Text only print
Full screen print
Seminar information archive
Seminar information archive ～04/07｜Today's seminar 04/08 | Future seminars 04/09～
FJ-LMI Seminar
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/
Tuesday Seminar on Topology
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Sogo Murakami (The University of Tokyo)
On the shadowing property of differentiable dynamical systems beyond structural stability (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Sogo Murakami (The University of Tokyo)
On the shadowing property of differentiable dynamical systems beyond structural stability (JAPANESE)
[ Abstract ]
The shadowing property, which has been extensively studied in connection with hyperbolic differentiable dynamical systems, is a dynamical concept ensuring that approximate orbits with small errors (commonly referred to as pseudo-orbits) can be traced by a true orbit. This property is one of the fundamental notions closely related to structural stability. In this talk, I will present the conditions under which the shadowing property holds for differentiable dynamical systems that are not structurally stable, in both discrete-time and continuous-time settings. In the first part of the talk, conditions guaranteeing the shadowing property for Axiom A diffeomorphisms will be discussed. In particular, I will explain the T^{s,u}-condition, and its relationship with the C^0-transversality condition introduced by PetrovPilyugin. I will then give a sufficient condition for having the shadowing property for Axiom A diffeomorphisms. In the second part, results concerning the shadowing property on chain recurrent sets for flows will be presented. While Robinson (1977) showed that every hyperbolic set exhibits the shadowing property, it is known that no singular hyperbolic set with non-isolated hyperbolic singularity, such as the Lorenz attractor, admits the shadowing property (Wen-Wen, 2020). Motivated by this, Arbieto et al. conjectured that any chain recurrent set with attached (non-isolated) hyperbolic singularities cannot possess the shadowing property. In this talk, a counterexample to this conjecture will be constructed.
[ Reference URL ]The shadowing property, which has been extensively studied in connection with hyperbolic differentiable dynamical systems, is a dynamical concept ensuring that approximate orbits with small errors (commonly referred to as pseudo-orbits) can be traced by a true orbit. This property is one of the fundamental notions closely related to structural stability. In this talk, I will present the conditions under which the shadowing property holds for differentiable dynamical systems that are not structurally stable, in both discrete-time and continuous-time settings. In the first part of the talk, conditions guaranteeing the shadowing property for Axiom A diffeomorphisms will be discussed. In particular, I will explain the T^{s,u}-condition, and its relationship with the C^0-transversality condition introduced by PetrovPilyugin. I will then give a sufficient condition for having the shadowing property for Axiom A diffeomorphisms. In the second part, results concerning the shadowing property on chain recurrent sets for flows will be presented. While Robinson (1977) showed that every hyperbolic set exhibits the shadowing property, it is known that no singular hyperbolic set with non-isolated hyperbolic singularity, such as the Lorenz attractor, admits the shadowing property (Wen-Wen, 2020). Motivated by this, Arbieto et al. conjectured that any chain recurrent set with attached (non-isolated) hyperbolic singularities cannot possess the shadowing property. In this talk, a counterexample to this conjecture will be constructed.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lectures
16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Nobuo Sato (National Taiwan University)
反復ベータ積分とその応用 (日本語)
Nobuo Sato (National Taiwan University)
反復ベータ積分とその応用 (日本語)
2026/01/09
FJ-LMI Seminar
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/
2026/01/07
Algebraic Geometry Seminar
10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Jun-Muk Hwang (IBS Center for Complex Geometry)
Fundamental forms and infinitesimal symmetries of projective varieties
Jun-Muk Hwang (IBS Center for Complex Geometry)
Fundamental forms and infinitesimal symmetries of projective varieties
[ Abstract ]
We give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset P^n$ in terms of its fundamental forms at a general point. Moreover, we show that the bound is achieved precisely when $Z \subset P^n$ is projectively equivalent to an Euler-symmetric variety. As a by-product, we determine the Lie algebra of infinitesimal automorphisms of an Euler-symmetric variety and also obtain a rigidity result on the specialization of an Euler-symmetric variety preserving the isomorphism type of the fundamental forms. This is a joint work with Qifeng Li.
We give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset P^n$ in terms of its fundamental forms at a general point. Moreover, we show that the bound is achieved precisely when $Z \subset P^n$ is projectively equivalent to an Euler-symmetric variety. As a by-product, we determine the Lie algebra of infinitesimal automorphisms of an Euler-symmetric variety and also obtain a rigidity result on the specialization of an Euler-symmetric variety preserving the isomorphism type of the fundamental forms. This is a joint work with Qifeng Li.
2026/01/06
Tuesday Seminar on Topology
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Xiaokun Xia (The University of Tokyo)
Reflection vectors in the quantum cohomology of a blowup (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Xiaokun Xia (The University of Tokyo)
Reflection vectors in the quantum cohomology of a blowup (ENGLISH)
[ Abstract ]
Let $X$ be a smooth projective variety with a semi-simple quantum cohomology. It is known that the blowup $\operatorname{Bl}_{\rm pt}(X)$ of $X$ at one point also has semi-simple quantum cohomology. In particular, the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ is a reflection group. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ depending only on the geometry of the exceptional divisor.
[ Reference URL ]Let $X$ be a smooth projective variety with a semi-simple quantum cohomology. It is known that the blowup $\operatorname{Bl}_{\rm pt}(X)$ of $X$ at one point also has semi-simple quantum cohomology. In particular, the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ is a reflection group. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ depending only on the geometry of the exceptional divisor.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/01/05
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yasufumi Nitta (Tokyo Univ. of Science)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yasufumi Nitta (Tokyo Univ. of Science)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/12/26
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Nao Moriyama (Kyoto University)
Remarks on the minimal model theory for log surfaces in the analytic setting
Nao Moriyama (Kyoto University)
Remarks on the minimal model theory for log surfaces in the analytic setting
[ Abstract ]
In 2022, Fujino introduced a complex analytic framework for discussing the minimal model theory, in particular the minimal model program for projective morphisms of complex analytic spaces.
In this talk, I will discuss the minimal model theory for log surfaces in this setting. More precisely, I will show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of complex surfaces that are projective over complex analytic varieties.
In 2022, Fujino introduced a complex analytic framework for discussing the minimal model theory, in particular the minimal model program for projective morphisms of complex analytic spaces.
In this talk, I will discuss the minimal model theory for log surfaces in this setting. More precisely, I will show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of complex surfaces that are projective over complex analytic varieties.
Colloquium
15:30-16:30 Room #NISSAY Lecture Hall (大講義室) (Graduate School of Math. Sci. Bldg.)
Tatsuro Kawakami (Graduate School of Mathematical Sciences, The University of Tokyo)
Singularities and differential forms in positive characteristic (日本語)
Tatsuro Kawakami (Graduate School of Mathematical Sciences, The University of Tokyo)
Singularities and differential forms in positive characteristic (日本語)
[ Abstract ]
In this talk, I will focus on the local aspects of differential forms on algebraic varieties. I begin by reviewing prior results in characteristic zero concerning the extension problem, which asks whether reflexive differential forms can be lifted to birational models such as resolutions of singularities. I will then introduce a new approach to the extension problem in positive characteristic using the Cartier operator. If time permits, I will also discuss a new class of singularities in positive characteristic, defined via the Cartier operator.
In this talk, I will focus on the local aspects of differential forms on algebraic varieties. I begin by reviewing prior results in characteristic zero concerning the extension problem, which asks whether reflexive differential forms can be lifted to birational models such as resolutions of singularities. I will then introduce a new approach to the extension problem in positive characteristic using the Cartier operator. If time permits, I will also discuss a new class of singularities in positive characteristic, defined via the Cartier operator.
2025/12/23
Tuesday Seminar on Topology
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Mayuko Yamashita (Perimeter Institute for Theoretical Physics / RIKEN)
Geometric engineering in Topological Modular Forms (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Mayuko Yamashita (Perimeter Institute for Theoretical Physics / RIKEN)
Geometric engineering in Topological Modular Forms (JAPANESE)
[ Abstract ]
I will explain my ongoing project to construct a functor from the category of conformal field theories to the TMF-module category, and realizing the symmetry of CFTs in genuine equivariance in TMF. I will explain the progress on the cases related to the K3 sigma model, with the motivation coming from the Mathieu moonshine.
[ Reference URL ]I will explain my ongoing project to construct a functor from the category of conformal field theories to the TMF-module category, and realizing the symmetry of CFTs in genuine equivariance in TMF. I will explain the progress on the cases related to the K3 sigma model, with the motivation coming from the Mathieu moonshine.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/12/22
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Keiji Oguiso (Univ. of Tokyo)
Algebraic dynamics of Calabi-Yau manifolds of Wehler type (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Keiji Oguiso (Univ. of Tokyo)
Algebraic dynamics of Calabi-Yau manifolds of Wehler type (Japanese)
[ Abstract ]
A general hypersurface $X$ of multi-degree 2 in $(\Bbb P^1)^{d+1}$ is called a Calabi-Yau manifold of Wehler type (of dimension $d$). In this talk, after recalling some remarkable properties of $X$ found by Cantat and me, I would like to show that $X$ has a birational primitive automorphism, in particular a birational automorphism with Zariski dense orbit, in any $d \ge 2$.
[ Reference URL ]A general hypersurface $X$ of multi-degree 2 in $(\Bbb P^1)^{d+1}$ is called a Calabi-Yau manifold of Wehler type (of dimension $d$). In this talk, after recalling some remarkable properties of $X$ found by Cantat and me, I would like to show that $X$ has a birational primitive automorphism, in particular a birational automorphism with Zariski dense orbit, in any $d \ge 2$.
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo-Nagoya Algebra Seminar
16:30-18:00 Online
Riku Fushimi (Nagoya University)
siltingとsimple-minded collectionの双対性 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Riku Fushimi (Nagoya University)
siltingとsimple-minded collectionの双対性 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/12/20
Seminar on Probability and Statistics
10:30-17:10 Room # (Graduate School of Math. Sci. Bldg.)
- (-)
- (-)
[ Reference URL ]
https://sites.google.com/view/yuimatutorial2025/
- (-)
- (-)
[ Reference URL ]
https://sites.google.com/view/yuimatutorial2025/
2025/12/19
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Hokuto Konno (University of Tokyo)
On diffeomorphisms of complex surfaces
Hokuto Konno (University of Tokyo)
On diffeomorphisms of complex surfaces
[ Abstract ]
Many basic questions about the diffeomorphism groups of complex surfaces remain unresolved. For example, until recently it was unknown whether there exists a simply-connected complex surface admitting a diffeomorphism that acts trivially on the intersection form but is not isotopic to the identity. We have recently answered this question by showing that certain elliptic surfaces do admit such diffeomorphisms. These diffeomorphisms are obtained as suitable compositions of reflections along (-2)-curves. Moreover, this result also provides a negative answer to a question of Donaldson in symplectic geometry. This talk is based on joint work with David Baraglia, and with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
Many basic questions about the diffeomorphism groups of complex surfaces remain unresolved. For example, until recently it was unknown whether there exists a simply-connected complex surface admitting a diffeomorphism that acts trivially on the intersection form but is not isotopic to the identity. We have recently answered this question by showing that certain elliptic surfaces do admit such diffeomorphisms. These diffeomorphisms are obtained as suitable compositions of reflections along (-2)-curves. Moreover, this result also provides a negative answer to a question of Donaldson in symplectic geometry. This talk is based on joint work with David Baraglia, and with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
Algebraic Geometry Seminar
15:15-16:45 Room #118 (Graduate School of Math. Sci. Bldg.)
JongHae Keum (Korea Institute for Advanced Study)
Fake quadric surfaces
JongHae Keum (Korea Institute for Advanced Study)
Fake quadric surfaces
[ Abstract ]
A smooth projective complex surface S is called a Q-homology quadric if it has the same Betti numbers as the smooth quadric surface.
Let S be a Q-homology quadric. Then its cohomology lattice is of rank 2, (even or odd) unimodular.
By the classification theory of surfaces, S is either rational or of general type.
In the latter case, S is called a fake Q-homology quadric.
There is an unsolved question raised by Hirzebruch: does there exist a surface of general type which is homeomorphic to the smooth quadric surface?
I will report recent progress on these surfaces.
A smooth projective complex surface S is called a Q-homology quadric if it has the same Betti numbers as the smooth quadric surface.
Let S be a Q-homology quadric. Then its cohomology lattice is of rank 2, (even or odd) unimodular.
By the classification theory of surfaces, S is either rational or of general type.
In the latter case, S is called a fake Q-homology quadric.
There is an unsolved question raised by Hirzebruch: does there exist a surface of general type which is homeomorphic to the smooth quadric surface?
I will report recent progress on these surfaces.
2025/12/18
Discrete mathematical modelling seminar
17:00-18:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Ian Marquette (La Trobe University)
The classification of superintegrable systems with higher-order symmetries and related algebraic structures (English)
Ian Marquette (La Trobe University)
The classification of superintegrable systems with higher-order symmetries and related algebraic structures (English)
[ Abstract ]
Superintegrable systems admit more symmetries than degrees of freedom. The case of maximally superintegrable systems is characterized by 2n-1 integrals for n degrees of freedom. They possess rich mathematical structures and are related to orthogonal polynomials, special functions, and representation theory. The problem of classifying superintegrable systems was solved for quadratically superintegrable Hamiltonians in 2D conformally flat spaces about 20 years ago. The classification of superintegrable systems in higher-dimensional Riemannian spaces or with higher-order integrals is much more involved, and some partial results are known in three dimensions. These systems have attracted interest because they lead to algebraic structures known as polynomial algebras, which also appear in other contexts of mathematical physics.
This talk is devoted to discussing different approaches and recent results related to the classification of superintegrable systems with second-order and higher-order symmetries and the associated algebraic structures. In the direct approach, consisting of solving systems of partial differential equations, compatibility equations can be related to the works of Bureau, Chazy, and Cosgrove on higher-order nonlinear differential equations and Painlevé transcendents. I will present some examples related to the fourth and sixth Painlevé transcendents and demonstrate that their integrals lead to polynomial algebras. We discuss how these algebraic structures can still be used to gain insight into the spectrum.
I will discuss another and more recent approach to classifying superintegrable systems, which build a completely algebraic setting and on higher-degree polynomials in the enveloping algebra of Lie algebras. This allows the construction of algebraic Hamiltonians, integrals, and new perspectives on their associated algebraic structures. This approach offers greater flexibility, as different realizations can be used. This notion of the commutant leads to generalizations of Racah-type algebras.
Superintegrable systems admit more symmetries than degrees of freedom. The case of maximally superintegrable systems is characterized by 2n-1 integrals for n degrees of freedom. They possess rich mathematical structures and are related to orthogonal polynomials, special functions, and representation theory. The problem of classifying superintegrable systems was solved for quadratically superintegrable Hamiltonians in 2D conformally flat spaces about 20 years ago. The classification of superintegrable systems in higher-dimensional Riemannian spaces or with higher-order integrals is much more involved, and some partial results are known in three dimensions. These systems have attracted interest because they lead to algebraic structures known as polynomial algebras, which also appear in other contexts of mathematical physics.
This talk is devoted to discussing different approaches and recent results related to the classification of superintegrable systems with second-order and higher-order symmetries and the associated algebraic structures. In the direct approach, consisting of solving systems of partial differential equations, compatibility equations can be related to the works of Bureau, Chazy, and Cosgrove on higher-order nonlinear differential equations and Painlevé transcendents. I will present some examples related to the fourth and sixth Painlevé transcendents and demonstrate that their integrals lead to polynomial algebras. We discuss how these algebraic structures can still be used to gain insight into the spectrum.
I will discuss another and more recent approach to classifying superintegrable systems, which build a completely algebraic setting and on higher-degree polynomials in the enveloping algebra of Lie algebras. This allows the construction of algebraic Hamiltonians, integrals, and new perspectives on their associated algebraic structures. This approach offers greater flexibility, as different realizations can be used. This notion of the commutant leads to generalizations of Racah-type algebras.
2025/12/16
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Laurent Mertz (City University of Hong Kong)
A Control Variate Method Driven by Diffusion Approximation (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Laurent Mertz (City University of Hong Kong)
A Control Variate Method Driven by Diffusion Approximation (English)
[ Abstract ]
We present a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic forces. The control variate is the expectation of the same functional for the limit diffusion process that approximates the original process when the mean-reversion time goes to zero. To get an efficient control variate estimator, we propose a coupling method to build the original process and the limit diffusion process. We show that the correlation between the two processes indeed goes to one when the mean reversion time goes to zero and we quantify the convergence rate, which makes it possible to characterize the variance reduction of the proposed control variate method. The efficiency of the method is illustrated on a few examples. This is joint work with Josselin Garnier (École Polytechnique, France). Link to the paper: https://doi.org/10.1002/cpa.21976
[ Reference URL ]We present a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic forces. The control variate is the expectation of the same functional for the limit diffusion process that approximates the original process when the mean-reversion time goes to zero. To get an efficient control variate estimator, we propose a coupling method to build the original process and the limit diffusion process. We show that the correlation between the two processes indeed goes to one when the mean reversion time goes to zero and we quantify the convergence rate, which makes it possible to characterize the variance reduction of the proposed control variate method. The efficiency of the method is illustrated on a few examples. This is joint work with Josselin Garnier (École Polytechnique, France). Link to the paper: https://doi.org/10.1002/cpa.21976
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Tomoshige Yukita (Ashikaga University)
Continuity and minimality of growth rates of Coxeter systems (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tomoshige Yukita (Ashikaga University)
Continuity and minimality of growth rates of Coxeter systems (JAPANESE)
[ Abstract ]
A pair (G, S) consisting of a group G and an ordered finite generating set S is called a marked group. On the set of all marked groups, one can define a distance that measures how similar the neighborhoods of the identity element in their Cayley graphs are. This space is called the space of marked groups. For a marked group, the function that counts the number of elements whose word length with respect to S is k is called the growth function, and the quantity describing its rate of divergence is called the growth rate. In this talk, we will discuss the continuity of the growth rate for marked Coxeter systems, and the problem of determining the minimal growth rate among Coxeter systems that are lattices in the isometry group of hyperbolic space.
[ Reference URL ]A pair (G, S) consisting of a group G and an ordered finite generating set S is called a marked group. On the set of all marked groups, one can define a distance that measures how similar the neighborhoods of the identity element in their Cayley graphs are. This space is called the space of marked groups. For a marked group, the function that counts the number of elements whose word length with respect to S is k is called the growth function, and the quantity describing its rate of divergence is called the growth rate. In this talk, we will discuss the continuity of the growth rate for marked Coxeter systems, and the problem of determining the minimal growth rate among Coxeter systems that are lattices in the isometry group of hyperbolic space.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/12/11
Tokyo-Nagoya Algebra Seminar
13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Hybrid meeting, Zoom ID 895 8731 1175 Password 489352
Paul Balmer (UCLA)
The stable permutation category of a finite group (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Hybrid meeting, Zoom ID 895 8731 1175 Password 489352
Paul Balmer (UCLA)
The stable permutation category of a finite group (English)
[ Abstract ]
In this joint work with Martin Gallauer, we discuss the definition of the stable permutation category in modular representation theory. That category should be to the ordinary stable module category what the derived permutation category is to the ordinary derived category. Our construction is inspired by the picture provided by tensor-triangular geometry. We also use this geometric picture to decide when this new stable permutation category is connected or not, and to compute some components.
[ Reference URL ]In this joint work with Martin Gallauer, we discuss the definition of the stable permutation category in modular representation theory. That category should be to the ordinary stable module category what the derived permutation category is to the ordinary derived category. Our construction is inspired by the picture provided by tensor-triangular geometry. We also use this geometric picture to decide when this new stable permutation category is connected or not, and to compute some components.
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/12/10
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Paul Balmer (University of California, Los Angeles)
The spectrum of Artin motives
Paul Balmer (University of California, Los Angeles)
The spectrum of Artin motives
[ Abstract ]
In this joint work with Martin Gallauer, we investigate the tensor-triangular geometry of the category of Artin motives with coefficients of positive characteristic. This problem relates to modular representation theory of profinite groups and to the category of permutation modules. We shall explain some of the techniques that come into play in the study of the latter.
In this joint work with Martin Gallauer, we investigate the tensor-triangular geometry of the category of Artin motives with coefficients of positive characteristic. This problem relates to modular representation theory of profinite groups and to the category of permutation modules. We shall explain some of the techniques that come into play in the study of the latter.
2025/12/09
Tuesday Seminar of Analysis
16:00-17:30 Room # 002 (Graduate School of Math. Sci. Bldg.)
Marco Squassina (Università Cattolica del Sacro Cuore)
Log-concave solutions of the log-Schrodinger equation in a convex domain (English)
Marco Squassina (Università Cattolica del Sacro Cuore)
Log-concave solutions of the log-Schrodinger equation in a convex domain (English)
[ Abstract ]
First, we discuss some recent results on power concavity for certain classes of quasi-linear elliptic problems. We then turn our attention to a new problem involving the so-called log-Schrödinger equation, which cannot be addressed within the standard framework. To handle this, we introduce new techniques that lead to the existence of log-concave solutions to the log-Schrödinger equation in convex domains. Finally, we conclude with a brief discussion of (quantitative) partial concavity results for both elliptic and parabolic problems, as well as some perspectives on future developments concerning (quantitative) quasi-radiality results for problems in the ball.
First, we discuss some recent results on power concavity for certain classes of quasi-linear elliptic problems. We then turn our attention to a new problem involving the so-called log-Schrödinger equation, which cannot be addressed within the standard framework. To handle this, we introduce new techniques that lead to the existence of log-concave solutions to the log-Schrödinger equation in convex domains. Finally, we conclude with a brief discussion of (quantitative) partial concavity results for both elliptic and parabolic problems, as well as some perspectives on future developments concerning (quantitative) quasi-radiality results for problems in the ball.
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Dan Voiculescu (UC Berkeley)
Around entropy in free probability theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Dan Voiculescu (UC Berkeley)
Around entropy in free probability theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Yusuke Kuno (Tsuda University)
Emergent version of Drinfeld's associator equations (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yusuke Kuno (Tsuda University)
Emergent version of Drinfeld's associator equations (JAPANESE)
[ Abstract ]
In 2012, Alekseev and Torossian proved that any solution of Drinfeld's associator equations gives rise to a solution of the Kashiwara-Vergne equations. Both equations arise in natural topological contexts. For the former, these are knots and braids in 3-space, and for the latter there are at least two contexts: one is the w-foams, a certain Reidemeister theory of singular surfaces in 4-space, and the other is the Goldman-Turaev loop operations on oriented 2-manifolds. With the hope of getting a better understanding of the relations among these topological objects, we introduce the concept of emergent braids, a low-degree Vassiliev quotient of braids over a punctured disk. Then we discuss a work in progress on the associated formality equations, the emergent version of Drinfeld's associator equations. This talk is partially based on a joint work with D. Bar-Natan, Z, Dancso, T. Hogan and D. Lin.
[ Reference URL ]In 2012, Alekseev and Torossian proved that any solution of Drinfeld's associator equations gives rise to a solution of the Kashiwara-Vergne equations. Both equations arise in natural topological contexts. For the former, these are knots and braids in 3-space, and for the latter there are at least two contexts: one is the w-foams, a certain Reidemeister theory of singular surfaces in 4-space, and the other is the Goldman-Turaev loop operations on oriented 2-manifolds. With the hope of getting a better understanding of the relations among these topological objects, we introduce the concept of emergent braids, a low-degree Vassiliev quotient of braids over a punctured disk. Then we discuss a work in progress on the associated formality equations, the emergent version of Drinfeld's associator equations. This talk is partially based on a joint work with D. Bar-Natan, Z, Dancso, T. Hogan and D. Lin.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Numerical Analysis Seminar
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Dorin Bucur (Université Savoie Mont Blanc)
On polygonal nonlocal isoperimetric inequalities: Hardy-Littlewood, Riesz, Faber-Krahn (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Dorin Bucur (Université Savoie Mont Blanc)
On polygonal nonlocal isoperimetric inequalities: Hardy-Littlewood, Riesz, Faber-Krahn (English)
[ Abstract ]
The starting point is the Faber-Krahn inequality on the first eigenvalue of the Dirichlet Laplacian. Many refinements were obtained in the last years, mainly due to the use of recent techniques based on the analysis of vectorial free boundary problems. It turns out that the polygonal version of this inequality, very easy to state, is extremely hard to prove and remains open since 1947, when it was conjectured by Polya. I will connect this question to somehow easier problems, like polygonal versions of Hardy-Littlewood and Riesz inequalities and I will discuss the local minimality of regular polygons and the possibility to prove the conjecture by a mixed approach. This talk is based on joint works with Beniamin Bogosel and Ilaria Fragala.
[ Reference URL ]The starting point is the Faber-Krahn inequality on the first eigenvalue of the Dirichlet Laplacian. Many refinements were obtained in the last years, mainly due to the use of recent techniques based on the analysis of vectorial free boundary problems. It turns out that the polygonal version of this inequality, very easy to state, is extremely hard to prove and remains open since 1947, when it was conjectured by Polya. I will connect this question to somehow easier problems, like polygonal versions of Hardy-Littlewood and Riesz inequalities and I will discuss the local minimality of regular polygons and the possibility to prove the conjecture by a mixed approach. This talk is based on joint works with Beniamin Bogosel and Ilaria Fragala.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2025/12/08
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Rei Murakami (Tohoku Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Rei Murakami (Tohoku Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203 Next >
