La semaine de l’IMB

Quantum computers are great news for physicists and virologists but terrible news for cybersecurity. In this talk, we’ll demystify how modern cryptography works, why Shor’s algorithm changes the rules, and what "post‑quantum" actually means. We will meet the main protagonists: lattices, codes, multivariate systems, hash functions and isogenies, and explain what is hybridization. We will also see why we have to quickly switch to post-quantum cryptography because of the “harvest now, decrypt later”. It is a high-level presentation, so you don't need to be a professional cryptographer to attend ;).

In this talk, I will discuss optimal transport between probability measures supported on the same finite metric space, where the ground cost comes from a distance induced by a weighted connected graph. Building on recent work showing that the Kantorovich distance can be written as a minimum over the spanning trees of the graph, I will explain what this reformulation tells us about how to build optimal transport plans and dual potentials from the spanning tree minimising this optimization problem.

I will then show how a simple condition leads to uniqueness of the dual potential and forces a specific structure on the support of the optimal plan. Finally, I will sketch the main ideas behind the algorithms we propose to compute optimal transport plans. This is joint work with Jérémie Bigot.

Séminaire commun avec Optimal

Understanding the behavior of the human eye is challenging due to the complex interactions between various physical phenomena, such as heat transfer, fluid dynamics, and tissue deformation. Although medical data can offer valuable insights into ocular physiopathology, the available information can be scarce and noisy. Moreover, in experimental studies, multiple factors come into play and it is difficult to isolate the contributions of individual mechanisms. Therefore, developing a robust and accurate digital twin for ocular applications can enhance our understanding of this complex system, by integrating governing mechanisms and data variability. 

This talk presents our ongoing efforts in this direction, focusing on the thermo-fluid dynamics governing aqueous humor flow in the anterior and posterior chambers and its coupling with heat transfer throughout the eyeball. Our methodology involves developing a comprehensive mathematical and computational model based on the finite element method, rigorously validated against experimental data and numerical studies. To facilitate real-time feedback, we derived a reliable reduced-order model using the certified reduced basis method. We performed forward uncertainty quantification studies with the reduced model, utilizing experimental based stochastic inputs, and conducted global sensitivity analysis to address variability and noise. We will illustrate these developments, discuss their applications, and address the remaining challenges, including inverse problems and parameter identification.

The presentation is based on a joint work with Thomas Saigre (Inria, Strasbourg), Vincent Chabannes (Cemosis, Univ. de Strasbourg) and Christophe Prud'homme (Cemosis, Univ. de Strasbourg).

After we recall some background on Arakelov theory and modular curves, we discuss the computation of the self-intersection of Arakelov canonical sheaf for modular curves. We enter in more detail in the case of the modular curve X_0(N) giving, for some models, the asymptotic behaviour of the Arakelov canonical sheaf. Finally, we explain how and when this information gives an effective version of Bogomolov conjecture for curves.