Journée Bézout des doctorant.e.s et des stagiaires de M2

Contribution List

6. Presentation of the day and the Bézout Research Federation and Graduate Program

5/21/25, 10:15 AM

2. Ecology in the Age of Randomness : How Random Matrix Theory Explains Species Coexistence

Mohammed-Younes Gueddari (LIGM)

5/21/25, 10:45 AM

We study the stability of large ecosystems by modeling species interactions with random matrices within the Lotka–Volterra framework. Since real interaction data are difficult and costly to collect, we adopt a probabilistic approach.
I will introduce key concepts from Random Matrix Theory to analyze the typical behaviour of ecological equilibria. Unlike classical spectral questions, our focus...

7. The computational and mathematical challenges of simulating non-equilibrium molecular systems

Shiva Darshan (CERMICS)

5/21/25, 11:15 AM

Statistical physics gives a probabilistic description of the microscopic dynamics of a system allowing one to deduce its macroscopic properties. The numerical realization of this idea: molecular dynamics, i.e the simulation of the dynamics of molecular and atomistic systems, provides scientists a "numerical microscopic" to conduct computer experiments allowing them to test physical theories...

1. The primitive equations of the ocean and the atmosphere

Valentin Lemarié (LAMA)

5/21/25, 11:45 AM

With the aim of predicting meteorological phenomena, in 1922 the mathematician and meteorologist Richardson proposed and used a simplified version of the Navier-Stokes equations: the primitive atmospheric equations. These equations proved to be a good model for studying large-scale flows where the vertical component of motion is, in this case, much weaker than the horizontal component. Bryan...

3. Braid normal forms and combinatorics.

June Roupin (LIGM)

5/21/25, 1:30 PM

A mathematical braid is a set of threads whose topological structure we wish to study. These objects can also be seen as an equivalence class of words, where each word corresponds to a different way of producing the same braid. A very natural problem is the choice of a single representative word for each braid, in order to be able to compare efficiently and make quick computations on the...

5. Enhancing Sampling in Molecular Dynamics: Integrating Autoencoders and Linear Discriminant Analysis for Efficient Collective Variables

Charlotte Chapelier (CERMICS)

5/21/25, 2:00 PM

In molecular dynamics, transitions between conformations are rare events, posing significant challenges for sampling. Enhanced sampling methods, such as the extended Adapted Biasing Force (eABF), utilize collective variables (CVs) to capture the slow components of these transitions. While intuitive selection of CVs can sometimes be effective, it often fails to capture critical transitions....

4. Disc flow on discrete sweepouts of a sphere by closed curves.

Jean Chartier (LAMA)

5/21/25, 2:30 PM

Simple closed geodesics on Riemannian spheres have been the subject of many incomplete existence proofs throughout the 20th century, since Birkhoff's first paper in 1908. One stumbling block is preserving the simplicity of the curves by using shortening flows. In 1994, Hass and Scott described a new flow for shortening curves: the disc flow, which solves the simplicity issue, but brings other...