. An additional problem to take care of is the subsampling of the images. Once the PSF is correctly modelled, we need to derive the shear from galaxy shapes.

In a recent paper (Schmitz et al 2018) we shown that optimal transport (OT) techniques allow to extremely well represent the evolution of the PSF with the wavelength and on-going work (Morgan et al, 2018) consists in building a 3D Euclid PSF modelling, which takes into account both the spatial variation of the PSF and the PSF wavelength dependency. However even if OT produces beautiful results, its use is extremely limited in practice due to a prohibitive computational cost, and we cannot consider to use our OT PSF modeling for the huge Euclid set.

The goal of the PhD consists first in finding an efficient way to build such a 3D PSF model. A solution could be to use the Deep Wasserstein Embedding technique (Courty, Flamary and Ducoffe, 2017) to get an approximation mechanism that allows to break the complexity. The second step will be to interpolate, from the reconstructed 3D PSFs at stars position, the PSF at any position in the field. This will done by extending to the third dimension the 2D interpolation on a Graph Laplacian we proposed in (Schmitz, Starck and Ngole, 2018), which allows us to interpolate the PSF on the adequate manifold. The final step will be to quantify the modelling errors by studying using simulations the propagation of the reconstructed PSFs errors to cosmological parameters.