Séminaire Doctorants
organisé par l'équipe DOCT
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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 conférences 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.