Séminaire Doctorants
organisé par l'équipe DOCT
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Salim Alloun
La garde-robe que Riemann n'avait pas vue.
8 janvier 2026 - 16:30Salle de conférences IRMA
Bernhard Riemann (1826-1866) dans sa thèse avait construit pour ainsi dire de ses propres mains ce qu'on appelle aujourd'hui les surfaces de Riemann. Elles généralisaient le plan complexe, et en géomètre-analytique Riemann avait réussi à calculer la dimension de l'espace paramétrisant ces surfaces. Plus tard Werner Fenchel (1905-1988) et Jakob Nielsen (1890-1959) proposèrent une autre façon qui elle mit en jeu la géométrie hyperbolique et les découpes en pantalons. Pour vous montrer les surfaces comme vous ne les avez jamais vues, je présenterai les propriétés topologiques de ces découpes que je formulerai dans un deuxième temps en des termes algébriques à l'aide de la bigèbre de Goldman-Turaev. -
Kenza Memlouk
Towards the motivic Galois group for a double zeta value
15 janvier 2026 - 16:30Salle de conférences IRMA
The goal of this talk is to discuss the motivic Galois group of a double zeta value. To do so, I will recall some elements of Galois theory. Then, I will introduce periods and more precisely multiple zeta values. We will see that the Galois philosophy can be used to study periods. At the end, I will express the motivic Galois group of a single zeta value and I will compare it to the case of a double zeta value. -
Lucas Toury
Vous reprendrez bien un peu de structure ?
22 janvier 2026 - 16:30Salle de conférences IRMA
Dans cet exposé on se propose d’étudier une algèbre naturellement associée à un graphe. Il s’agit d’une algèbre de Hall provenant d’un ensemble simplicial mais dont nous ne donnerons pas plus de détails que le nom. Étudier cette algèbre signifie, dans notre cas, essayer de donner une présentation par générateurs et relations. L’algèbre étant commutative on pourrait motiver l’intérêt d’une telle présentation pour obtenir cette algèbre comme l’anneau de cohomologie d’un espace topologique. Pour parvenir à notre fin, on se propose d’enrichir la structure d’algèbre avec une notion duale, celle de cogèbre. On s’intéressera alors aux éléments primitifs pour le coproduit qui sont souvent de bons candidats pour les générateurs de notre présentation. Presque arrivés au bout de cette histoire, c’est la compatibilité entre les deux structures duales s’associant dans la notion de bigèbre tordue qui nous donnera la présentation de l’algèbre. Cet exposé espère mettre en lumière à quel point l’apport de structure permet une meilleure compréhension des objets étudiés. -
Perrine Jouteur
Quantum deformation of rational numbers from a combinatorial perspective
29 janvier 2026 - 16:30Salle de conférences IRMA
Quantum analogues of real numbers are a generalization of q-deformed integers (also called Gaussian q-integers), which consist of replacing integers by polynomials in an indeterminate "q", in such a way that the specialization q=1 gives the initial number back. This idea can be found in generating series, and was already used by Euler to solve combinatorial problems. A good deformation must be compatible with the structural properties of the object that is being quantized. For instance, q-deformed binomial coefficients have a quantized Pascal rule. In 2020, Sophie Morier-Genoud and Valentin Ovsienko proposed a quantization of rational numbers, generalizing the q-deformed integers, with good combinatorial properties. In this talk, I will define these q-rational numbers by three different ways, first via continued fractions, then via the Farey graph, and finally by an action of the modular group. We will see how this last definition discloses a twin version of q-rational numbers, known as the left one. I will then extend the quantized action of the modular group to unify the left and the right versions. In the remaining time, I will introduce a combinatorial interpretation of q-rationals based on fence posets, bridging the gap to the cluster algebra theory. -
Auriane Mazuir
Towards a Signal-Based Analysis of Karyotyping for the Detection of Chromosomal Abnormalities
5 février 2026 - 16:30Salle de conférences IRMA
Karyotyping still largely relies on expert visual analysis and is subject to substantial variability. This work proposes a signal-based representation of chromosomes to enable robust and interpretable comparisons, in support of cytogenetic diagnosis. -
Arthur Douay
A p-adic 2πi
12 février 2026 - 16:30Salle de conférences IRMA
The goal of this talk is to define a p-adic analogue of 2πi by seeing it as the residue of a holomorphic function at zero, and hopefully convince you that the answer to this question is both deep and satisfying. We will firstly explain why the naive approach to this question doesn't work, and how algebraic geometers think of 2πi. Then we will try and copy the definition we found in the p-adic setting and see how it leads us to the construction of an element of a ring with a specific behavior with respect to the Galois action, and hence why the p-adic analogue of the complex numbers is not the first thing that comes to mind. -
Sophie Baland
A branching model for telomere length dynamics in blood cells.
19 février 2026 - 16:30Salle de séminaires IRMA
In the fields of biology and medicine, mathematical modeling of cell development remains a key area of study.
In this presentation, we will focus on telomeres: small structures located at the ends of eukaryotic chromosomes that act as protective caps to preserve the integrity of the genome.
In the first part, I will discuss the structure and functions of telomeres, their role in the aging process, and in diseases resulting from changes in their length, which is a determining factor in their proper functioning. In addition, I will briefly present two biological mechanisms: the process of DNA replication and hematopoiesis, which is the process of blood cell production, in order to introduce the concepts necessary for understanding a model describing the dynamics of telomere length.
In the second part, I will introduce a branching model that will help us understand the mechanism of hematopoiesis and reproduces cellular behavior during cell divisions, taking into account the length of their telomeres. This is a stochastic model of the evolution of a population of cells and their chromosomes, involving several factors such as telomere attrition, the action of telomerase, and the phenomena of self-renewal, differentiation, and cell death.
I will then present a result, called the law of large numbers, related to the behavior of the model in large populations, as well as the main steps of the proof. -
Lauriane Turelier
An introduction to the Besov spaces and an application to PDEs.
5 mars 2026 - 16:30Salle de conférences IRMA
In the study of PDEs, it is essential to identify the relevant functional space and to know its properties. The two most commonly used types of spaces are Lebesgue spaces and Sobolev spaces. In this talk, I will introduce another class of functional spaces : Besov spaces, with some of their topological properties. Finally, I will present an application to the study of PDEs. -
Antoine Rodrigues
An introduction to Floer theory via classical mechanics
12 mars 2026 - 16:30Salle de conférences IRMA
Hamiltonian mechanics on symplectic manifolds can be seen as a general setting for physical problems in classical mechanics. The goal of this talk is to present this setting and show how Floer homology appears as a natural construction to answer dynamical questions. If the time allows it, we will present an application of this general theory to the research of periodic trajectories on a given energy level. -
Pierre Charitat
Inferring the brain structure by observing its neurons
19 mars 2026 - 16:30Salle de conférences IRMA
Neurophysiologists are able to observe the activity of individual neurons, known as their "spikes". However, this can only be performed for a small amount of neurons, compared to the real size of the network. The goal of this talk is to present a new approach that can estimate the connection proportion between neurons, from the observation of few neurons. We then compare this new approach on a toy model to the actual method generally used by neurophysiologists. -
Ons Rameh
Autour du phénomène de Cut-off pour des systèmes de particules
25 mars 2026 - 16:00Salle de conférences IRMA
Considérons un système de particules aléatoires. quand peut-on dire qu'il est proche de l'équilibre ? Parfois, le système atteint rapidement l'équilibre de manière abrupte, ce que l'on qualifie de phénomène de cut-off. Le but de l'exposé est de présenter ce phénomène et d'expliquer quels renseignements fournit le comportement macroscopique d'un système sur le temps de mélange. -
Louise Martineau
Topology and neuroscience : applying persistent homology to spike train analysis
2 avril 2026 - 16:30Salle de conférences IRMA
Persistent homology is a field that has emerged in data analysis over the past two decades. Its primary goal is to recover the topology of a point cloud. In this talk, we explore the applications of persistent homology to another type of data that is ubiquitous in neuroscience : spike trains. A spike train is a collection of binary time series corresponding to neuronal activity. We define the persistent homology of a spike train via a filtration based on the frequencies of cofiring neurons, and we explore the performance of this method with both simulated and real data. -
Simon Alonso
A walk towards the Langlands program
9 avril 2026 - 16:30Salle de conférences IRMA
The aim of this talk is to present the different questions that arise in the Langlands program. To make this very obscure subject a bit less mysterious, I will start with an illustration of how the methods used in the Langlands program, namely modularity, yield interesting arithmetic results. Then, I will highlight the different generalisations that give rise to the various branches of the area. If time permits, I would like to give more details about whatever the audience is more interested in. -
Xiabing Ruan
From and Beyond Lie Algebras: Enveloping Algebras and PBW theorem
16 avril 2026 - 16:30Salle de conférences IRMA
Non-associative algebras arise in many mathematical settings, with the Lie algebra being a significant example. A powerful tool to study a Lie algebra is its universal enveloping algebra, which is an associative algebra, whose representation coincides with the representation of that Lie algebra. The classical Poincaré-Birkhoff-Witt (PBW) theorem plays a role by giving a vector space basis of the enveloping algebra. We will generalise the notion of enveloping algebra to arbitrary (non-associative) algebra and present the generalised PBW theorem via giving examples. If time permits, we could talk about a more generalised perspective — universal enveloping Operads. -
Yufei Qian
Toric Varieties – Combinatorial Method in Algebraic geometry
30 avril 2026 - 16:30Salle de conférences IRMA
Toric varieties are a special kind of algebraic varieties whose geometry is governed by combinatorial data: cones, fans and lattice polytopes. This makes them both explicitly computable and surprisingly rich. In this talk, I will give an introduction to toric varieties, emphasizing the dictionary between geometry and combinatorics and illustrating the theory through concrete examples. If time allows, I will also discuss their broad applications. -
Jose Sao Joao
Spheres and Cobordisms
7 mai 2026 - 16:30Salle de conférences IRMA
Continuing from last year, on my side quest into the land of cobordisms, I come to the question of why we study cobordisms? Interestingly, cobordisms are closely related to maps between spheres. In this talk I will speak about what are homotopy and homology groups and how they are really just two definitions of holes. I will speak about the homotopy groups of spheres and how studying them we may come to framed cobordisms. Finally, should there be time I will explain how the homotopy of spheres and cobordisms may motivate more advanced homotopy topics such as stable homotopy and rational homotopy. -
Nicolas Pailliez
Neural Methods with Natural Gradient Acceleration for Plasma Simulations
13 mai 2026 - 16:30Salle de conférences IRMA
In nuclear fusion, simulations are essential for understanding and controlling tokamak instabilities, phenomena that can severely damage reactors. Neural approaches for solving partial differential equations (PDEs) are gaining interest due to their mesh-free nature, flexibility, and scalability. These methods rely on neural networks as approximation spaces instead of classical polynomial bases, and this work investigates the efficiency of several neural techniques applied to plasma simulations. We first study stationary elliptic equations, with particular attention to the Grad–Shafranov equation, solved using Physics-Informed Neural Networks (PINNs). We then address time-dependent problems such as anisotropic diffusion, relying on adapted neural schemes, including Discrete PINNs and Neural Galerkin methods. In both cases, the Natural Gradient method is employed to significantly accelerate and stabilize the optimization process during training. -
Anna Marduel
Gromov non-squeezing theorem
21 mai 2026 - 16:30Salle de conférences IRMA
The Gromov non-squeezing theorem is a famous result in symplectic geometry that illustrates the notion of symplectic rigidity. It states that, to symplectically embed a closed ball into a cylinder, the radius of the ball must be smaller than that of the cylinder. In this talk, I will present the proof for linear symplectomorphisms and explain why the Gromov non-squeezing theorem is surprising when compared to the linear case and the volume-preserving diffeomorphism case.