## 日仏数学拠点FJ-LMIセミナー

過去の記録 ～09/11｜次回の予定｜今後の予定 09/12～

担当者 | 小林俊行, ミカエル ペブズナー |
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**過去の記録**

### 2024年09月11日(水)

13:30-14:30 数理科学研究科棟(駒場) 122号室

Counting limit theorems for representations of Gromov-hyperbolic groups (英語)

https://fj-lmi.cnrs.fr/seminars/

**Çağrı SERT 氏**(Univeristy of Warwick)Counting limit theorems for representations of Gromov-hyperbolic groups (英語)

[ 講演概要 ]

Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).

Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.

[ 講演参考URL ]Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).

Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.

https://fj-lmi.cnrs.fr/seminars/

### 2024年06月10日(月)

13:30-14:30 数理科学研究科棟(駒場) 002号室

Affine Anosov representations

https://fj-lmi.cnrs.fr/seminars/

**Sourav GHOSH 氏**(Ashoka University, India)Affine Anosov representations

[ 講演概要 ]

In this survey talk I will give a brief overview of affine Anosov representations. These are appropriate analogues of Anosov representations inside affine Lie groups and are closely related with proper affine actions of hyperbolic groups.

[ 講演参考URL ]In this survey talk I will give a brief overview of affine Anosov representations. These are appropriate analogues of Anosov representations inside affine Lie groups and are closely related with proper affine actions of hyperbolic groups.

https://fj-lmi.cnrs.fr/seminars/

### 2024年04月24日(水)

15:00-16:00 数理科学研究科棟(駒場) 056号室

Some aspects of Schrödinger models (英語)

https://fj-lmi.cnrs.fr/seminars/

**Laurent Di Menza 氏**(Université de Reims Champagne-Ardenne, CNRS)Some aspects of Schrödinger models (英語)

[ 講演概要 ]

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.

[ 講演参考URL ]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.

https://fj-lmi.cnrs.fr/seminars/

### 2024年04月10日(水)

16:00-17:00 数理科学研究科棟(駒場) 056号室

Galois outer representation and the problem of Oda

(英語)

https://fj-lmi.cnrs.fr/seminars/

**Séverin PHILIP 氏**(京都大学 数理解析研究所, RIMS, Kyoto University)Galois outer representation and the problem of Oda

(英語)

[ 講演概要 ]

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.

[ 講演参考URL ]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.

https://fj-lmi.cnrs.fr/seminars/

### 2024年03月11日(月)

13:30-14:30 数理科学研究科棟(駒場) 117号室

Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior. (英語)

https://fj-lmi.cnrs.fr/seminars/

**Florian SALIN 氏**(Université de Lyon - Tohoku University)Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior. (英語)

[ 講演概要 ]

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.

[ 講演参考URL ]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.

https://fj-lmi.cnrs.fr/seminars/

### 2024年01月30日(火)

16:30-17:30 数理科学研究科棟(駒場) 号室

Convergence of solutions of a one-phase Stefan problem with Neumann boundary data to a self-similar profile. (英語)

https://fj-lmi.cnrs.fr/seminars/

**Danielle HILHORST 氏**(CNRS, Université de Paris-Saclay, France)Convergence of solutions of a one-phase Stefan problem with Neumann boundary data to a self-similar profile. (英語)

[ 講演概要 ]

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.

[ 講演参考URL ]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.

https://fj-lmi.cnrs.fr/seminars/

### 2024年01月23日(火)

13:30-14:40 数理科学研究科棟(駒場) 118号室

Particle systems with geometrical constraints and applications (英語)

https://fj-lmi.cnrs.fr/seminars/

**Antoine DIEZ 氏**(京都大学, Kyoto University, ASHBi)Particle systems with geometrical constraints and applications (英語)

[ 講演概要 ]

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.

[ 講演参考URL ]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.

https://fj-lmi.cnrs.fr/seminars/

### 2023年12月04日(月)

14:00- 数理科学研究科棟(駒場) 056号室

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

https://fj-lmi.cnrs.fr/seminars/

**Philippe G. LEFLOCH 氏**(Sorbonne University & CNRS)An introduction to Einstein constraints and the seed-to-solution method

[ 講演概要 ]

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).

[ 講演参考URL ]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).

https://fj-lmi.cnrs.fr/seminars/

### 2023年11月28日(火)

16:00- 数理科学研究科棟(駒場) 117号室

Some contributions on variable selection in nonlinear mixed-effects models

https://fj-lmi.cnrs.fr/seminars/

**Maud DELATTRE 氏**(Université Paris-Saclay, INRAE)Some contributions on variable selection in nonlinear mixed-effects models

[ 講演概要 ]

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.

References

[1] Delattre, M., Lavielle, M. and Poursat, M.A. (2014) A note on BIC in mixed effects models, Electronic Journal of Statistics 8(1) p. 456-475.

[2] Delattre, M. and Poursat, M.A. (2020) An iterative algorithm for joint covariate and random effect selection in mixed effects models., The International Journal of Biostatistics 16(2), 20190082.

[3] Naveau, M., Kon Kam King, G., Rincent, R., Sansonnet, L. and Delattre, M. Bayesian high dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm. hal-03685060.

[ 講演参考URL ]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.

References

[1] Delattre, M., Lavielle, M. and Poursat, M.A. (2014) A note on BIC in mixed effects models, Electronic Journal of Statistics 8(1) p. 456-475.

[2] Delattre, M. and Poursat, M.A. (2020) An iterative algorithm for joint covariate and random effect selection in mixed effects models., The International Journal of Biostatistics 16(2), 20190082.

[3] Naveau, M., Kon Kam King, G., Rincent, R., Sansonnet, L. and Delattre, M. Bayesian high dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm. hal-03685060.

https://fj-lmi.cnrs.fr/seminars/

### 2023年11月24日(金)

14:00-14:40 数理科学研究科棟(駒場) 117号室

Surgery equivalence relations on 3-manifolds (English)

https://fj-lmi.cnrs.fr/seminars/

**Gwénaël MASSUYEAU 氏**(Université de Bourgogne & CNRS)Surgery equivalence relations on 3-manifolds (English)

[ 講演概要 ]

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.

[ 講演参考URL ]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.

https://fj-lmi.cnrs.fr/seminars/