The Fédération de Recherche d’Animation Bézout Day will take place on Tuesday, September 29, 2026 in Université Gustave Eiffel – 5 Boulevard Descartes, 77420 Champs-sur-Marne.
All talks will be in the second floor of Copernic building – Room 2B115
9:00-9:30 : Welcome coffee –room 2V080
Axe Mathématiques discrètes et algorithmes
9:30-10:05 : Marie-Pierre Béal (LIGM)
Title Substitutions and symbolic dynamics
Abstract We present substitutions and symbolic dynamics, focusing on recognizability. Specifically, we provide a very simple proof of the recognizability of a substitution for aperiodic points, using the full recognizability of elementary substitutions for aperiodic points.
10:05-10:30 : Lu Yu (CERMICS)
Title A Combinatorial Approach to Equipartition of a Segment
Abstract Consider a continuous real-valued function defined on the intervals of a segment. A theorem of Avvakumov and Karasev (2023) states that, if the function takes the same value on all degenerate intervals, then the segment can be partitioned into any prescribed positive integer number of intervals on which the function takes the same value. The result is motivated by envy-free division problems. The proof relies on advanced topological arguments and requires several perturbation steps. In this talk, I will present a combinatorial approach to this equipartition theorem and show that the original topological argument can be reformulated in discrete, combinatorial terms, making it potentially more amenable to constructive or algorithmic interpretations. Joint work with Frédéric Meunier.
Axe Phénomènes en grande dimension
10:30-11:05 : François-Xavier Vialard (LIGM)
Title Nonnegative cross-curvature of compact lie groups using a synthetic approach, convexity of the entropy on generalized geodesics.
11:05-11:35 : Coffee break –room 2V080
11:35-12:00 : Colin Petitjean (LAMA)
Title Un bref aperçu des espaces Lipschitz-libres.
Abstract Après avoir introduit les espaces Lipschitz-libres du point de vue du transport optimal, ce court exposé aura pour but de présenter quelques aspects importants de leur étude et de souligner les liens qui apparaissent naturellement avec d’autres domaines des mathématiques, tels que la théorie de la mesure, la géométrie métrique ou encore la théorie des opérateurs. Nous illustrerons brièvement l’une de ces interactions en montrant comment certains travaux de A. Naor sur les partitions aléatoires peuvent être utilisés pour obtenir des informations sur la structure des espaces Lipschitz-libres.
Axe Image et géométrie
12:00-12:35 : Giada Franz (LAMA)
Title Free boundary minimal surfaces in the unit ball
Abstract Minimal surfaces are surfaces that locally minimize the area. They are a central topic in Geometric Analysis and are studied in several different settings. In this talk, we will concentrate on surfaces in the three-dimensional Euclidean unit ball that have boundary constrained to move in the boundary of the ball (i.e., the unit sphere). We will explain what it means for these surfaces to locally minimize the area, namely to be a free boundary minimal surface, and we will review some recent results about the construction of these objects.
12:35-14:00 : Lunch at Copernic Building -Université Gustave Eiffel -Room 2V080
14:00-14:25 : Raphael Achddou (LIGM)
Title Dead Leaves Models as Interpretable Priors for Learned Image Restoration.
Abstract Imaging inverse problems were long addressed by variational methods with analytic priors; deep learning now outperforms them, but the regularity it learns implicitly from real data can neither be inspected nor adjusted, and hallucinated structures may appear in the reconstructed images. The approach presented here aims at combining the strengths of both paradigms: an explicit prior expressed as a parametric image sampling model, exploited to its full extent by an expressive neural network trained on the resulting data. The Dead Leaves model, an occlusion-based process in which random shapes are sequentially superimposed, serves as a starting point: only a handful of parameters suffice to define it, yet it reproduces key statistics of natural images. In this talk, I will show that this simple process yields high-quality training data for a range of restoration tasks such as image denoising and super-resolution. I will then introduce an extended version in which texture, depth cues and more complex object geometry are incorporated. Networks trained on these synthetic samples reach performance comparable to those trained on real photographs, with additional benefits that will be discussed, such as controlled ablation studies and invariance properties.
Axe modèles stochastiques et déterministes
14:25-15:00 : Pierre Monmarché (LAMA)
Title optimisation accélérée dans les mesures de probabilités
Abstract des modèles et des algorithmes variés, en physique statistique ou en apprentissage par exemple, peuvent s’interpréter comme des problèmes d’optimisation dans un espace de mesures de probabilités. On discutera dans ce contexte d’un sujet classique d’optimisation, la notion d’accélération de Nesterov : le fait que certaines méthodes dotées d’inertie peuvent converger plus vite qu’une descente de gradient standard.
15:00-15:25 : Andrew McRae (CERMICS)
Title Optimization geometry in estimation
Abstract I will discuss, via a variety of applications in imaging, machine learning, and computer science, recent work on aspects of optimization in inference problems. A natural way to estimate an unknown from data is to find the candidate that fits the data the best. For many practical applications, the resulting optimization problem is nonconvex. In general, nonconvex optimization is challenging algorithmically due to the possible presence of spurious local optima. However, in some applications, due to the mathematical structure of the data, this nonconvexity is « benign »: there are no spurious local optima. This has significant algorithmic implications. Furthermore, even when there are spurious local optima, this can sometimes be overcome by (mild) relaxation, that is, adding a small number of variables.
15:25-16:00 : Coffee break –room 2V080
Axe 5 : Villes intelligentes
16:00-16:30 : Laurent Hauswirth (LAMA)
Title Géométrie différentielle pour l’architecture
