Institut de recherche mathématique avancée

Résumé : The Epoch of Reionization (EoR) designates the first billion years of the Universe history. During these times, the first stars and galaxies produced ulraviolet radiations and X-rays that ionized the cosmic gas, leading to the fully ionized Universe that we know today. In particular, it is expected that the primeval spatial distribution of neutral gas and radiation should follow the large scale structures of the Universe, leading to a network of ionized bubbles colocated with the inital light emitters. The rise of these first emitting objects is currently under great scrutiny thanks to instruments such as the James Webb Space Telescope JWST or the upcoming Square Kilometer radio Array SKA. These distant times surely hold the keys to understand how current galaxies were formed and how they shaped the Universe for the subsequent 13 billion years.

At the Strasbourg Observatory, we have been involved in the theory and modelisation of the EoR physics for two decades. We developed numerical simulation tools, notably powered by GPUs to anwser the specific challenges posed by the Reionization. We also explored how machine learning techniques can be used to emulate the evolving geometry of the EoR. Finally, we applied and developped formalisms derived from large-scale structures topology to the specific case of EoR. I will present a synthesis of these developments, for which the physics of cosmic Reionization and its understanding acted as a constant and rich driver.


Dominique Aubert obtained his PhD at the Observatoire de Paris in 2005. After a postdoctoral position at the CEA in Saclay, he joined Strasbourg Observatory where he is now a professor. He is specialist of the reionisation of the universe focusing on numerical modeling and high perfomance computating.

Résumé : Even periodization is an operation which approximates a spectral stack as closely as possible by affines corresponding to even periodic ring spectra. We will discuss how this recovers and geometrizes the even filtration of Hahn-Raksit-Wilson, and how it gives rise to canonical spectral enhancements of versions of the prismatization stacks of Bhatt-Lurie and Drinfeld, extending the approach to prismatic cohomology via topological Hochschild homology of Bhatt-Morrow-Scholze.

Résumé : Les applications harmoniques jouent un rôle central dans la théorie de Teichmüller. Dans cet exposé, nous présenterons des résultats récents caractérisant les homéomorphismes de Weil-Petersson en termes de leurs extensions harmoniques. Plus précisément, nous montrerons que la différentielle de Beltrami associée à l’extension harmonique est de carré intégrable et établirons une propriété de minimisation de l'énergie antiholomorphe de cette extension. Il s'agit d'un travail en collaboration avec Vladimir Marković et Abderrahim Mesbah.

Résumé : An elliptic curve is made from complex plane by wrapping up in two independent directions. Changing the directions continuously gives a family of elliptic curves. I will introduce their parameter space and then explain how divisibility by a prime number defines a notion of distance on this space. By wrapping the complex plane more tightly, we move points within this space. I will describe this phenomenon by a numerical invariant from my recent work.