Séminaire des doctorants

Février 2025

• Mercredi 05 février 2025 - 16h30 - Michelle MALARA (INRAE)

  A venir

  

Janvier 2025

• Mercredi 15 janvier 2025 - 16h30 - Paul STOS

  Introduction aux réseaux de neurones

  

• Vendredi 10 janvier 2025 - 16h - Sacha QUAYLE (LPSM, Sorbonne Université)

  A venir

  

Décembre 2024

• Mercredi 11 décembre 2024 - 16h30 - Alexis GUERIN

  A venir

  

Novembre 2024

• Mercredi 27 novembre 2024 - 16h30 - Clément LEGRAND

  Links between braids and links

  Un des principaux enjeux de la théorie des nœuds consiste à construire des invariants pour les entrelacs. Une des manières de procéder consiste à voir un entrelacs comme la fermeture d'une tresse puis d'utiliser des représentations du groupe de tresse pour fabriquer des invariants de l'entrelacs.
  
  Dans ce premier exposé nous introduirons les définitions d'un entrelacs et d'une tresse. Nous verrons ensuite que tout entrelacs peut être obtenu comme la clôture d'une tresse. Nous terminerons avec le théorème de Markov qui permet de ramener l'étude des entrelacs à l'étude des tresses modulo certains mouvements dit de Markov.

  Afficher le contenu...

  

Octobre 2024

• Mercredi 16 octobre 2024 - 16h30 - ER-RONDI Mariam

  Enhancing Agro-climatic Understanding through Advanced Climate Datasets

  Agriculture is extremely vulnerable to climate change. The assessment of how the current (and future) climate conditions are suitable for agriculture is essential. Accurately understanding the complex interactions between agriculture systems and climatic conditions require long samples of reliable climate datasets describing both spatial and temporal variability. However, obtaining such datasets poses a significant challenge.
  
  This presentation aims to demonstrate how various mathematical techniques and approaches are used to help overcome this issue. By leveraging advanced statistical models, we can create high-resolution climate datasets that provide valuable insights. The focus will be specifically on the methods used to generate high-resolution (daily, 1 km) climate data with the required temporal and spatial precision for both historical (1979 to 2021) and future projections (2030, 2040, and 2050). This work not only meets the demand for reliable climate data for agro-climatic studies but also provides valuable insights for anticipating and adapting to future scenarios, thereby supporting sustainable agricultural practices at a local scale in France.

  Afficher le contenu...

  

Septembre 2024

• Mercredi 18 septembre 2024 - Tristan GUYON

  (soutenance blanche) Non-reversible Markov-chain Monte Carlo algorithms: beyond translational flows and applications to the simulation of dimer systems

  Event-chain Monte Carlo is a class of non-reversible Markov-chain Monte Carlo algorithms, breaking free from the time-reversal symmetry at the heart of the all-purpose, reversible Metropolis-Hastings framework. In particle systems, Event-chain schemes amount to moving one particle at a time along a certain deterministic flow, until an event given by an inhomogeneous Poisson process, where the moving particle is changed. These methods can be characterized as generating Piecewise-deterministic Markov Processes, and while the deterministic flow is a degree of freedom of the algorithm, few instances of non-translational, non-reversible samples are available in the literature. This manuscript presents two contributions. The main contribution is a detailed study of the necessary and sufficient conditions appearing in Event-chain Monte Carlo. A class of uniform-ideal flows is explored, to guide the design of non-reversible sampling algorithms in practice. Explicit rotational flows are constructed following this method for sphere and dimer systems, and studied at the numerical level for hard spheres and hard dimers. The second contribution is still ongoing work, and deals with the parallelization of Event-chain Monte Carlo. A framework for domain decomposition in Piecewise-deterministic Markov Processes is sketched, and a dimer parallelization scheme is presented.

  Afficher le contenu...

  

• Mercredi 04 septembre 2024 - Léo Hahn Lecler

  (soutenance blanche) Interacting Run-and-Tumble Particles as Piecewise Deterministic Markov Processes : Invariant Distribution and Convergence

  This thesis investigates the long-time behavior of run-and-tumble particles (RTPs), a model
  for bacteria’s moves and interactions in out-of-equilibrium statistical mechanics, using piece-
  wise deterministic Markov processes (PDMPs). The motivation is to improve the particle-
  level understanding of active phenomena, in particular motility induced phase separation
  (MIPS). The invariant measure for two jamming RTPs on a 1D torus is determined for
  general tumbling and jamming, revealing two out-of-equilibrium universality classes. Fur-
  thermore, the dependence of the mixing time on model parameters is established using
  coupling techniques and the continuous PDMP model is rigorously linked to a known on-
  lattice model. In the case of two jamming RTPs on the real line interacting through an
  attractive potential, the invariant measure displays qualitative differences based on model
  parameters, reminiscent of shape transitions and universality classes. Sharp quantitative
  convergence bounds are again obtained through coupling techniques. Additionally, the ex-
  plicit invariant measure of three jamming RTPs on the 1D torus is computed. Finally,
  hypocoercive convergence results are extended to RTPs, achieving sharp L 2 convergence
  rates in a general setting that also covers kinetic Langevin and sampling PDMPs.

  Afficher le contenu...