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Seminar information archive
Seminar information archive ～01/13｜Today's seminar 01/14 | Future seminars 01/15～
2025/04/23
FJ-LMI Seminar
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/
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Dat Pham (C.N.R.S., IMJ-PRG, Sorbonne Université)
Prismatic F-crystals and "Lubin--Tate" crystalline Galois representations.
https://webusers.imj-prg.fr/~dat.pham/
Dat Pham (C.N.R.S., IMJ-PRG, Sorbonne Université)
Prismatic F-crystals and "Lubin--Tate" crystalline Galois representations.
[ Abstract ]
An important question in integral p-adic Hodge theory is the study of lattices in crystalline Galois representations. There have been various classifications of such objects, such as Fontaine--Lafaille’s theory, Breuil’s theory of strongly divisible lattices, and Kisin’s theory of Breuil--Kisin modules. Using their prismatic theory, Bhatt--Scholze give a site-theoretic description of such lattices, which has the nice feature that it can specialize to many of the previous classifications by "evaluating" suitably. In this talk, we will recall their result and explain an extension to the Lubin--Tate context.
[ Reference URL ]An important question in integral p-adic Hodge theory is the study of lattices in crystalline Galois representations. There have been various classifications of such objects, such as Fontaine--Lafaille’s theory, Breuil’s theory of strongly divisible lattices, and Kisin’s theory of Breuil--Kisin modules. Using their prismatic theory, Bhatt--Scholze give a site-theoretic description of such lattices, which has the nice feature that it can specialize to many of the previous classifications by "evaluating" suitably. In this talk, we will recall their result and explain an extension to the Lubin--Tate context.
https://webusers.imj-prg.fr/~dat.pham/
2025/04/22
Tuesday Seminar on Topology
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Takayuki Okuda (Hiroshima University)
Coarse coding theory and discontinuous groups on homogeneous spaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Takayuki Okuda (Hiroshima University)
Coarse coding theory and discontinuous groups on homogeneous spaces (JAPANESE)
[ Abstract ]
Let $M$ and $\mathcal{I}$ be sets, and consider a surjective map
\[ R : M \times M \to \mathcal{I}. \]
For each subset $\mathcal{A} \subseteq \mathcal{I}$, we define $\mathcal{A}$-free codes on $M$ as subsets $C \subseteq M$ satisfying
\[ R(C \times C) \cap \mathcal{A} = \emptyset. \]
This definition encompasses various types of codes, including error-correcting codes, spherical codes, and those defined on association schemes or homogeneous spaces. In this talk, we introduce a "pre-bornological coarse structure" on $\mathcal{I}$ and define the notion of coarsely $\mathcal{A}$-free codes on $M$. This extends the concept of $\mathcal{A}$-free codes introduced above. As a main result, we establish relationships between coarse coding theory on Riemannian homogeneous spaces $M = G/K$ and discontinuous group theory on non-Riemannian homogeneous spaces $X = G/H$.
[ Reference URL ]Let $M$ and $\mathcal{I}$ be sets, and consider a surjective map
\[ R : M \times M \to \mathcal{I}. \]
For each subset $\mathcal{A} \subseteq \mathcal{I}$, we define $\mathcal{A}$-free codes on $M$ as subsets $C \subseteq M$ satisfying
\[ R(C \times C) \cap \mathcal{A} = \emptyset. \]
This definition encompasses various types of codes, including error-correcting codes, spherical codes, and those defined on association schemes or homogeneous spaces. In this talk, we introduce a "pre-bornological coarse structure" on $\mathcal{I}$ and define the notion of coarsely $\mathcal{A}$-free codes on $M$. This extends the concept of $\mathcal{A}$-free codes introduced above. As a main result, we establish relationships between coarse coding theory on Riemannian homogeneous spaces $M = G/K$ and discontinuous group theory on non-Riemannian homogeneous spaces $X = G/H$.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Numerical Analysis Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yasutoshi Taniguchi (Graduate School of Mathematical Sciences, The University of Tokyo)
A Hyperelastic Extended Kirchhoff–Love Shell Model: Formulation and Isogeometric Discretization (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Yasutoshi Taniguchi (Graduate School of Mathematical Sciences, The University of Tokyo)
A Hyperelastic Extended Kirchhoff–Love Shell Model: Formulation and Isogeometric Discretization (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2025/04/21
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Nakamura (Institute of Science Tokyo)
Continuity method for the Mabuchi soliton on the extremal Fano manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Satoshi Nakamura (Institute of Science Tokyo)
Continuity method for the Mabuchi soliton on the extremal Fano manifolds (Japanese)
[ Abstract ]
We run the continuity method for Mabuchi's generalization of Kähler-Einstein metrics, assuming the existence of an extremal Kähler metric. It gives an analytic proof (without minimal model program) of the recent existence result obtained by Apostolov, Lahdili and Nitta. Our key observation is the boundedness of an energy functional along the continuity method. This talk is based on arXiv:2409.00886, the joint work with Tomoyuki Hisamoto.
[ Reference URL ]We run the continuity method for Mabuchi's generalization of Kähler-Einstein metrics, assuming the existence of an extremal Kähler metric. It gives an analytic proof (without minimal model program) of the recent existence result obtained by Apostolov, Lahdili and Nitta. Our key observation is the boundedness of an energy functional along the continuity method. This talk is based on arXiv:2409.00886, the joint work with Tomoyuki Hisamoto.
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Masahisa Ebina (Kyoto Univercity)
Malliavin-Stein approach to local limit theorems
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Masahisa Ebina (Kyoto Univercity)
Malliavin-Stein approach to local limit theorems
[ Abstract ]
Malliavin-Stein's method is a fruitful combination of the Malliavin calculus and Stein's method. It provides a powerful probabilistic technique for establishing the quantitative central limit theorems, particularly for functionals of Gaussian processes.
In this talk, we will see how the theory of generalized functionals in the Malliavin calculus can be combined with Malliavin-Stein's method to obtain quantitative local central limit theorems. If time allows, we will also discuss some applications to Wiener chaos. Part of this talk is based on the ongoing joint research with Ivan Nourdin and Giovanni Peccati.
Malliavin-Stein's method is a fruitful combination of the Malliavin calculus and Stein's method. It provides a powerful probabilistic technique for establishing the quantitative central limit theorems, particularly for functionals of Gaussian processes.
In this talk, we will see how the theory of generalized functionals in the Malliavin calculus can be combined with Malliavin-Stein's method to obtain quantitative local central limit theorems. If time allows, we will also discuss some applications to Wiener chaos. Part of this talk is based on the ongoing joint research with Ivan Nourdin and Giovanni Peccati.
2025/04/17
FJ-LMI Seminar
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
FJ-LMI Seminar
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/
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Shuhei KITANO (The University of Tokyo)
On Calderón–Zygmund Estimates for Fully Nonlinear Equations (Japanese)
Shuhei KITANO (The University of Tokyo)
On Calderón–Zygmund Estimates for Fully Nonlinear Equations (Japanese)
[ Abstract ]
The Calderón–Zygmund estimate provides a bound on the $L^p$ norms of second-order derivatives of solutions to elliptic equations. Caffarelli extended this result to fully nonlinear equations, requiring the exponent $p$ to be sufficiently large. In this work, we explore two generalizations of Caffarelli’s result: one concerning small values of $p$ and the other involving equations with $L^n$ drift terms.
The Calderón–Zygmund estimate provides a bound on the $L^p$ norms of second-order derivatives of solutions to elliptic equations. Caffarelli extended this result to fully nonlinear equations, requiring the exponent $p$ to be sufficiently large. In this work, we explore two generalizations of Caffarelli’s result: one concerning small values of $p$ and the other involving equations with $L^n$ drift terms.
2025/04/15
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Yuji Ito (TOYOTA CENTRAL R&D LABS., INC.)
Control of uncertain and unknown systems (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Yuji Ito (TOYOTA CENTRAL R&D LABS., INC.)
Control of uncertain and unknown systems (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kento Sakai (The University of Tokyo)
Harmonic maps and uniform degeneration of hyperbolic surfaces with boundary (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kento Sakai (The University of Tokyo)
Harmonic maps and uniform degeneration of hyperbolic surfaces with boundary (JAPANESE)
[ Abstract ]
If holomorphic quadratic differentials on a punctured Riemann surface have poles of order >1 at the punctures, they correspond to hyperbolic surfaces with geodesic boundary via harmonic maps. This correspondence is known as the harmonic map parametrization of hyperbolic surfaces. In this talk, we use this parametrization to describe the degeneration of hyperbolic surfaces via Gromov-Hausdorff convergence. As an application, we study the limit of a one-parameter family of hyperbolic surfaces in the Thurston boundary of Teichmüller space.
[ Reference URL ]If holomorphic quadratic differentials on a punctured Riemann surface have poles of order >1 at the punctures, they correspond to hyperbolic surfaces with geodesic boundary via harmonic maps. This correspondence is known as the harmonic map parametrization of hyperbolic surfaces. In this talk, we use this parametrization to describe the degeneration of hyperbolic surfaces via Gromov-Hausdorff convergence. As an application, we study the limit of a one-parameter family of hyperbolic surfaces in the Thurston boundary of Teichmüller space.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Room # ハイブリッド開催/128 (Graduate School of Math. Sci. Bldg.)
Parth Shimpi (University of Glasgow)
Torsion pairs for McKay quivers (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Parth Shimpi (University of Glasgow)
Torsion pairs for McKay quivers (English)
[ Abstract ]
Classifying torsion classes in the module category has been a problem of much interest in the representation theory of preprojective algebras, owing to its immediate applications in the study of t-structures, bricks, and spherical objects in the derived category. When the preprojective algebra arises from a Dynkin quiver, all such torsion classes must lead to algebraic intermediate hearts— in particular, they arise from tilting modules and therefore admit a finite combinatorial description. Affine ADE quivers, on the other hand, produce infinitely many tilting modules and moreover have geometric hearts arising from the McKay correspondence. By realising the geometric hearts as `limits’ of algebraic ones, I will explain how all torsion pairs for affine preprojective algebras can be described using the above two possibilities; in particular a complete classification is achieved.
Zoom ID 813 0345 0035 Password 706679
[ Reference URL ]Classifying torsion classes in the module category has been a problem of much interest in the representation theory of preprojective algebras, owing to its immediate applications in the study of t-structures, bricks, and spherical objects in the derived category. When the preprojective algebra arises from a Dynkin quiver, all such torsion classes must lead to algebraic intermediate hearts— in particular, they arise from tilting modules and therefore admit a finite combinatorial description. Affine ADE quivers, on the other hand, produce infinitely many tilting modules and moreover have geometric hearts arising from the McKay correspondence. By realising the geometric hearts as `limits’ of algebraic ones, I will explain how all torsion pairs for affine preprojective algebras can be described using the above two possibilities; in particular a complete classification is achieved.
Zoom ID 813 0345 0035 Password 706679
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/04/14
FJ-LMI Seminar
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
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hisashi Kasuya (Univ. of Nagoya)
Non-abelian Hodge correspondence and moduli spaces of flat bundles on Sasakian manifolds with fixed basic structures (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Hisashi Kasuya (Univ. of Nagoya)
Non-abelian Hodge correspondence and moduli spaces of flat bundles on Sasakian manifolds with fixed basic structures (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Masato Hoshino (Science Tokyo)
On the proofs of BPHZ theorem and future progress
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Masato Hoshino (Science Tokyo)
On the proofs of BPHZ theorem and future progress
[ Abstract ]
Hairer’s theory of regularity structures (2014) provides a robust framework to guarantee the renormalizability of stochastic partial differential equations (SPDEs). This theory is established in several steps, among which the final and most technically involved step is the proof of the so-called "BPHZ theorem." There are two main approaches to this proof: a graph-theoretic approach developed by Chandra and Hairer (2016+), and a Malliavin calculus-based inductive approach introduced by Linares, Otto, Tempelmayr, and Tsatsoulis (2024). As for Gaussian noises, the latter is simpler and more inductive. While the language used by Otto and his coauthors is different from that of regularity structures, similar arguments have been formulated in the language of regularity structures by Hairer and Steele (2024) and Bailleul and Hoshino (2023+) by different approaches. In this talk, I will first give an overview of the theory of regularity structures, then compare the outlines of the proofs of BPHZ theorem. If time permits, I will also discuss some current researches and future problems.
Hairer’s theory of regularity structures (2014) provides a robust framework to guarantee the renormalizability of stochastic partial differential equations (SPDEs). This theory is established in several steps, among which the final and most technically involved step is the proof of the so-called "BPHZ theorem." There are two main approaches to this proof: a graph-theoretic approach developed by Chandra and Hairer (2016+), and a Malliavin calculus-based inductive approach introduced by Linares, Otto, Tempelmayr, and Tsatsoulis (2024). As for Gaussian noises, the latter is simpler and more inductive. While the language used by Otto and his coauthors is different from that of regularity structures, similar arguments have been formulated in the language of regularity structures by Hairer and Steele (2024) and Bailleul and Hoshino (2023+) by different approaches. In this talk, I will first give an overview of the theory of regularity structures, then compare the outlines of the proofs of BPHZ theorem. If time permits, I will also discuss some current researches and future problems.
2025/04/08
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Masahito Hayashi (The Chinese University of Hong Kong, Shenzhen/Nagoya University)
Indefinite causal order strategy nor adaptive strategy does not improve the estimation of group action
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Masahito Hayashi (The Chinese University of Hong Kong, Shenzhen/Nagoya University)
Indefinite causal order strategy nor adaptive strategy does not improve the estimation of group action
[ 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.
Asuka Takatsu (The University of Tokyo)
Concavity and Dirichlet heat flow (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Asuka Takatsu (The University of Tokyo)
Concavity and Dirichlet heat flow (JAPANESE)
[ Abstract ]
In a convex domain of Euclidean space, the Dirichlet heat flow transmits log-concavity from the initial time to any time. I first introduce a notion of generalized concavity and specify a concavity preserved by the Dirichlet heat flow. Then I show that in a totally convex domain of a Riemannian manifold, if some concavity is preserved by the Dirichlet heat flow, then the sectional curvature must vanish on the domain. The first part is based on joint work with Kazuhiro Ishige and Paolo Salani, and the second part is based on joint work with Kazuhiro Ishige and Haruto Tokunaga.
[ Reference URL ]In a convex domain of Euclidean space, the Dirichlet heat flow transmits log-concavity from the initial time to any time. I first introduce a notion of generalized concavity and specify a concavity preserved by the Dirichlet heat flow. Then I show that in a totally convex domain of a Riemannian manifold, if some concavity is preserved by the Dirichlet heat flow, then the sectional curvature must vanish on the domain. The first part is based on joint work with Kazuhiro Ishige and Paolo Salani, and the second part is based on joint work with Kazuhiro Ishige and Haruto Tokunaga.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/04/02
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Koji Matsushita (The University of Tokyo)
因子類群が$\mathbb{Z}^2$であるトーリック環の非可換クレパント特異点解消について (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Koji Matsushita (The University of Tokyo)
因子類群が$\mathbb{Z}^2$であるトーリック環の非可換クレパント特異点解消について (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/03/27
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Ryota Iitsuka (Nagoya University)
Reduction理論における変異が誘導する三角圏構造 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Ryota Iitsuka (Nagoya University)
Reduction理論における変異が誘導する三角圏構造 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/03/21
Lie Groups and Representation Theory
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Wentao Teng (The University of Tokyo)
A positive product formula of integral kernels of $k$-Hankel transforms (English)
Wentao Teng (The University of Tokyo)
A positive product formula of integral kernels of $k$-Hankel transforms (English)
[ Abstract ]
Let $R$ be a root system in $\mathbb R^N$ and $G$ be the finite subgroup generated by the reflections associated to the root system.
We establish a positive radial product formula for the integral kernels $B_{k,1}(x,y)$ of $(k,1)$-generalized Fourier transforms (or the $k$-Hankel transforms) $F_{k,1}$
$$B_{k,1}(x,z)j_{2\left\langle k\right\rangle+N-2}\left(2\sqrt{t\left|z\right|}\right)=\int_{\mathbb R^N} B_{k,1}(\xi,z)\,d\sigma_{x,t}^{k,1}(\xi),$$
where $j_{\lambda}$ is the normalized Bessel function, and $\sigma_{x,t}^{k,1}(\xi)$ is the unique probability measure. Such a product formula is equivalent to the following representation of the generalized spherical mean operator $f\mapsto M_f,\;f\in C_b(\mathbb{R}^N)$ in $(k,1)$-generalized Fourier analysis
\begin{align*} M_f(x,t)=\int_{\mathbb{R}^N}f\,d\sigma_{x,t}^{k,1},\;(x,t)\in\mathbb{R}^N\times{\mathbb{R}}_+.\end{align*}
We will then analyze the representing measure $\sigma_{x,t}^{k,1}(\xi)$ and show that the support of the measure is contained in
$$\left\{\xi\in\mathbb{R}^N:\sqrt{\vert\xi\vert}\geq\vert\sqrt{\vert x\vert}-\sqrt t\vert\right\}\cap\left(\bigcup_{g\in G}\{\xi\in\mathbb{R}^N:d(\xi,gx)\leq\sqrt t\}\right),$$
where $d\left(x,y\right)=\sqrt{\left|x\right|+\left|y\right|-\sqrt{2\left(\left|x\right|\left|y\right|+\left\langle x,y\right\rangle\right)}}$.
Based on the support of the representing measure $\sigma_{x,t}^{k,1}$, we will get a weak Huygens's principle for the deformed wave equation in $(k,1)$-generalized Fourier analysis.
Moreover, for $N\geq 2$, if we assume that $F_{k,1}\left(\mathcal S(\mathbb{R}^N)\right)$ consists of rapidly decreasing functions at infinity, then we get two different results on $\text{supp}\sigma_{x,t}^{k,1}$, which indirectly denies such assumption.
Let $R$ be a root system in $\mathbb R^N$ and $G$ be the finite subgroup generated by the reflections associated to the root system.
We establish a positive radial product formula for the integral kernels $B_{k,1}(x,y)$ of $(k,1)$-generalized Fourier transforms (or the $k$-Hankel transforms) $F_{k,1}$
$$B_{k,1}(x,z)j_{2\left\langle k\right\rangle+N-2}\left(2\sqrt{t\left|z\right|}\right)=\int_{\mathbb R^N} B_{k,1}(\xi,z)\,d\sigma_{x,t}^{k,1}(\xi),$$
where $j_{\lambda}$ is the normalized Bessel function, and $\sigma_{x,t}^{k,1}(\xi)$ is the unique probability measure. Such a product formula is equivalent to the following representation of the generalized spherical mean operator $f\mapsto M_f,\;f\in C_b(\mathbb{R}^N)$ in $(k,1)$-generalized Fourier analysis
\begin{align*} M_f(x,t)=\int_{\mathbb{R}^N}f\,d\sigma_{x,t}^{k,1},\;(x,t)\in\mathbb{R}^N\times{\mathbb{R}}_+.\end{align*}
We will then analyze the representing measure $\sigma_{x,t}^{k,1}(\xi)$ and show that the support of the measure is contained in
$$\left\{\xi\in\mathbb{R}^N:\sqrt{\vert\xi\vert}\geq\vert\sqrt{\vert x\vert}-\sqrt t\vert\right\}\cap\left(\bigcup_{g\in G}\{\xi\in\mathbb{R}^N:d(\xi,gx)\leq\sqrt t\}\right),$$
where $d\left(x,y\right)=\sqrt{\left|x\right|+\left|y\right|-\sqrt{2\left(\left|x\right|\left|y\right|+\left\langle x,y\right\rangle\right)}}$.
Based on the support of the representing measure $\sigma_{x,t}^{k,1}$, we will get a weak Huygens's principle for the deformed wave equation in $(k,1)$-generalized Fourier analysis.
Moreover, for $N\geq 2$, if we assume that $F_{k,1}\left(\mathcal S(\mathbb{R}^N)\right)$ consists of rapidly decreasing functions at infinity, then we get two different results on $\text{supp}\sigma_{x,t}^{k,1}$, which indirectly denies such assumption.
2025/03/20
Lectures
13:00-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Pre-registration is necessary to participate.
Mayuko Yamashita (Kyoto University)
場の理論と代数トポロジー その可能性の中心 --- カナダ出発に際しての置き土産
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSdFXVfYg9D7OgoUymOqhCiUJoGxk4x-bqyB1_odjH0QQBdfWw/viewform?usp=dialog
Pre-registration is necessary to participate.
Mayuko Yamashita (Kyoto University)
場の理論と代数トポロジー その可能性の中心 --- カナダ出発に際しての置き土産
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSdFXVfYg9D7OgoUymOqhCiUJoGxk4x-bqyB1_odjH0QQBdfWw/viewform?usp=dialog
2025/03/17
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
The day of the week and the room are different from the usual ones.
Ingo Runkel (Univ. Hamburg)
Lattice models and topological symmetries from 2d conformal field theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
The day of the week and the room are different from the usual ones.
Ingo Runkel (Univ. Hamburg)
Lattice models and topological symmetries from 2d conformal field theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tokyo-Nagoya Algebra Seminar
14:30-16:00 Online
Junyang Liu (University of Science and Technology of China)
On Amiot's conjecture (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Junyang Liu (University of Science and Technology of China)
On Amiot's conjecture (English)
[ Abstract ]
In 2010, Claire Amiot conjectured that algebraic 2-Calabi-Yau categories with cluster-tilting object must come from quivers with potential. This would extend a structure theorem obtained by Keller-Reiten in the case where the endomorphism algebra of the cluster-tilting object is hereditary. Many other classes of examples are also known. We will report on the proof of the conjecture in the general case for categories with *algebraic* 2-Calabi-Yau structure. This result has been obtained in joint work with Bernhard Keller and is based on Van den Bergh's structure theorem for complete Calabi-Yau algebras. We also generalize his structure theorem to the relative case and use it to prove a relative variant of the conjecture.
ミーティング ID: 853 1951 5047
パスコード: 900788
[ Reference URL ]In 2010, Claire Amiot conjectured that algebraic 2-Calabi-Yau categories with cluster-tilting object must come from quivers with potential. This would extend a structure theorem obtained by Keller-Reiten in the case where the endomorphism algebra of the cluster-tilting object is hereditary. Many other classes of examples are also known. We will report on the proof of the conjecture in the general case for categories with *algebraic* 2-Calabi-Yau structure. This result has been obtained in joint work with Bernhard Keller and is based on Van den Bergh's structure theorem for complete Calabi-Yau algebras. We also generalize his structure theorem to the relative case and use it to prove a relative variant of the conjecture.
ミーティング ID: 853 1951 5047
パスコード: 900788
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/02/21
Operator Algebra Seminars
13:30-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)
The day of the week, the time slot and the room are different from the usual ones.
David O'Connell (OIST)
Colimits of $C^*$-algebras in Quantum Field Theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
The day of the week, the time slot and the room are different from the usual ones.
David O'Connell (OIST)
Colimits of $C^*$-algebras in Quantum Field Theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2025/02/20
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
The day of the week is different from the usual one.
Christoph Schweigert (Univ. Hamburg)
Nakayama functors, relative Serre functors and some applications
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
The day of the week is different from the usual one.
Christoph Schweigert (Univ. Hamburg)
Nakayama functors, relative Serre functors and some applications
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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