**April 24 (Wed) at 15:00 — 056 号室**

**Laurent DI MENZA (Université de Reims Champagne-Ardenne)**

**Some aspects of Schrödinger models**

In this talk, we focus on basic facts about the Schrödinger equation that arises in various physical contexts, from quantum mechanics to gravita-tional systems. This kind of equation has been intensively studied in the literature and many properties are known, either from a qualitative and quantitative point of view. The goal of this presentation is to give basic properties of solutions in different regimes. A particular effort will be paid for the numerical computation of solitons that consist in solutions that propagate with shape invariance.

- April 10 (Wed) at 16:00 — 056 号室

Séverin PHILIP (RIMS, Kyoto).

Galois outer representation and the problem of Oda

Oda’s problem stems from considering the pro-l outer Galois actions on the moduli spaces of hyperbolic curves. These actions come from a generalization by Oda of the standard étale homotopy exact sequence for algebraic varieties over the rationals. We will introduce these geometric Galois actions and present some of the mathematics that they have stimulated over the past 30 years along with the classical problem of Oda. In the second and last part of this talk, we will see how a cyclic special loci version of this problem can be formulated and resolved in the case of simple cyclic groups using the maximal degeneration method of Ihara and Nakamura adapted to this setting.

- March 11 (Mon) at 13:30 — 117 号室

Florian SALIN (Institut Camille Jordan, Lyon & Tohoku University)

Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior

This talk will discuss a fractional nonlinear diffusion equation on bounded domains. This equation arises by combining fractional (in space) diffusion, with a nonlinearity of porous medium or fast diffusion type. It is known that, in the porous medium case, the energy of the solutions to this equation decays algebraically, and in the fast diffusion case, solutions extinct in finite time. Based on these estimates, we will study the fine large-time asymptotic behavior of the solutions. In particular, we will show that the solutions approach separate variable solutions as the time converges to infinity in the porous medium case, or as it converges to the extinction time in the fast diffusion case. However, the extinction time is not known analytically, and to compute it, we will introduce a numerical scheme that satisfies the same decay estimates as the continuous equation.

- January 30 (Tue) at 16:30 — 002 号室

Danielle HILHORST (CNRS, Université de Paris-Saclay)

We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary.

We construct a unique self-similar solution and show that for a large class of initial data, the solution of the time evolution problem converges to this self-similar solution as time tends to infinity. Similar results were already obtained by Bouguezzi, Hilhorst, Miyamoto, and Scheid in the case of Dirichlet data on the fixed boundary. However, they had to show that the space derivative of the solution uniformly converges to its limit. Here, our proof requires less regularity, which should make our arguments easier to adapt to different settings. This is a joint work with Sabrina Roscani and Piotr Rybka.

- January 23 (Tue) at 13:30 — 118 号室

Antoine DIEZ (京都大学, Kyoto University, ASHBi)

*Particle systems with geometrical constraints and applications*

Since the pioneering work of Boltzmann, statistical physics has moti-vated the mathematical study or large systems of interacting particles, especially at the interface between stochastic analysis and PDE. More recently, there has been a surge of interest to consider applications to life sciences, where particles can be seen as convenient modeling entities to represent e.g. cell aggregates, bacterial swarms or animal societies. An important question in this context is the link between the microscopic agent-based description and the macroscopic continuum PDE description. Unlike physical systems which generally obey conservation laws, biological systems are rather subjects to constraints which are more geometrical in nature: volume constraints, shape or internal structure for instance. This poses a number of challenges on the modeling, analytical and numerical aspects. In this talk, I will first review earlier works on the study of particle systems with geometrical constraints. Then I will introduce a new framework, based on optimal transport theory, to model particles with arbitrary shapes and deformability properties. I will discuss potential applications in biology and compare this novel approach to other more classical methods.

- December 4 (Mon) at 14:00 — 056 号室

Philippe G. LEFLOCH (Sorbonne University & CNRS)

*An introduction to Einstein constraints and the seed-to-solution method*

I will present an introduction to the constraint equations associated with Einstein’s field equations of general relativity, and to recent developments based on the seed-to-solution method developed in collaboration with The-Cang Nguyen (Montpellier) and Bruno Le Floch (LPTHE, Sorbonne).

- November 28 (Tue) at 16:00 — 117 号室

Maud DELATTRE (Université Paris-Saclay, INRAE)

*Some contributions on variable selection in nonlinear mixed-effects models.*

In the first part of this presentation, we will introduce the general formalism of nonlinear mixed effects models (NLMEM) that are specifically designed models to describe dynamic phenomena

from repeated data on several subjects. In the second part, we will focus on specific variable selection technics for NLMEM through two contributions. In the first one, we will discuss the proper definition and use of the Bayesian information criterion (BIC) for variable selection in a low dimensional setting. High dimensional variable selection is the subject of the second contribution.

- November 24 (Fri) at 15:00 — 117 号室

Gwénaël MASSUYEAU (Université de Bourgogne & CNRS)

*Surgery equivalence relations on 3-manifolds*

Abstract. By some classical results in low-dimensional topology, any two 3-manifolds (with the “same” boundaries) are related one to the other by surgery operations. In this survey talk, we shall review this basic fact and, next, by restricting the type of surgeries, we shall consider several families of non-trivial equivalence relations on the set of (homeomorphism classes of) 3-manifolds. Those “surgery equivalence relations” are defined in terms of filtrations of the mapping class groups of surfaces, and their characterization / classification involves the notion of “finite-type invariant” which arises in quantum topology.