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FJ-LMI Seminar
Seminar information archive ～01/16｜Next seminar｜Future seminars 01/17～
| Organizer(s) | Toshiyuki Kobayashi, Michael Pevzner |
|---|
Seminar information archive
2026/01/15
15:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
[ Reference URL ]Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
https://fj-lmi.cnrs.fr/seminars/
2026/01/14
15:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
[ Reference URL ]Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
https://fj-lmi.cnrs.fr/seminars/
2026/01/13
15:15-17:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
[ Reference URL ]Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
https://fj-lmi.cnrs.fr/seminars/
2026/01/09
10:00-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
[ Reference URL ]Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
https://fj-lmi.cnrs.fr/seminars/
2025/11/12
15:00-15:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
This talk will provide an overview of a mini-course to be taught in January 2026 at the University of Tokyo, aimed at describing how Shannon entropy, a tool that was originally developed for and motivated by a rigorous mathematical analysis of communications engineering, later led to developments that can to some extent be viewed as taking place in a converse direction, where Shannon entropy provided insight into central basic questions in several fields of pure mathematics.
This talk will provide an overview of a mini-course to be taught in January 2026 at the University of Tokyo, aimed at describing how Shannon entropy, a tool that was originally developed for and motivated by a rigorous mathematical analysis of communications engineering, later led to developments that can to some extent be viewed as taking place in a converse direction, where Shannon entropy provided insight into central basic questions in several fields of pure mathematics.
2025/11/12
15:45-16:20 Room #056 (Graduate School of Math. Sci. Bldg.)
Raphaël LEFEVERE (Université de Paris Cité)
Macroscopic diffusion in random lattice Lorentz gases (英語)
https://fj-lmi.cnrs.fr/seminars/
Raphaël LEFEVERE (Université de Paris Cité)
Macroscopic diffusion in random lattice Lorentz gases (英語)
[ Abstract ]
I will present the general issues that have to be tackled when deriving macroscopic laws from microscopic deterministic laws of motion and a toy model where these issues may be solved.
[ Reference URL ]I will present the general issues that have to be tackled when deriving macroscopic laws from microscopic deterministic laws of motion and a toy model where these issues may be solved.
https://fj-lmi.cnrs.fr/seminars/
2025/10/21
16:00-16:40 Room #128 (Graduate School of Math. Sci. Bldg.)
Ramla ABDELLATIF (Université de Picardie)
Studying $p$-modular representations of $p$-adic groups in the setting of the Langlands programme (英語)
Ramla ABDELLATIF (Université de Picardie)
Studying $p$-modular representations of $p$-adic groups in the setting of the Langlands programme (英語)
[ Abstract ]
This talk aims to introduce the context of my primary research topic, namely $p$-modular representations of $p$-adic groups, as well as a current state of the art in the field, including some related questions I am currently exploring. After motivating the study of classical and modular Langlands correspondences for $p$-adic groups, I will explain why the $p$-modular setting (i.e. when representations of $p$-adic groups have coefficients in a field of positive characteristic equal to $p$) differs significantly from other settings (namely the complex and $\ell$-modular ones, with $\ell$ a prime distinct from $p$), then I will present the main results known so far about $p$-modular irreducible smooth representations of $p$-adic groups, with a particular focus on the special linear group $\mathrm{SL}_{2}$.
This talk aims to introduce the context of my primary research topic, namely $p$-modular representations of $p$-adic groups, as well as a current state of the art in the field, including some related questions I am currently exploring. After motivating the study of classical and modular Langlands correspondences for $p$-adic groups, I will explain why the $p$-modular setting (i.e. when representations of $p$-adic groups have coefficients in a field of positive characteristic equal to $p$) differs significantly from other settings (namely the complex and $\ell$-modular ones, with $\ell$ a prime distinct from $p$), then I will present the main results known so far about $p$-modular irreducible smooth representations of $p$-adic groups, with a particular focus on the special linear group $\mathrm{SL}_{2}$.
2025/10/08
15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Sourav Ghosh (Ashoka University)
Proper actions on group manifolds (英語)
Sourav Ghosh (Ashoka University)
Proper actions on group manifolds (英語)
[ Abstract ]
In this talk, I will show how to use known examples of flat affine manifolds to obtain new examples of proper actions of discrete groups on group manifolds. This is a joint work with Toshiyuki Kobayashi.
In this talk, I will show how to use known examples of flat affine manifolds to obtain new examples of proper actions of discrete groups on group manifolds. This is a joint work with Toshiyuki Kobayashi.
2025/05/13
14:30-15:15 Room #002 (Graduate School of Math. Sci. Bldg.)
Matthew CELLOT (University of Lille (France))
Homotopy quantum field theories and 3-types (英語)
https://fj-lmi.cnrs.fr/seminars/
Matthew CELLOT (University of Lille (France))
Homotopy quantum field theories and 3-types (英語)
[ Abstract ]
Quantum topology is a field that came about in the 1980s following remarkable discoveries by Jones, Drinfeld and Witten, whose work dramatically renewed topology, in particular in low dimension. A fundamental notion in quantum topology is that of topological quantum field theory (TQFT) formulated by Witten and Atiyah. This notion originates in ideas from quantum physics and constitutes a framework that organizes certain topological invariants of manifolds, called quantum invariants, which are defined by means of quantum groups. Homotopy quantum field theories (HQFTs) are a generalization of TQFTs. The idea is to use TQFT techniques to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a (fixed) topological space called the target.
Turaev and Virelizier have recently constructed 3-dimensional HQFTs (by state-sum) when the target space is aspherical (i.e. its n-th homotopy groups are trivial for n>1) and Sözer and Virelizier have constructed 3-dimensional HQFTs when the target space is a 2-type (i.e. its n-th homotopy groups are trivial for n>2). Using state sum techniques, Douglas and Reutter have constructed 4-dimensional TQFTs from spherical fusion 2-categories. In this talk, we combine both these approaches: we construct state sum 4-dimensional HQFTs with a 3-type target from fusion 2-categories graded by a 2-crossed module.
[ Reference URL ]Quantum topology is a field that came about in the 1980s following remarkable discoveries by Jones, Drinfeld and Witten, whose work dramatically renewed topology, in particular in low dimension. A fundamental notion in quantum topology is that of topological quantum field theory (TQFT) formulated by Witten and Atiyah. This notion originates in ideas from quantum physics and constitutes a framework that organizes certain topological invariants of manifolds, called quantum invariants, which are defined by means of quantum groups. Homotopy quantum field theories (HQFTs) are a generalization of TQFTs. The idea is to use TQFT techniques to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a (fixed) topological space called the target.
Turaev and Virelizier have recently constructed 3-dimensional HQFTs (by state-sum) when the target space is aspherical (i.e. its n-th homotopy groups are trivial for n>1) and Sözer and Virelizier have constructed 3-dimensional HQFTs when the target space is a 2-type (i.e. its n-th homotopy groups are trivial for n>2). Using state sum techniques, Douglas and Reutter have constructed 4-dimensional TQFTs from spherical fusion 2-categories. In this talk, we combine both these approaches: we construct state sum 4-dimensional HQFTs with a 3-type target from fusion 2-categories graded by a 2-crossed module.
https://fj-lmi.cnrs.fr/seminars/
2025/04/23
13:30-14:15 Room #056 (Graduate School of Math. Sci. Bldg.)
Alexandre BROUSTE (Le Mans Université)
Fast and efficient inference for large and high-frequency data (英語)
https://fj-lmi.cnrs.fr/seminars/
Alexandre BROUSTE (Le Mans Université)
Fast and efficient inference for large and high-frequency data (英語)
[ Abstract ]
The theory of Local Asymptotic Normality (LAN), initiated by Lucien Le Cam, provides a powerful framework for studying the asymptotic optimality of estimators. When the LAN property holds for a statistical experiment with a non-singular Fisher information matrix, minimax theorems can be applied, allowing for the derivation of a lower bound for the variance of estimators.
Beyond the classical i.i.d. setting, the LAN property has been established for various statistical models. However, for several high-frequency statistical experiments, only weak LAN properties were derived with a singular Fisher information matrix, preventing the application of minimax theorems. For these experiments, it has also remained unclear for a long time whether the maximum likelihood estimator (MLE) possesses any form of asymptotic optimality.
Moreover, when the MLE achieves optimality, its computation is generally time-consuming, making it challenging for handling large or high-frequency datasets and alternative estimation methods are therefore needed for different applications.
In this talk, we review our previous results obtained with M. Fukasawa on fractional Gaussian noise and H. Masuda on stable processes observed at high frequency as well as the various progress made since then. We also present our efforts to popularize the one-step procedure as a fast and asymptotically efficient alternative to the MLE.
[ Reference URL ]The theory of Local Asymptotic Normality (LAN), initiated by Lucien Le Cam, provides a powerful framework for studying the asymptotic optimality of estimators. When the LAN property holds for a statistical experiment with a non-singular Fisher information matrix, minimax theorems can be applied, allowing for the derivation of a lower bound for the variance of estimators.
Beyond the classical i.i.d. setting, the LAN property has been established for various statistical models. However, for several high-frequency statistical experiments, only weak LAN properties were derived with a singular Fisher information matrix, preventing the application of minimax theorems. For these experiments, it has also remained unclear for a long time whether the maximum likelihood estimator (MLE) possesses any form of asymptotic optimality.
Moreover, when the MLE achieves optimality, its computation is generally time-consuming, making it challenging for handling large or high-frequency datasets and alternative estimation methods are therefore needed for different applications.
In this talk, we review our previous results obtained with M. Fukasawa on fractional Gaussian noise and H. Masuda on stable processes observed at high frequency as well as the various progress made since then. We also present our efforts to popularize the one-step procedure as a fast and asymptotically efficient alternative to the MLE.
https://fj-lmi.cnrs.fr/seminars/
2025/04/17
15:00-15:45 Room #056 (Graduate School of Math. Sci. Bldg.)
Pierre SCHAPIRA (IMJ - Sorbonne University)
Sheaves for spacetime (英語)
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/02/Tokyo25Sem.pdf
Pierre SCHAPIRA (IMJ - Sorbonne University)
Sheaves for spacetime (英語)
[ Abstract ]
We shall study the Cauchy problem on globally hyperbolic manifolds with the only tools of microlocal sheaf theory and the precise Cauchy-Kowalevski theorem.
A causal manifold is a manifold $M$ endowed with a closed convex proper cone $\lambda\subset T^*M$. On such a manifold, one defines the $\lambda$-topology and the associated notion of a causal pre-order. One introduces the notion of a G-causal manifold, those for which there exists a time function. On a G-manifold, sheaves satisfying a suitable condition on their micro-support and defined on a neighborhood of a Cauchy hypersurface extend to the whole space. When the sheaf is the complex of hyperfunction solutions of a hyperbolic $\mathcal D$-module, this proves that the Cauchy problem is globally well-posed.
We will also describe a ``shifted spacetime'' associated with the quantization of an Hamiltonian isotopy.
This talk is partly based on papers in collaboration with Benoît Jubin, Stéphane Guillermou and Masaki Kashiwara.
[ Reference URL ]We shall study the Cauchy problem on globally hyperbolic manifolds with the only tools of microlocal sheaf theory and the precise Cauchy-Kowalevski theorem.
A causal manifold is a manifold $M$ endowed with a closed convex proper cone $\lambda\subset T^*M$. On such a manifold, one defines the $\lambda$-topology and the associated notion of a causal pre-order. One introduces the notion of a G-causal manifold, those for which there exists a time function. On a G-manifold, sheaves satisfying a suitable condition on their micro-support and defined on a neighborhood of a Cauchy hypersurface extend to the whole space. When the sheaf is the complex of hyperfunction solutions of a hyperbolic $\mathcal D$-module, this proves that the Cauchy problem is globally well-posed.
We will also describe a ``shifted spacetime'' associated with the quantization of an Hamiltonian isotopy.
This talk is partly based on papers in collaboration with Benoît Jubin, Stéphane Guillermou and Masaki Kashiwara.
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/02/Tokyo25Sem.pdf
2025/04/17
15:45-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Giuseppe DITO (Université Bourgogne Europe)
Deformation quantization and Wightman distributions (英語)
https://fj-lmi.cnrs.fr/seminars/
Giuseppe DITO (Université Bourgogne Europe)
Deformation quantization and Wightman distributions (英語)
[ Abstract ]
Twisted $\hbar$-deformations by classical wave operators are introduced for a scalar field theory in Minkowski spacetime. These deformations are non-perturbative in the coupling constant. The corresponding Wightman $n$-functions are defined as evaluations at $0$ of the $n$-fold deformed products of classical solutions of the classical wave equation. We show that, in this setting, the $2$-point function is well-defined as a formal series in $\hbar$ of tempered distributions. Interestingly, these twisted deformations appear to possess an inherent renormalization scheme.
[ Reference URL ]Twisted $\hbar$-deformations by classical wave operators are introduced for a scalar field theory in Minkowski spacetime. These deformations are non-perturbative in the coupling constant. The corresponding Wightman $n$-functions are defined as evaluations at $0$ of the $n$-fold deformed products of classical solutions of the classical wave equation. We show that, in this setting, the $2$-point function is well-defined as a formal series in $\hbar$ of tempered distributions. Interestingly, these twisted deformations appear to possess an inherent renormalization scheme.
https://fj-lmi.cnrs.fr/seminars/
2025/04/14
17:00-18:00 Room #Main Lecture Hall (Graduate School of Math. Sci. Bldg.)
FJ-LMI Distinguished Lecture
Pierre SCHAPIRA (IMJ - Sorbonne University)
Microlocal sheaf theory and elliptic pairs (英語)
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/03/Tokyo25Colloq.pdf
FJ-LMI Distinguished Lecture
Pierre SCHAPIRA (IMJ - Sorbonne University)
Microlocal sheaf theory and elliptic pairs (英語)
[ Abstract ]
On a complex manifold $X$, an elliptic pair $(\mathcal{M},G)$ is the data of a coherent $\mathcal{D}_X$-module $\mathcal{M}$ and an $\mathbb R$-constructible sheaf $G$ with the property that the characteristic variety $\operatorname{char}(\mathcal{M})$ and the micro-support $\mathrm{SS}(G)$ do not intersect outside the zero-section of $T^*X$. We prove a regularity result which generalizes the classical case of hyperfunction solutions of elliptic systems and a finiteness theorem when assuming that the support of the pair is compact.
Then we introduce the microlocal Euler class of $\mathcal{M}$ and that of $G$ and calculate the Euler-Poincar\'e index of the complex of holomorphic solutions of the pair as the integral over $T^*X$ of the cup product of these two characteristic classes. This construction gives a new approach to the Riemann--Roch or the Atiyah--Singer theorems.
I will start by briefly recalling all necessary notions of microlocal sheaf theory and $\mathcal{D}$-module theory.
[ Reference URL ]On a complex manifold $X$, an elliptic pair $(\mathcal{M},G)$ is the data of a coherent $\mathcal{D}_X$-module $\mathcal{M}$ and an $\mathbb R$-constructible sheaf $G$ with the property that the characteristic variety $\operatorname{char}(\mathcal{M})$ and the micro-support $\mathrm{SS}(G)$ do not intersect outside the zero-section of $T^*X$. We prove a regularity result which generalizes the classical case of hyperfunction solutions of elliptic systems and a finiteness theorem when assuming that the support of the pair is compact.
Then we introduce the microlocal Euler class of $\mathcal{M}$ and that of $G$ and calculate the Euler-Poincar\'e index of the complex of holomorphic solutions of the pair as the integral over $T^*X$ of the cup product of these two characteristic classes. This construction gives a new approach to the Riemann--Roch or the Atiyah--Singer theorems.
I will start by briefly recalling all necessary notions of microlocal sheaf theory and $\mathcal{D}$-module theory.
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/03/Tokyo25Colloq.pdf
2024/12/04
14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Jonathan Ditlevsen (The University of Tokyo)
Symmetry breaking operators for the pair (GL(n+1,R), GL(n,R)) (英語)
https://fj-lmi.cnrs.fr/seminars/
Jonathan Ditlevsen (The University of Tokyo)
Symmetry breaking operators for the pair (GL(n+1,R), GL(n,R)) (英語)
[ Abstract ]
In this talk, we construct explicit symmetry breaking operators (SBOs) between principal series representations of the group GL(n+1,R) and its subgroup GL(n,R). Using Bernstein–Sato identities, we find a holomorphic renormalization of a meromorphic family of SBOs. Finally, we identify certain differential SBOs as residues of this holomorphic family.
[ Reference URL ]In this talk, we construct explicit symmetry breaking operators (SBOs) between principal series representations of the group GL(n+1,R) and its subgroup GL(n,R). Using Bernstein–Sato identities, we find a holomorphic renormalization of a meromorphic family of SBOs. Finally, we identify certain differential SBOs as residues of this holomorphic family.
https://fj-lmi.cnrs.fr/seminars/
2024/11/27
14:30-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Ali BAKLOUTI (University of Sfax)
A proof of the Zariski closure conjecture for coadjoint orbits of exponential Lie groups (英語)
https://fj-lmi.cnrs.fr/seminars/
Ali BAKLOUTI (University of Sfax)
A proof of the Zariski closure conjecture for coadjoint orbits of exponential Lie groups (英語)
[ Abstract ]
I will begin by defining the Zariski Closure Conjecture for coadjoint orbits of exponential solvable Lie groups, examining some cases that have been solved, and addressing the ongoing challenges in resolving the conjecture fully. I will then introduce new approaches to explore the relationship between generating families of primitive ideals and the set of polynomials that vanish on the associated coadjoint orbits, ultimately aiming to advance toward a solution to the conjecture.
[ Reference URL ]I will begin by defining the Zariski Closure Conjecture for coadjoint orbits of exponential solvable Lie groups, examining some cases that have been solved, and addressing the ongoing challenges in resolving the conjecture fully. I will then introduce new approaches to explore the relationship between generating families of primitive ideals and the set of polynomials that vanish on the associated coadjoint orbits, ultimately aiming to advance toward a solution to the conjecture.
https://fj-lmi.cnrs.fr/seminars/
2024/11/27
13:30-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Hidenori FUJIWARA (OCAMI, Kindai University)
Inductions and restrictions of unitary representations for exponential solvable Lie groups. (英語)
https://fj-lmi.cnrs.fr/seminars/
Hidenori FUJIWARA (OCAMI, Kindai University)
Inductions and restrictions of unitary representations for exponential solvable Lie groups. (英語)
[ Abstract ]
Let $G = \exp \mathfrak g$ be a connected and simply connected real nilpotent Lie group with Lie algebra $\mathfrak g$, $H = \exp \mathfrak h$ an analytic subgroup of $G$ with Lie algebra $\mathfrak h$, $\chi$ a unitary character of $H$ and $\tau = \text{ind}_H^G \chi$ the monomial representation of $G$ induced from $\chi$. Let $D_{\tau}(G/H)$ be the algebra of the $G$-invariant differential operators on the line bundle over $G/H$ associated to the data $(H,\chi)$. We denote by $C_{\tau}$ the center of $D_{\tau}(G/H)$. We know that $\chi$ is written as ${\chi}_f$, where $\chi_f(\exp X) = e^{if(X)} (X \in \mathfrak h)$ with a certain $f \in {\mathfrak g}^*$ verifying $f([\mathfrak h,\mathfrak h]) = \{0\}$. Let $S(\mathfrak g)$ be the symmetric algebra of $\mathfrak g$ and ${\mathfrak a}_{\tau} = \{X + \sqrt{-1}f(X) ; X \in \mathfrak h\}.$ We regard $S(\mathfrak g)$ as the algebra of polynomial functions on ${\mathfrak g}^*$ by $X(\ell) = \sqrt{-1}\ell(X)$ for $X \in \mathfrak g, \ell \in {\mathfrak g}^*$. Now, $S(\mathfrak g)$ possesses the Poisson structure $\{,\}$ well determined by the equality $\{X,Y\} = [X,Y]$ if $X, Y$ are in $\mathfrak g$. Let us consider the algebra $(S(\mathfrak g)/S(\mathfrak g)\overline{{\mathfrak a}_{\tau}})^H$ of the $H$-invariant polynomial functions on the affine subspace ${\Gamma}_{\tau} = \{\ell \in {\mathfrak g}^* : \ell(X) = f(X), X \in \mathfrak h\}$ of ${\mathfrak g}^*$. This inherits the Poisson structure from $S(\mathfrak g)$. We denote by $Z_{\tau}$ its Poisson center. Michel Duflo asked: the two algebras $C_{\tau}$ and $Z_{\tau}$, are they isomorphic? Here we provide a positive answer to this question.
[ Reference URL ]Let $G = \exp \mathfrak g$ be a connected and simply connected real nilpotent Lie group with Lie algebra $\mathfrak g$, $H = \exp \mathfrak h$ an analytic subgroup of $G$ with Lie algebra $\mathfrak h$, $\chi$ a unitary character of $H$ and $\tau = \text{ind}_H^G \chi$ the monomial representation of $G$ induced from $\chi$. Let $D_{\tau}(G/H)$ be the algebra of the $G$-invariant differential operators on the line bundle over $G/H$ associated to the data $(H,\chi)$. We denote by $C_{\tau}$ the center of $D_{\tau}(G/H)$. We know that $\chi$ is written as ${\chi}_f$, where $\chi_f(\exp X) = e^{if(X)} (X \in \mathfrak h)$ with a certain $f \in {\mathfrak g}^*$ verifying $f([\mathfrak h,\mathfrak h]) = \{0\}$. Let $S(\mathfrak g)$ be the symmetric algebra of $\mathfrak g$ and ${\mathfrak a}_{\tau} = \{X + \sqrt{-1}f(X) ; X \in \mathfrak h\}.$ We regard $S(\mathfrak g)$ as the algebra of polynomial functions on ${\mathfrak g}^*$ by $X(\ell) = \sqrt{-1}\ell(X)$ for $X \in \mathfrak g, \ell \in {\mathfrak g}^*$. Now, $S(\mathfrak g)$ possesses the Poisson structure $\{,\}$ well determined by the equality $\{X,Y\} = [X,Y]$ if $X, Y$ are in $\mathfrak g$. Let us consider the algebra $(S(\mathfrak g)/S(\mathfrak g)\overline{{\mathfrak a}_{\tau}})^H$ of the $H$-invariant polynomial functions on the affine subspace ${\Gamma}_{\tau} = \{\ell \in {\mathfrak g}^* : \ell(X) = f(X), X \in \mathfrak h\}$ of ${\mathfrak g}^*$. This inherits the Poisson structure from $S(\mathfrak g)$. We denote by $Z_{\tau}$ its Poisson center. Michel Duflo asked: the two algebras $C_{\tau}$ and $Z_{\tau}$, are they isomorphic? Here we provide a positive answer to this question.
https://fj-lmi.cnrs.fr/seminars/
2024/11/13
13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Stefano OLLA (Université de Paris Dauphine - PSL Research University)
Diffusive behaviour in extended completely integrable dynamics (英語)
https://fj-lmi.cnrs.fr/seminars/
Stefano OLLA (Université de Paris Dauphine - PSL Research University)
Diffusive behaviour in extended completely integrable dynamics (英語)
[ Abstract ]
On a diffusive space-time scaling, density fluctuations behave very differently in extended completely integrable systems with respect to chaotic systems. I will expose some recent results concerning the one dimensional hard rods infinite dynamics and the box-ball cellular automata (an ultradiscretization of the KdV equation). Joint works with Pablo Ferrari, Makiko Sasada, Hayate Suda.
[ Reference URL ]On a diffusive space-time scaling, density fluctuations behave very differently in extended completely integrable systems with respect to chaotic systems. I will expose some recent results concerning the one dimensional hard rods infinite dynamics and the box-ball cellular automata (an ultradiscretization of the KdV equation). Joint works with Pablo Ferrari, Makiko Sasada, Hayate Suda.
https://fj-lmi.cnrs.fr/seminars/
2024/11/01
14:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Thomas GILETTI (Université Clermont-Auvergne)
Propagating behaviour of solutions of multistable reaction-diffusion equations (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas GILETTI (Université Clermont-Auvergne)
Propagating behaviour of solutions of multistable reaction-diffusion equations (英語)
[ Abstract ]
This talk will be devoted to propagation phenomena for a general scalar reaction-diffusion PDE, when it may admit an arbitrarily large number of stationary states. It is well known that, in some simple cases, special travelling front solutions (depending on a single variable moving with a constant speed) arise in the large time behaviour of solutions. Due to this feature, reaction-diffusion equations have become ubiquituous in the modelling of spatial invasions in ecology, population dynamics and biology. However, in general, large time propagation can no longer be described by a single front, but by a family of several successive fronts (or `propagating terrace') involving intermediate transient equilibria. I will review several methods, including a connection with Sturm-Liouville theory, to handle such dynamics.
[ Reference URL ]This talk will be devoted to propagation phenomena for a general scalar reaction-diffusion PDE, when it may admit an arbitrarily large number of stationary states. It is well known that, in some simple cases, special travelling front solutions (depending on a single variable moving with a constant speed) arise in the large time behaviour of solutions. Due to this feature, reaction-diffusion equations have become ubiquituous in the modelling of spatial invasions in ecology, population dynamics and biology. However, in general, large time propagation can no longer be described by a single front, but by a family of several successive fronts (or `propagating terrace') involving intermediate transient equilibria. I will review several methods, including a connection with Sturm-Liouville theory, to handle such dynamics.
https://fj-lmi.cnrs.fr/seminars/
2024/10/02
13:30-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Daniel CARO (Université de Caen Normandie)
Introduction to arithmetic D-modules (英語)
https://fj-lmi.cnrs.fr/seminars/
Daniel CARO (Université de Caen Normandie)
Introduction to arithmetic D-modules (英語)
[ Abstract ]
In this talk, I will give a brief overview of the theory of D-arithmetic modules, initiated by P. Berthelot in the 90's. By replacing the analytic or complex algebraic varieties by algebraic varieties defined over a field of characteristic p>0, this corresponds to an arithmetic analogue of the usual theory of D-modules. This makes it possible to obtain categories of p-adic objects associated with varieties of characteristic p; these p-adic coefficients satisfying a six functors formalism as expected. Via the de Rham cohomology associated with the constant arithmetic D-module, we obtain a p-adic interpretation and the rationality of the Weil zeta function, an arithmetic avatar of the Riemann zeta function, as well as a p-adic analogue of the Riemann hypothesis.
[ Reference URL ]In this talk, I will give a brief overview of the theory of D-arithmetic modules, initiated by P. Berthelot in the 90's. By replacing the analytic or complex algebraic varieties by algebraic varieties defined over a field of characteristic p>0, this corresponds to an arithmetic analogue of the usual theory of D-modules. This makes it possible to obtain categories of p-adic objects associated with varieties of characteristic p; these p-adic coefficients satisfying a six functors formalism as expected. Via the de Rham cohomology associated with the constant arithmetic D-module, we obtain a p-adic interpretation and the rationality of the Weil zeta function, an arithmetic avatar of the Riemann zeta function, as well as a p-adic analogue of the Riemann hypothesis.
https://fj-lmi.cnrs.fr/seminars/
2024/09/11
13:30-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Çağrı SERT (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (英語)
https://fj-lmi.cnrs.fr/seminars/
Çağrı SERT (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (英語)
[ Abstract ]
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.
[ Reference 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/
2024/06/10
13:30-14:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Sourav GHOSH (Ashoka University, India)
Affine Anosov representations
https://fj-lmi.cnrs.fr/seminars/
Sourav GHOSH (Ashoka University, India)
Affine Anosov representations
[ Abstract ]
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.
[ Reference 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/
2024/04/24
15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Laurent Di Menza (Université de Reims Champagne-Ardenne, CNRS)
Some aspects of Schrödinger models (英語)
https://fj-lmi.cnrs.fr/seminars/
Laurent Di Menza (Université de Reims Champagne-Ardenne, CNRS)
Some aspects of Schrödinger models (英語)
[ Abstract ]
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.
[ Reference 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/
2024/04/10
16:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Séverin PHILIP (京都大学 数理解析研究所, RIMS, Kyoto University)
Galois outer representation and the problem of Oda
(英語)
https://fj-lmi.cnrs.fr/seminars/
Séverin PHILIP (京都大学 数理解析研究所, RIMS, Kyoto University)
Galois outer representation and the problem of Oda
(英語)
[ Abstract ]
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.
[ Reference 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/
2024/03/11
13:30-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Florian SALIN (Université de Lyon - 東北大学)
Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior. (英語)
https://fj-lmi.cnrs.fr/seminars/
Florian SALIN (Université de Lyon - 東北大学)
Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior. (英語)
[ Abstract ]
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.
[ Reference 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/
2024/01/30
16:30-17:30 Room # (Graduate School of Math. Sci. Bldg.)
Danielle HILHORST (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)
https://fj-lmi.cnrs.fr/seminars/
Danielle HILHORST (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)
[ Abstract ]
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.
[ Reference 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/
